/// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: nil -*- #include #if HAL_CPU_CLASS >= HAL_CPU_CLASS_150 /* optionally turn down optimisation for debugging */ // #pragma GCC optimize("O0") #include "AP_NavEKF.h" #include #include #include #include /* parameter defaults for different types of vehicle. The APM_BUILD_DIRECTORY is taken from the main vehicle directory name where the code is built. Note that this trick won't work for arduino builds on APM2, but NavEKF doesn't run on APM2, so that's OK */ #if APM_BUILD_TYPE(APM_BUILD_ArduCopter) // copter defaults #define VELNE_NOISE_DEFAULT 0.5f #define VELD_NOISE_DEFAULT 0.7f #define POSNE_NOISE_DEFAULT 0.5f #define ALT_NOISE_DEFAULT 1.0f #define MAG_NOISE_DEFAULT 0.05f #define GYRO_PNOISE_DEFAULT 0.015f #define ACC_PNOISE_DEFAULT 0.25f #define GBIAS_PNOISE_DEFAULT 1E-06f #define ABIAS_PNOISE_DEFAULT 0.00005f #define MAGE_PNOISE_DEFAULT 0.0003f #define MAGB_PNOISE_DEFAULT 0.0003f #define VEL_GATE_DEFAULT 5 #define POS_GATE_DEFAULT 10 #define HGT_GATE_DEFAULT 10 #define MAG_GATE_DEFAULT 3 #define MAG_CAL_DEFAULT 1 #define GLITCH_ACCEL_DEFAULT 100 #define GLITCH_RADIUS_DEFAULT 25 #define FLOW_MEAS_DELAY 10 #define FLOW_NOISE_DEFAULT 0.25f #define FLOW_GATE_DEFAULT 3 #elif APM_BUILD_TYPE(APM_BUILD_APMrover2) // rover defaults #define VELNE_NOISE_DEFAULT 0.5f #define VELD_NOISE_DEFAULT 0.7f #define POSNE_NOISE_DEFAULT 0.5f #define ALT_NOISE_DEFAULT 1.0f #define MAG_NOISE_DEFAULT 0.05f #define GYRO_PNOISE_DEFAULT 0.015f #define ACC_PNOISE_DEFAULT 0.25f #define GBIAS_PNOISE_DEFAULT 8E-06f #define ABIAS_PNOISE_DEFAULT 0.00005f #define MAGE_PNOISE_DEFAULT 0.0003f #define MAGB_PNOISE_DEFAULT 0.0003f #define VEL_GATE_DEFAULT 5 #define POS_GATE_DEFAULT 10 #define HGT_GATE_DEFAULT 10 #define MAG_GATE_DEFAULT 3 #define MAG_CAL_DEFAULT 1 #define GLITCH_ACCEL_DEFAULT 150 #define GLITCH_RADIUS_DEFAULT 15 #define FLOW_MEAS_DELAY 25 #define FLOW_NOISE_DEFAULT 0.15f #define FLOW_GATE_DEFAULT 5 #else // generic defaults (and for plane) #define VELNE_NOISE_DEFAULT 0.5f #define VELD_NOISE_DEFAULT 0.7f #define POSNE_NOISE_DEFAULT 0.5f #define ALT_NOISE_DEFAULT 0.5f #define MAG_NOISE_DEFAULT 0.05f #define GYRO_PNOISE_DEFAULT 0.015f #define ACC_PNOISE_DEFAULT 0.5f #define GBIAS_PNOISE_DEFAULT 8E-06f #define ABIAS_PNOISE_DEFAULT 0.00005f #define MAGE_PNOISE_DEFAULT 0.0003f #define MAGB_PNOISE_DEFAULT 0.0003f #define VEL_GATE_DEFAULT 6 #define POS_GATE_DEFAULT 30 #define HGT_GATE_DEFAULT 20 #define MAG_GATE_DEFAULT 3 #define MAG_CAL_DEFAULT 0 #define GLITCH_ACCEL_DEFAULT 150 #define GLITCH_RADIUS_DEFAULT 20 #define FLOW_MEAS_DELAY 25 #define FLOW_NOISE_DEFAULT 0.3f #define FLOW_GATE_DEFAULT 3 #endif // APM_BUILD_DIRECTORY extern const AP_HAL::HAL& hal; #define earthRate 0.000072921f // earth rotation rate (rad/sec) // when the wind estimation first starts with no airspeed sensor, // assume 3m/s to start #define STARTUP_WIND_SPEED 3.0f // initial imu bias uncertainty (deg/sec) #define INIT_ACCEL_BIAS_UNCERTAINTY 0.3f // Define tuning parameters const AP_Param::GroupInfo NavEKF::var_info[] PROGMEM = { // @Param: VELNE_NOISE // @DisplayName: GPS horizontal velocity measurement noise scaler // @Description: This is the scaler that is applied to the speed accuracy reported by the receiver to estimate the horizontal velocity observation noise. If the model of receiver used does not provide a speed accurcy estimate, then a speed acuracy of 1 is assumed. Increasing it reduces the weighting on these measurements. // @Range: 0.05 5.0 // @Increment: 0.05 // @User: Advanced AP_GROUPINFO("VELNE_NOISE", 0, NavEKF, _gpsHorizVelNoise, VELNE_NOISE_DEFAULT), // @Param: VELD_NOISE // @DisplayName: GPS vertical velocity measurement noise scaler // @Description: This is the scaler that is applied to the speed accuracy reported by the receiver to estimate the vertical velocity observation noise. If the model of receiver used does not provide a speed accurcy estimate, then a speed acuracy of 1 is assumed. Increasing it reduces the weighting on this measurement. // @Range: 0.05 5.0 // @Increment: 0.05 // @User: Advanced AP_GROUPINFO("VELD_NOISE", 1, NavEKF, _gpsVertVelNoise, VELD_NOISE_DEFAULT), // @Param: POSNE_NOISE // @DisplayName: GPS horizontal position measurement noise (m) // @Description: This is the RMS value of noise in the GPS horizontal position measurements. Increasing it reduces the weighting on these measurements. // @Range: 0.1 10.0 // @Increment: 0.1 // @User: Advanced // @Units: meters AP_GROUPINFO("POSNE_NOISE", 2, NavEKF, _gpsHorizPosNoise, POSNE_NOISE_DEFAULT), // @Param: ALT_NOISE // @DisplayName: Altitude measurement noise (m) // @Description: This is the RMS value of noise in the altitude measurement. Increasing it reduces the weighting on this measurement. // @Range: 0.1 10.0 // @Increment: 0.1 // @User: Advanced // @Units: meters AP_GROUPINFO("ALT_NOISE", 3, NavEKF, _baroAltNoise, ALT_NOISE_DEFAULT), // @Param: MAG_NOISE // @DisplayName: Magnetometer measurement noise (Gauss) // @Description: This is the RMS value of noise in magnetometer measurements. Increasing it reduces the weighting on these measurements. // @Range: 0.01 0.5 // @Increment: 0.01 // @User: Advanced AP_GROUPINFO("MAG_NOISE", 4, NavEKF, _magNoise, MAG_NOISE_DEFAULT), // @Param: EAS_NOISE // @DisplayName: Equivalent airspeed measurement noise (m/s) // @Description: This is the RMS value of noise in equivalent airspeed measurements. Increasing it reduces the weighting on these measurements. // @Range: 0.5 5.0 // @Increment: 0.1 // @User: Advanced // @Units: m/s AP_GROUPINFO("EAS_NOISE", 5, NavEKF, _easNoise, 1.4f), // @Param: WIND_PNOISE // @DisplayName: Wind velocity process noise (m/s^2) // @Description: This noise controls the growth of wind state error estimates. Increasing it makes wind estimation faster and noisier. // @Range: 0.01 1.0 // @Increment: 0.1 // @User: Advanced AP_GROUPINFO("WIND_PNOISE", 6, NavEKF, _windVelProcessNoise, 0.1f), // @Param: WIND_PSCALE // @DisplayName: Height rate to wind procss noise scaler // @Description: Increasing this parameter increases how rapidly the wind states adapt when changing altitude, but does make wind speed estimation noiser. // @Range: 0.0 1.0 // @Increment: 0.1 // @User: Advanced AP_GROUPINFO("WIND_PSCALE", 7, NavEKF, _wndVarHgtRateScale, 0.5f), // @Param: GYRO_PNOISE // @DisplayName: Rate gyro noise (rad/s) // @Description: This noise controls the growth of estimated error due to gyro measurement errors excluding bias. Increasing it makes the flter trust the gyro measurements less and other measurements more. // @Range: 0.001 0.05 // @Increment: 0.001 // @User: Advanced // @Units: rad/s AP_GROUPINFO("GYRO_PNOISE", 8, NavEKF, _gyrNoise, GYRO_PNOISE_DEFAULT), // @Param: ACC_PNOISE // @DisplayName: Accelerometer noise (m/s^2) // @Description: This noise controls the growth of estimated error due to accelerometer measurement errors excluding bias. Increasing it makes the flter trust the accelerometer measurements less and other measurements more. // @Range: 0.05 1.0 // @Increment: 0.01 // @User: Advanced // @Units: m/s/s AP_GROUPINFO("ACC_PNOISE", 9, NavEKF, _accNoise, ACC_PNOISE_DEFAULT), // @Param: GBIAS_PNOISE // @DisplayName: Rate gyro bias process noise (rad/s) // @Description: This noise controls the growth of gyro bias state error estimates. Increasing it makes rate gyro bias estimation faster and noisier. // @Range: 0.0000001 0.00001 // @User: Advanced // @Units: rad/s AP_GROUPINFO("GBIAS_PNOISE", 10, NavEKF, _gyroBiasProcessNoise, GBIAS_PNOISE_DEFAULT), // @Param: ABIAS_PNOISE // @DisplayName: Accelerometer bias process noise (m/s^2) // @Description: This noise controls the growth of the vertical acelerometer bias state error estimate. Increasing it makes accelerometer bias estimation faster and noisier. // @Range: 0.00001 0.001 // @User: Advanced // @Units: m/s/s AP_GROUPINFO("ABIAS_PNOISE", 11, NavEKF, _accelBiasProcessNoise, ABIAS_PNOISE_DEFAULT), // @Param: MAGE_PNOISE // @DisplayName: Earth magnetic field process noise (gauss/s) // @Description: This noise controls the growth of earth magnetic field state error estimates. Increasing it makes earth magnetic field bias estimation faster and noisier. // @Range: 0.0001 0.01 // @User: Advanced // @Units: gauss/s AP_GROUPINFO("MAGE_PNOISE", 12, NavEKF, _magEarthProcessNoise, MAGE_PNOISE_DEFAULT), // @Param: MAGB_PNOISE // @DisplayName: Body magnetic field process noise (gauss/s) // @Description: This noise controls the growth of body magnetic field state error estimates. Increasing it makes compass offset estimation faster and noisier. // @Range: 0.0001 0.01 // @User: Advanced // @Units: gauss/s AP_GROUPINFO("MAGB_PNOISE", 13, NavEKF, _magBodyProcessNoise, MAGB_PNOISE_DEFAULT), // @Param: VEL_DELAY // @DisplayName: GPS velocity measurement delay (msec) // @Description: This is the number of msec that the GPS velocity measurements lag behind the inertial measurements. // @Range: 0 500 // @Increment: 10 // @User: Advanced // @Units: milliseconds AP_GROUPINFO("VEL_DELAY", 14, NavEKF, _msecVelDelay, 220), // @Param: POS_DELAY // @DisplayName: GPS position measurement delay (msec) // @Description: This is the number of msec that the GPS position measurements lag behind the inertial measurements. // @Range: 0 500 // @Increment: 10 // @User: Advanced // @Units: milliseconds AP_GROUPINFO("POS_DELAY", 15, NavEKF, _msecPosDelay, 220), // @Param: GPS_TYPE // @DisplayName: GPS mode control // @Description: This parameter controls use of GPS measurements : 0 = use 3D velocity & 2D position, 1 = use 2D velocity and 2D position, 2 = use 2D position, 3 = use no GPS (optical flow will be used if available) // @Values: 0:GPS 3D Vel and 2D Pos, 1:GPS 2D vel and 2D pos, 2:GPS 2D pos, 3:No GPS use optical flow // @User: Advanced AP_GROUPINFO("GPS_TYPE", 16, NavEKF, _fusionModeGPS, 0), // @Param: VEL_GATE // @DisplayName: GPS velocity measurement gate size // @Description: This parameter sets the number of standard deviations applied to the GPS velocity measurement innovation consistency check. Decreasing it makes it more likely that good measurements willbe rejected. Increasing it makes it more likely that bad measurements will be accepted. // @Range: 1 100 // @Increment: 1 // @User: Advanced AP_GROUPINFO("VEL_GATE", 17, NavEKF, _gpsVelInnovGate, VEL_GATE_DEFAULT), // @Param: POS_GATE // @DisplayName: GPS position measurement gate size // @Description: This parameter sets the number of standard deviations applied to the GPS position measurement innovation consistency check. Decreasing it makes it more likely that good measurements will be rejected. Increasing it makes it more likely that bad measurements will be accepted. // @Range: 1 100 // @Increment: 1 // @User: Advanced AP_GROUPINFO("POS_GATE", 18, NavEKF, _gpsPosInnovGate, POS_GATE_DEFAULT), // @Param: HGT_GATE // @DisplayName: Height measurement gate size // @Description: This parameter sets the number of standard deviations applied to the height measurement innovation consistency check. Decreasing it makes it more likely that good measurements will be rejected. Increasing it makes it more likely that bad measurements will be accepted. // @Range: 1 100 // @Increment: 1 // @User: Advanced AP_GROUPINFO("HGT_GATE", 19, NavEKF, _hgtInnovGate, HGT_GATE_DEFAULT), // @Param: MAG_GATE // @DisplayName: Magnetometer measurement gate size // @Description: This parameter sets the number of standard deviations applied to the magnetometer measurement innovation consistency check. Decreasing it makes it more likely that good measurements will be rejected. Increasing it makes it more likely that bad measurements will be accepted. // @Range: 1 100 // @Increment: 1 // @User: Advanced AP_GROUPINFO("MAG_GATE", 20, NavEKF, _magInnovGate, MAG_GATE_DEFAULT), // @Param: EAS_GATE // @DisplayName: Airspeed measurement gate size // @Description: This parameter sets the number of standard deviations applied to the airspeed measurement innovation consistency check. Decreasing it makes it more likely that good measurements will be rejected. Increasing it makes it more likely that bad measurements will be accepted. // @Range: 1 100 // @Increment: 1 // @User: Advanced AP_GROUPINFO("EAS_GATE", 21, NavEKF, _tasInnovGate, 10), // @Param: MAG_CAL // @DisplayName: Magnetometer calibration mode // @Description: EKF_MAG_CAL = 0 enables calibration based on flying speed and altitude and is the default setting for Plane users. EKF_MAG_CAL = 1 enables calibration based on manoeuvre level and is the default setting for Copter and Rover users. EKF_MAG_CAL = 2 prevents magnetometer calibration regardless of flight condition and is recommended if in-flight magnetometer calibration is unreliable. // @Values: 0:Speed and Height,1:Acceleration,2:Never,3:Always // @User: Advanced AP_GROUPINFO("MAG_CAL", 22, NavEKF, _magCal, MAG_CAL_DEFAULT), // @Param: GLITCH_ACCEL // @DisplayName: GPS glitch accel gate size (cm/s^2) // @Description: This parameter controls the maximum amount of difference in horizontal acceleration between the value predicted by the filter and the value measured by the GPS before the GPS position data is rejected. If this value is set too low, then valid GPS data will be regularly discarded, and the position accuracy will degrade. If this parameter is set too high, then large GPS glitches will cause large rapid changes in position. // @Range: 100 500 // @Increment: 50 // @User: Advanced AP_GROUPINFO("GLITCH_ACCEL", 23, NavEKF, _gpsGlitchAccelMax, GLITCH_ACCEL_DEFAULT), // @Param: GLITCH_RAD // @DisplayName: GPS glitch radius gate size (m) // @Description: This parameter controls the maximum amount of difference in horizontal position (in m) between the value predicted by the filter and the value measured by the GPS before the long term glitch protection logic is activated and an offset is applied to the GPS measurement to compensate. Position steps smaller than this value will be temporarily ignored, but will then be accepted and the filter will move to the new position. Position steps larger than this value will be ignored initially, but the filter will then apply an offset to the GPS position measurement. // @Range: 10 50 // @Increment: 5 // @User: Advanced // @Units: meters AP_GROUPINFO("GLITCH_RAD", 24, NavEKF, _gpsGlitchRadiusMax, GLITCH_RADIUS_DEFAULT), // @Param: GND_GRADIENT // @DisplayName: Terrain Gradient % RMS // @Description: This parameter sets the RMS terrain gradient percentage assumed by the terrain height estimation. Terrain height can be estimated using optical flow and/or range finder sensor data if fitted. Smaller values cause the terrain height estimate to be slower to respond to changes in measurement. Larger values casue the terrain height estimate to be faster to respond, but also more noisy. Generally this value can be reduced if operating over very flat terrain and increased if operating over uneven terrain. // @Range: 1 - 50 // @Increment: 1 // @User: Advanced AP_GROUPINFO("GND_GRADIENT", 25, NavEKF, _gndGradientSigma, 2), // @Param: FLOW_NOISE // @DisplayName: Optical flow measurement noise (rad/s) // @Description: This is the RMS value of noise and errors in optical flow measurements. Increasing it reduces the weighting on these measurements. // @Range: 0.05 - 1.0 // @Increment: 0.05 // @User: Advanced // @Units: rad/s AP_GROUPINFO("FLOW_NOISE", 26, NavEKF, _flowNoise, FLOW_NOISE_DEFAULT), // @Param: FLOW_GATE // @DisplayName: Optical Flow measurement gate size // @Description: This parameter sets the number of standard deviations applied to the optical flow innovation consistency check. Decreasing it makes it more likely that good measurements will be rejected. Increasing it makes it more likely that bad measurements will be accepted. // @Range: 1 - 100 // @Increment: 1 // @User: Advanced AP_GROUPINFO("FLOW_GATE", 27, NavEKF, _flowInnovGate, FLOW_GATE_DEFAULT), // @Param: FLOW_DELAY // @DisplayName: Optical Flow measurement delay (msec) // @Description: This is the number of msec that the optical flow measurements lag behind the inertial measurements. It is the time from the end of the optical flow averaging period and does not include the time delay due to the 100msec of averaging within the flow sensor. // @Range: 0 - 500 // @Increment: 10 // @User: Advanced // @Units: milliseconds AP_GROUPINFO("FLOW_DELAY", 28, NavEKF, _msecFLowDelay, FLOW_MEAS_DELAY), // @Param: RNG_GATE // @DisplayName: Range finder measurement gate size // @Description: This parameter sets the number of standard deviations applied to the range finder innovation consistency check. Decreasing it makes it more likely that good measurements will be rejected. Increasing it makes it more likely that bad measurements will be accepted. // @Range: 1 - 100 // @Increment: 1 // @User: Advanced AP_GROUPINFO("RNG_GATE", 29, NavEKF, _rngInnovGate, 5), // @Param: MAX_FLOW // @DisplayName: Maximum valid optical flow rate // @Description: This parameter sets the magnitude maximum optical flow rate in rad/sec that will be accepted by the filter // @Range: 1.0 - 4.0 // @Increment: 0.1 // @User: Advanced AP_GROUPINFO("MAX_FLOW", 30, NavEKF, _maxFlowRate, 2.5f), // @Param: FALLBACK // @DisplayName: Fallback strictness // @Description: This parameter controls the conditions necessary to trigger a fallback to DCM and INAV. A value of 1 will cause fallbacks to occur on loss of GPS and other conditions. A value of 0 will trust the EKF more. // @Values: 0:Trust EKF more, 1:Trust DCM more // @User: Advanced AP_GROUPINFO("FALLBACK", 31, NavEKF, _fallback, 1), // @Param: ALT_SOURCE // @DisplayName: Primary height source // @Description: This parameter controls which height sensor is used by the EKF during optical flow navigation (when EKF_GPS_TYPE = 3). A value of will 0 cause it to always use baro altitude. A value of 1 will casue it to use range finder if available. // @Values: 0:Use Baro, 1:Use Range Finder // @User: Advanced AP_GROUPINFO("ALT_SOURCE", 32, NavEKF, _altSource, 1), AP_GROUPEND }; // constructor NavEKF::NavEKF(const AP_AHRS *ahrs, AP_Baro &baro, const RangeFinder &rng) : _ahrs(ahrs), _baro(baro), _rng(rng), state(*reinterpret_cast(&states)), gpsNEVelVarAccScale(0.05f), // Scale factor applied to horizontal velocity measurement variance due to manoeuvre acceleration - used when GPS doesn't report speed error gpsDVelVarAccScale(0.07f), // Scale factor applied to vertical velocity measurement variance due to manoeuvre acceleration - used when GPS doesn't report speed error gpsPosVarAccScale(0.05f), // Scale factor applied to horizontal position measurement variance due to manoeuvre acceleration msecHgtDelay(60), // Height measurement delay (msec) msecMagDelay(40), // Magnetometer measurement delay (msec) msecTasDelay(240), // Airspeed measurement delay (msec) gpsRetryTimeUseTAS(10000), // GPS retry time with airspeed measurements (msec) gpsRetryTimeNoTAS(7000), // GPS retry time without airspeed measurements (msec) gpsFailTimeWithFlow(5000), // If we have no GPS for longer than this and we have optical flow, then we will switch across to using optical flow (msec) hgtRetryTimeMode0(10000), // Height retry time with vertical velocity measurement (msec) hgtRetryTimeMode12(5000), // Height retry time without vertical velocity measurement (msec) tasRetryTime(5000), // True airspeed timeout and retry interval (msec) magFailTimeLimit_ms(10000), // number of msec before a magnetometer failing innovation consistency checks is declared failed (msec) magVarRateScale(0.05f), // scale factor applied to magnetometer variance due to angular rate gyroBiasNoiseScaler(2.0f), // scale factor applied to imu gyro bias learning before the vehicle is armed accelBiasNoiseScaler(1.0f), // scale factor applied to imu accel bias learning before the vehicle is armed msecGpsAvg(200), // average number of msec between GPS measurements msecHgtAvg(100), // average number of msec between height measurements msecMagAvg(100), // average number of msec between magnetometer measurements msecBetaAvg(100), // average number of msec between synthetic sideslip measurements msecBetaMax(200), // maximum number of msec between synthetic sideslip measurements msecFlowAvg(100), // average number of msec between optical flow measurements dtVelPos(0.2f), // number of seconds between position and velocity corrections. This should be a multiple of the imu update interval. covTimeStepMax(0.07f), // maximum time (sec) between covariance prediction updates covDelAngMax(0.05f), // maximum delta angle between covariance prediction updates TASmsecMax(200), // maximum allowed interval between airspeed measurement updates DCM33FlowMin(0.71f), // If Tbn(3,3) is less than this number, optical flow measurements will not be fused as tilt is too high. fScaleFactorPnoise(1e-10f), // Process noise added to focal length scale factor state variance at each time step flowTimeDeltaAvg_ms(100), // average interval between optical flow measurements (msec) flowIntervalMax_ms(100), // maximum allowable time between flow fusion events gndEffectTimeout_ms(1000), // time in msec that baro ground effect compensation will timeout after initiation gndEffectBaroScaler(4.0f) // scaler applied to the barometer observation variance when operating in ground effect #if CONFIG_HAL_BOARD == HAL_BOARD_PX4 || CONFIG_HAL_BOARD == HAL_BOARD_VRBRAIN ,_perf_UpdateFilter(perf_alloc(PC_ELAPSED, "EKF_UpdateFilter")), _perf_CovariancePrediction(perf_alloc(PC_ELAPSED, "EKF_CovariancePrediction")), _perf_FuseVelPosNED(perf_alloc(PC_ELAPSED, "EKF_FuseVelPosNED")), _perf_FuseMagnetometer(perf_alloc(PC_ELAPSED, "EKF_FuseMagnetometer")), _perf_FuseAirspeed(perf_alloc(PC_ELAPSED, "EKF_FuseAirspeed")), _perf_FuseSideslip(perf_alloc(PC_ELAPSED, "EKF_FuseSideslip")) #endif { AP_Param::setup_object_defaults(this, var_info); } // Check basic filter health metrics and return a consolidated health status bool NavEKF::healthy(void) const { uint8_t faultInt; getFilterFaults(faultInt); if (faultInt > 0) { return false; } if (_fallback && velTestRatio > 1 && posTestRatio > 1 && hgtTestRatio > 1) { // all three metrics being above 1 means the filter is // extremely unhealthy. return false; } // Give the filter a second to settle before use if ((imuSampleTime_ms - ekfStartTime_ms) < 1000 ) { return false; } // barometer and position innovations must be within limits when on-ground float horizErrSq = sq(innovVelPos[3]) + sq(innovVelPos[4]); if (!vehicleArmed && (fabsf(innovVelPos[5]) > 1.0f || horizErrSq > 1.0f)) { return false; } // all OK return true; } // resets position states to last GPS measurement or to zero if in constant position mode void NavEKF::ResetPosition(void) { if (constPosMode || (PV_AidingMode != AID_ABSOLUTE)) { state.position.x = 0; state.position.y = 0; } else if (!gpsNotAvailable) { // write to state vector and compensate for GPS latency state.position.x = gpsPosNE.x + gpsPosGlitchOffsetNE.x + 0.001f*velNED.x*float(_msecPosDelay); state.position.y = gpsPosNE.y + gpsPosGlitchOffsetNE.y + 0.001f*velNED.y*float(_msecPosDelay); // the estimated states at the last GPS measurement are set equal to the GPS measurement to prevent transients on the first fusion statesAtPosTime.position.x = gpsPosNE.x; statesAtPosTime.position.y = gpsPosNE.y; } // stored horizontal position states to prevent subsequent GPS measurements from being rejected for (uint8_t i=0; i<=49; i++){ storedStates[i].position.x = state.position.x; storedStates[i].position.y = state.position.y; } } // Reset velocity states to last GPS measurement if available or to zero if in constant position mode or if PV aiding is not absolute // Do not reset vertical velocity using GPS as there is baro alt available to constrain drift void NavEKF::ResetVelocity(void) { if (constPosMode || PV_AidingMode != AID_ABSOLUTE) { state.velocity.zero(); state.vel1.zero(); state.vel2.zero(); } else if (!gpsNotAvailable) { // reset horizontal velocity states, applying an offset to the GPS velocity to prevent the GPS position being rejected when the GPS position offset is being decayed to zero. state.velocity.x = velNED.x + gpsVelGlitchOffset.x; // north velocity from blended accel data state.velocity.y = velNED.y + gpsVelGlitchOffset.y; // east velocity from blended accel data state.vel1.x = velNED.x + gpsVelGlitchOffset.x; // north velocity from IMU1 accel data state.vel1.y = velNED.y + gpsVelGlitchOffset.y; // east velocity from IMU1 accel data state.vel2.x = velNED.x + gpsVelGlitchOffset.x; // north velocity from IMU2 accel data state.vel2.y = velNED.y + gpsVelGlitchOffset.y; // east velocity from IMU2 accel data // over write stored horizontal velocity states to prevent subsequent GPS measurements from being rejected for (uint8_t i=0; i<=49; i++){ storedStates[i].velocity.x = velNED.x + gpsVelGlitchOffset.x; storedStates[i].velocity.y = velNED.y + gpsVelGlitchOffset.y; } } } // reset the vertical position state using the last height measurement void NavEKF::ResetHeight(void) { // read the altimeter readHgtData(); // write to the state vector state.position.z = -hgtMea; // down position from blended accel data state.posD1 = -hgtMea; // down position from IMU1 accel data state.posD2 = -hgtMea; // down position from IMU2 accel data // reset stored vertical position states to prevent subsequent GPS measurements from being rejected for (uint8_t i=0; i<=49; i++){ storedStates[i].position.z = -hgtMea; } terrainState = state.position.z + rngOnGnd; } // this function is used to initialise the filter whilst moving, using the AHRS DCM solution // it should NOT be used to re-initialise after a timeout as DCM will also be corrupted bool NavEKF::InitialiseFilterDynamic(void) { // this forces healthy() to be false so that when we ask for ahrs // attitude we get the DCM attitude regardless of the state of AHRS_EKF_USE statesInitialised = false; // If we are a plane and don't have GPS lock then don't initialise if (assume_zero_sideslip() && _ahrs->get_gps().status() < AP_GPS::GPS_OK_FIX_3D) { return false; } // If the DCM solution has not converged, then don't initialise, // unless at least 30s has passed if (_ahrs->get_error_rp() > 0.05f && _ahrs->uptime_ms() < 30000U) { return false; } // Set re-used variables to zero InitialiseVariables(); // get initial time deltat between IMU measurements (sec) dtIMUactual = dtIMUavg = 1.0f/_ahrs->get_ins().get_sample_rate(); // set number of updates over which gps and baro measurements are applied to the velocity and position states gpsUpdateCountMaxInv = (dtIMUavg * 1000.0f)/float(msecGpsAvg); gpsUpdateCountMax = uint8_t(1.0f/gpsUpdateCountMaxInv); hgtUpdateCountMaxInv = (dtIMUavg * 1000.0f)/float(msecHgtAvg); hgtUpdateCountMax = uint8_t(1.0f/hgtUpdateCountMaxInv); magUpdateCountMaxInv = (dtIMUavg * 1000.0f)/float(msecMagAvg); magUpdateCountMax = uint8_t(1.0f/magUpdateCountMaxInv); flowUpdateCountMaxInv = (dtIMUavg * 1000.0f)/float(msecFlowAvg); flowUpdateCountMax = uint8_t(1.0f/flowUpdateCountMaxInv); // calculate initial orientation and earth magnetic field states state.quat = calcQuatAndFieldStates(_ahrs->roll, _ahrs->pitch); // write to state vector state.gyro_bias.zero(); state.accel_zbias1 = 0; state.accel_zbias2 = 0; state.wind_vel.zero(); // read the GPS and set the position and velocity states readGpsData(); ResetVelocity(); ResetPosition(); // read the barometer and set the height state readHgtData(); ResetHeight(); // set stored states to current state StoreStatesReset(); // set to true now that states have be initialised statesInitialised = true; // define Earth rotation vector in the NED navigation frame calcEarthRateNED(earthRateNED, _ahrs->get_home().lat); // initialise IMU pre-processing states readIMUData(); // initialise the covariance matrix CovarianceInit(); return true; } // Initialise the states from accelerometer and magnetometer data (if present) // This method can only be used when the vehicle is static bool NavEKF::InitialiseFilterBootstrap(void) { // If we are a plane and don't have GPS lock then don't initialise if (assume_zero_sideslip() && _ahrs->get_gps().status() < AP_GPS::GPS_OK_FIX_3D) { statesInitialised = false; return false; } // set re-used variables to zero InitialiseVariables(); // get initial time deltat between IMU measurements (sec) dtIMUactual = dtIMUavg = 1.0f/_ahrs->get_ins().get_sample_rate(); // set number of updates over which gps and baro measurements are applied to the velocity and position states gpsUpdateCountMaxInv = (dtIMUavg * 1000.0f)/float(msecGpsAvg); gpsUpdateCountMax = uint8_t(1.0f/gpsUpdateCountMaxInv); hgtUpdateCountMaxInv = (dtIMUavg * 1000.0f)/float(msecHgtAvg); hgtUpdateCountMax = uint8_t(1.0f/hgtUpdateCountMaxInv); magUpdateCountMaxInv = (dtIMUavg * 1000.0f)/float(msecMagAvg); magUpdateCountMax = uint8_t(1.0f/magUpdateCountMaxInv); // acceleration vector in XYZ body axes measured by the IMU (m/s^2) Vector3f initAccVec; // TODO we should average accel readings over several cycles initAccVec = _ahrs->get_ins().get_accel(); // read the magnetometer data readMagData(); // normalise the acceleration vector float pitch=0, roll=0; if (initAccVec.length() > 0.001f) { initAccVec.normalize(); // calculate initial pitch angle pitch = asinf(initAccVec.x); // calculate initial roll angle roll = -asinf(initAccVec.y / cosf(pitch)); } // calculate initial orientation and earth magnetic field states Quaternion initQuat; initQuat = calcQuatAndFieldStates(roll, pitch); // check on ground status SetFlightAndFusionModes(); // write to state vector state.quat = initQuat; state.gyro_bias.zero(); state.accel_zbias1 = 0; state.accel_zbias2 = 0; state.wind_vel.zero(); state.body_magfield.zero(); // read the GPS and set the position and velocity states readGpsData(); ResetVelocity(); ResetPosition(); // read the barometer and set the height state readHgtData(); ResetHeight(); // set stored states to current state StoreStatesReset(); // set to true now we have intialised the states statesInitialised = true; // define Earth rotation vector in the NED navigation frame calcEarthRateNED(earthRateNED, _ahrs->get_home().lat); // initialise IMU pre-processing states readIMUData(); // initialise the covariance matrix CovarianceInit(); return true; } // Update Filter States - this should be called whenever new IMU data is available void NavEKF::UpdateFilter() { // zero the delta quaternion used by the strapdown navigation because it is published // and we need to return a zero rotation of the INS fails to update it correctedDelAngQuat.initialise(); // don't run filter updates if states have not been initialised if (!statesInitialised) { return; } // start the timer used for load measurement perf_begin(_perf_UpdateFilter); //get starting time for update step imuSampleTime_ms = hal.scheduler->millis(); // read IMU data and convert to delta angles and velocities readIMUData(); static bool prev_armed = false; bool armed = getVehicleArmStatus(); // the vehicle was previously disarmed and time has slipped // gyro auto-zero has likely just been done - skip this timestep if (!prev_armed && dtIMUactual > dtIMUavg*5.0f) { // stop the timer used for load measurement perf_end(_perf_UpdateFilter); prev_armed = armed; return; } prev_armed = armed; // detect if the filter update has been delayed for too long if (dtIMUactual > 0.2f) { // we have stalled for too long - reset states ResetVelocity(); ResetPosition(); ResetHeight(); StoreStatesReset(); //Initialise IMU pre-processing states readIMUData(); // stop the timer used for load measurement perf_end(_perf_UpdateFilter); return; } // check if on ground SetFlightAndFusionModes(); // Check arm status and perform required checks and mode changes performArmingChecks(); // run the strapdown INS equations every IMU update UpdateStrapdownEquationsNED(); // store the predicted states for subsequent use by measurement fusion StoreStates(); // sum delta angles and time used by covariance prediction summedDelAng = summedDelAng + correctedDelAng; summedDelVel = summedDelVel + correctedDelVel12; dt += dtIMUactual; // perform a covariance prediction if the total delta angle has exceeded the limit // or the time limit will be exceeded at the next IMU update if (((dt >= (covTimeStepMax - dtIMUactual)) || (summedDelAng.length() > covDelAngMax))) { CovariancePrediction(); } else { covPredStep = false; } // Read range finder data which is used by both position and optical flow fusion readRangeFinder(); // Update states using GPS, altimeter, compass, airspeed and synthetic sideslip observations SelectVelPosFusion(); SelectMagFusion(); SelectFlowFusion(); SelectTasFusion(); SelectBetaFusion(); // stop the timer used for load measurement perf_end(_perf_UpdateFilter); } // select fusion of velocity, position and height measurements void NavEKF::SelectVelPosFusion() { // check for and read new GPS data readGpsData(); // Specify which measurements should be used and check data for freshness if (PV_AidingMode == AID_ABSOLUTE) { // check if we can use opticalflow as a backup bool optFlowBackup = (flowDataValid && !hgtTimeout); // Set GPS time-out threshold depending on whether we have an airspeed sensor to constrain drift uint16_t gpsRetryTimeout = useAirspeed() ? gpsRetryTimeUseTAS : gpsRetryTimeNoTAS; // Set the time that copters will fly without a GPS lock before failing the GPS and switching to a non GPS mode uint16_t gpsFailTimeout = optFlowBackup ? gpsFailTimeWithFlow : gpsRetryTimeout; // If we haven't received GPS data for a while, then declare the position and velocity data as being timed out if (imuSampleTime_ms - lastFixTime_ms > gpsFailTimeout) { posTimeout = true; velTimeout = true; // If this happens in flight and we don't have airspeed or sideslip assumption or optical flow to constrain drift, then go into constant position mode. // Stay in that mode until the vehicle is re-armed. // If we can do optical flow nav (valid flow data and hieght above ground estimate, then go into flow nav mode. // Stay in that mode until the vehicle is dis-armed. if (vehicleArmed && !useAirspeed() && !assume_zero_sideslip()) { if (optFlowBackup) { // we can do optical flow only nav _fusionModeGPS = 3; PV_AidingMode = AID_RELATIVE; constVelMode = false; constPosMode = false; } else { constVelMode = false; // always clear constant velocity mode if constant velocity mode is active constPosMode = true; PV_AidingMode = AID_NONE; posTimeout = true; velTimeout = true; // reset the velocity ResetVelocity(); // store the current position to be used to keep reporting the last known position lastKnownPositionNE.x = state.position.x; lastKnownPositionNE.y = state.position.y; // reset the position ResetPosition(); } // set the position and velocity timeouts to indicate we are not using GPS data posTimeout = true; velTimeout = true; } } // command fusion of GPS data and reset states as required if (newDataGps && (PV_AidingMode == AID_ABSOLUTE)) { // reset data arrived flag newDataGps = false; // reset state updates and counter used to spread fusion updates across several frames to reduce 10Hz pulsing memset(&gpsIncrStateDelta[0], 0, sizeof(gpsIncrStateDelta)); gpsUpdateCount = 0; // use both if GPS use is enabled fuseVelData = true; fusePosData = true; // If a long time since last GPS update, then reset position and velocity and reset stored state history if (imuSampleTime_ms - secondLastFixTime_ms > gpsRetryTimeout) { // Apply an offset to the GPS position so that the position can be corrected gradually gpsPosGlitchOffsetNE.x = statesAtPosTime.position.x - gpsPosNE.x; gpsPosGlitchOffsetNE.y = statesAtPosTime.position.y - gpsPosNE.y; // limit the radius of the offset to 100m and decay the offset to zero radially decayGpsOffset(); ResetPosition(); ResetVelocity(); // record the fail time lastPosFailTime = imuSampleTime_ms; // Reset the normalised innovation to avoid false failing the bad position fusion test posTestRatio = 0.0f; } } else { fuseVelData = false; fusePosData = false; } } else if (constPosMode && covPredStep) { // in constant position mode use synthetic position measurements set to zero // only fuse synthetic measurements when rate of change of velocity is less than 0.5g to reduce attitude errors due to launch acceleration // do not use velocity fusion to reduce the effect of movement on attitude if (accNavMag < 4.9f) { fusePosData = true; } else { fusePosData = false; } fuseVelData = false; } else if (constVelMode && covPredStep) { // In constant velocity mode we fuse the last valid velocity vector // Reset the stored velocity vector when we enter the mode if (constVelMode && !lastConstVelMode) { heldVelNE.x = state.velocity.x; heldVelNE.y = state.velocity.y; } lastConstVelMode = constVelMode; // We do not fuse when manoeuvring to avoid corrupting the attitude if (accNavMag < 4.9f) { fuseVelData = true; } else { fuseVelData = false; } fusePosData = false; } else { fuseVelData = false; fusePosData = false; } // check for and read new height data readHgtData(); // If we haven't received height data for a while, then declare the height data as being timed out // set timeout period based on whether we have vertical GPS velocity available to constrain drift hgtRetryTime = (useGpsVertVel && !velTimeout) ? hgtRetryTimeMode0 : hgtRetryTimeMode12; if (imuSampleTime_ms - lastHgtMeasTime > hgtRetryTime) { hgtTimeout = true; } // command fusion of height data if (newDataHgt) { // reset data arrived flag newDataHgt = false; // reset state updates and counter used to spread fusion updates across several frames to reduce 10Hz pulsing memset(&hgtIncrStateDelta[0], 0, sizeof(hgtIncrStateDelta)); hgtUpdateCount = 0; // enable fusion fuseHgtData = true; } else { fuseHgtData = false; } // perform fusion if (fuseVelData || fusePosData || fuseHgtData) { // ensure that the covariance prediction is up to date before fusing data if (!covPredStep) CovariancePrediction(); FuseVelPosNED(); } // Fuse corrections to quaternion, position and velocity states across several time steps to reduce 5 and 10Hz pulsing in the output if (gpsUpdateCount < gpsUpdateCountMax) { gpsUpdateCount ++; for (uint8_t i = 0; i <= 9; i++) { states[i] += gpsIncrStateDelta[i]; } } if (hgtUpdateCount < hgtUpdateCountMax) { hgtUpdateCount ++; for (uint8_t i = 0; i <= 9; i++) { states[i] += hgtIncrStateDelta[i]; } } // Detect and declare bad GPS aiding status for minimum 10 seconds if a GPS rejection occurs after // rejection of GPS and reset to GPS position. This addresses failure case where errors cause ongoing rejection // of GPS and severe loss of position accuracy. uint32_t gpsRetryTime; if (useAirspeed()) { gpsRetryTime = gpsRetryTimeUseTAS; } else { gpsRetryTime = gpsRetryTimeNoTAS; } if ((posTestRatio > 2.0f) && ((imuSampleTime_ms - lastPosFailTime) < gpsRetryTime) && ((imuSampleTime_ms - lastPosFailTime) > gpsRetryTime/2) && fusePosData) { lastGpsAidBadTime_ms = imuSampleTime_ms; gpsAidingBad = true; } gpsAidingBad = gpsAidingBad && ((imuSampleTime_ms - lastGpsAidBadTime_ms) < 10000); } // select fusion of magnetometer data void NavEKF::SelectMagFusion() { // start performance timer perf_begin(_perf_FuseMagnetometer); // check for and read new magnetometer measurements readMagData(); // If we are using the compass and the magnetometer has been unhealthy for too long we declare a timeout if (magHealth) { magTimeout = false; lastHealthyMagTime_ms = imuSampleTime_ms; } else if ((imuSampleTime_ms - lastHealthyMagTime_ms) > magFailTimeLimit_ms && use_compass()) { magTimeout = true; } // determine if conditions are right to start a new fusion cycle bool dataReady = statesInitialised && use_compass() && newDataMag; if (dataReady) { // reset state updates and counter used to spread fusion updates across several frames to reduce 10Hz pulsing memset(&magIncrStateDelta[0], 0, sizeof(magIncrStateDelta)); magUpdateCount = 0; // ensure that the covariance prediction is up to date before fusing data if (!covPredStep) CovariancePrediction(); // fuse the three magnetometer componenents sequentially for (mag_state.obsIndex = 0; mag_state.obsIndex <= 2; mag_state.obsIndex++) FuseMagnetometer(); } // Fuse corrections to quaternion, position and velocity states across several time steps to reduce 10Hz pulsing in the output if (magUpdateCount < magUpdateCountMax) { magUpdateCount ++; for (uint8_t i = 0; i <= 9; i++) { states[i] += magIncrStateDelta[i]; } } // stop performance timer perf_end(_perf_FuseMagnetometer); } // select fusion of optical flow measurements void NavEKF::SelectFlowFusion() { // start performance timer perf_begin(_perf_FuseOptFlow); // Perform Data Checks // Check if the optical flow data is still valid flowDataValid = ((imuSampleTime_ms - flowValidMeaTime_ms) < 1000); // Check if the optical flow sensor has timed out bool flowSensorTimeout = ((imuSampleTime_ms - flowValidMeaTime_ms) > 5000); // Check if the fusion has timed out (flow measurements have been rejected for too long) bool flowFusionTimeout = ((imuSampleTime_ms - prevFlowFuseTime_ms) > 5000); // check is the terrain offset estimate is still valid gndOffsetValid = ((imuSampleTime_ms - gndHgtValidTime_ms) < 5000); // Perform tilt check bool tiltOK = (Tnb_flow.c.z > DCM33FlowMin); // Constrain measurements to zero if we are using optical flow and are on the ground if (_fusionModeGPS == 3 && !takeOffDetected && vehicleArmed) { flowRadXYcomp[0] = 0.0f; flowRadXYcomp[1] = 0.0f; flowRadXY[0] = 0.0f; flowRadXY[1] = 0.0f; omegaAcrossFlowTime.zero(); flowDataValid = true; } // If the flow measurements have been rejected for too long and we are relying on them, then revert to constant position mode if ((flowSensorTimeout || flowFusionTimeout) && PV_AidingMode == AID_RELATIVE) { constVelMode = false; // always clear constant velocity mode if constant velocity mode is active constPosMode = true; PV_AidingMode = AID_NONE; // reset the velocity ResetVelocity(); // store the current position to be used to keep reporting the last known position lastKnownPositionNE.x = state.position.x; lastKnownPositionNE.y = state.position.y; // reset the position ResetPosition(); } // if we do have valid flow measurements, fuse data into a 1-state EKF to estimate terrain height // we don't do terrain height estimation in optical flow only mode as the ground becomes our zero height reference if ((newDataFlow || newDataRng) && tiltOK) { // fuse range data into the terrain estimator if available fuseRngData = newDataRng; // fuse optical flow data into the terrain estimator if available and if there is no range data (range data is better) fuseOptFlowData = (newDataFlow && !fuseRngData); // Estimate the terrain offset (runs a one state EKF) EstimateTerrainOffset(); // Indicate we have used the range data newDataRng = false; // we don't do subsequent fusion of optical flow data into the main filter if GPS is good and terrain offset data is invalid // because an invalid height above ground estimate will cause the optical flow measurements to fight the GPS if (!gpsNotAvailable && !gndOffsetValid) { // turn off fusion permissions // reset the flags to indicate that no new range finder or flow data is available for fusion newDataFlow = false; } } // Fuse optical flow data into the main filter // if the filter is initialised, we have data to fuse and the vehicle is not excessively tilted, then perform optical flow fusion if (flowDataValid && newDataFlow && tiltOK && !constPosMode) { // reset state updates and counter used to spread fusion updates across several frames to reduce 10Hz pulsing memset(&flowIncrStateDelta[0], 0, sizeof(flowIncrStateDelta)); flowUpdateCount = 0; // Set the flow noise used by the fusion processes R_LOS = sq(max(_flowNoise, 0.05f)); // ensure that the covariance prediction is up to date before fusing data if (!covPredStep) CovariancePrediction(); // Fuse the optical flow X and Y axis data into the main filter sequentially for (flow_state.obsIndex = 0; flow_state.obsIndex <= 1; flow_state.obsIndex++) FuseOptFlow(); // reset flag to indicate that no new flow data is available for fusion newDataFlow = false; // indicate that flow fusion has been performed. This is used for load spreading. flowFusePerformed = true; } // Apply corrections to quaternion, position and velocity states across several time steps to reduce 10Hz pulsing in the output if (flowUpdateCount < flowUpdateCountMax) { flowUpdateCount ++; for (uint8_t i = 0; i <= 9; i++) { states[i] += flowIncrStateDelta[i]; } } // stop the performance timer perf_end(_perf_FuseOptFlow); } // select fusion of true airspeed measurements void NavEKF::SelectTasFusion() { // get true airspeed measurement readAirSpdData(); // If we haven't received airspeed data for a while, then declare the airspeed data as being timed out if (imuSampleTime_ms - lastAirspeedUpdate > tasRetryTime) { tasTimeout = true; } // if the filter is initialised, wind states are not inhibited and we have data to fuse, then perform TAS fusion tasDataWaiting = (statesInitialised && !inhibitWindStates && newDataTas); if (tasDataWaiting) { // ensure that the covariance prediction is up to date before fusing data if (!covPredStep) CovariancePrediction(); FuseAirspeed(); TASmsecPrev = imuSampleTime_ms; tasDataWaiting = false; newDataTas = false; } } // select fusion of synthetic sideslip measurements // synthetic sidelip fusion only works for fixed wing aircraft and relies on the average sideslip being close to zero // it requires a stable wind for best results and should not be used for aerobatic flight with manoeuvres that induce large sidslip angles (eg knife-edge, spins, etc) void NavEKF::SelectBetaFusion() { // set true when the fusion time interval has triggered bool f_timeTrigger = ((imuSampleTime_ms - BETAmsecPrev) >= msecBetaAvg); // set true when use of synthetic sideslip fusion is necessary because we have limited sensor data or are dead reckoning position bool f_required = !(use_compass() && useAirspeed() && posHealth); // set true when sideslip fusion is feasible (requires zero sideslip assumption to be valid and use of wind states) bool f_feasible = (assume_zero_sideslip() && !inhibitWindStates); // use synthetic sideslip fusion if feasible, required and enough time has lapsed since the last fusion if (f_feasible && f_required && f_timeTrigger) { // ensure that the covariance prediction is up to date before fusing data if (!covPredStep) CovariancePrediction(); FuseSideslip(); BETAmsecPrev = imuSampleTime_ms; } } // update the quaternion, velocity and position states using IMU measurements void NavEKF::UpdateStrapdownEquationsNED() { Vector3f delVelNav; // delta velocity vector calculated using a blend of IMU1 and IMU2 data Vector3f delVelNav1; // delta velocity vector calculated using IMU1 data Vector3f delVelNav2; // delta velocity vector calculated using IMU2 data // remove sensor bias errors correctedDelAng = dAngIMU - state.gyro_bias; correctedDelVel1 = dVelIMU1; correctedDelVel2 = dVelIMU2; correctedDelVel1.z -= state.accel_zbias1; correctedDelVel2.z -= state.accel_zbias2; // use weighted average of both IMU units for delta velocities correctedDelVel12 = correctedDelVel1 * IMU1_weighting + correctedDelVel2 * (1.0f - IMU1_weighting); // apply correction for earths rotation rate // % * - and + operators have been overloaded correctedDelAng = correctedDelAng - prevTnb * earthRateNED*dtIMUactual; // convert the rotation vector to its equivalent quaternion correctedDelAngQuat.from_axis_angle(correctedDelAng); // update the quaternion states by rotating from the previous attitude through // the delta angle rotation quaternion and normalise state.quat *= correctedDelAngQuat; state.quat.normalize(); // calculate the body to nav cosine matrix Matrix3f Tbn_temp; state.quat.rotation_matrix(Tbn_temp); prevTnb = Tbn_temp.transposed(); float delVelGravity1_z = GRAVITY_MSS*dtDelVel1; float delVelGravity2_z = GRAVITY_MSS*dtDelVel2; float delVelGravity_z = delVelGravity1_z * IMU1_weighting + delVelGravity2_z * (1.0f - IMU1_weighting); // transform body delta velocities to delta velocities in the nav frame // * and + operators have been overloaded // blended IMU calc delVelNav = Tbn_temp*correctedDelVel12; delVelNav.z += delVelGravity_z; // single IMU calcs delVelNav1 = Tbn_temp*correctedDelVel1; delVelNav1.z += delVelGravity1_z; delVelNav2 = Tbn_temp*correctedDelVel2; delVelNav2.z += delVelGravity2_z; // calculate the rate of change of velocity (used for launch detect and other functions) velDotNED = delVelNav / dtIMUactual; // apply a first order lowpass filter velDotNEDfilt = velDotNED * 0.05f + velDotNEDfilt * 0.95f; // calculate a magnitude of the filtered nav acceleration (required for GPS // variance estimation) accNavMag = velDotNEDfilt.length(); accNavMagHoriz = pythagorous2(velDotNEDfilt.x , velDotNEDfilt.y); // save velocity for use in trapezoidal intergration for position calcuation Vector3f lastVelocity = state.velocity; Vector3f lastVel1 = state.vel1; Vector3f lastVel2 = state.vel2; // sum delta velocities to get velocity state.velocity += delVelNav; state.vel1 += delVelNav1; state.vel2 += delVelNav2; // apply a trapezoidal integration to velocities to calculate position state.position += (state.velocity + lastVelocity) * (dtIMUactual*0.5f); state.posD1 += (state.vel1.z + lastVel1.z) * (dtIMUactual*0.5f); state.posD2 += (state.vel2.z + lastVel2.z) * (dtIMUactual*0.5f); // capture current angular rate to augmented state vector for use by optical flow fusion state.omega = correctedDelAng / dtIMUactual; // LPF the yaw rate using a 1 second time constant yaw rate and determine if we are doing continual // fast rotations that can cause problems due to gyro scale factor errors. float alphaLPF = constrain_float(dtIMUactual, 0.0f, 1.0f); yawRateFilt += (state.omega.z - yawRateFilt)*alphaLPF; if (fabsf(yawRateFilt) > 1.0f) { highYawRate = true; } else { highYawRate = false; } // limit states to protect against divergence ConstrainStates(); } // calculate the predicted state covariance matrix void NavEKF::CovariancePrediction() { perf_begin(_perf_CovariancePrediction); float windVelSigma; // wind velocity 1-sigma process noise - m/s float dAngBiasSigma;// delta angle bias 1-sigma process noise - rad/s float dVelBiasSigma;// delta velocity bias 1-sigma process noise - m/s float magEarthSigma;// earth magnetic field 1-sigma process noise float magBodySigma; // body magnetic field 1-sigma process noise float daxCov; // X axis delta angle variance rad^2 float dayCov; // Y axis delta angle variance rad^2 float dazCov; // Z axis delta angle variance rad^2 float dvxCov; // X axis delta velocity variance (m/s)^2 float dvyCov; // Y axis delta velocity variance (m/s)^2 float dvzCov; // Z axis delta velocity variance (m/s)^2 float dvx; // X axis delta velocity (m/s) float dvy; // Y axis delta velocity (m/s) float dvz; // Z axis delta velocity (m/s) float dax; // X axis delta angle (rad) float day; // Y axis delta angle (rad) float daz; // Z axis delta angle (rad) float q0; // attitude quaternion float q1; // attitude quaternion float q2; // attitude quaternion float q3; // attitude quaternion float dax_b; // X axis delta angle measurement bias (rad) float day_b; // Y axis delta angle measurement bias (rad) float daz_b; // Z axis delta angle measurement bias (rad) float dvz_b; // Z axis delta velocity measurement bias (rad) // calculate covariance prediction process noise // use filtered height rate to increase wind process noise when climbing or descending // this allows for wind gradient effects. // filter height rate using a 10 second time constant filter float alpha = 0.1f * dt; hgtRate = hgtRate * (1.0f - alpha) - state.velocity.z * alpha; // use filtered height rate to increase wind process noise when climbing or descending // this allows for wind gradient effects. if (!inhibitWindStates) { windVelSigma = dt * constrain_float(_windVelProcessNoise, 0.01f, 1.0f) * (1.0f + constrain_float(_wndVarHgtRateScale, 0.0f, 1.0f) * fabsf(hgtRate)); } else { windVelSigma = 0.0f; } dAngBiasSigma = dt * constrain_float(_gyroBiasProcessNoise, 1e-7f, 1e-5f); dVelBiasSigma = dt * constrain_float(_accelBiasProcessNoise, 1e-5f, 1e-3f); if (!inhibitMagStates) { magEarthSigma = dt * constrain_float(_magEarthProcessNoise, 1e-4f, 1e-2f); magBodySigma = dt * constrain_float(_magBodyProcessNoise, 1e-4f, 1e-2f); } else { magEarthSigma = 0.0f; magBodySigma = 0.0f; } for (uint8_t i= 0; i<=9; i++) processNoise[i] = 1.0e-9f; for (uint8_t i=10; i<=12; i++) processNoise[i] = dAngBiasSigma; // scale gyro bias noise when disarmed to allow for faster bias estimation for (uint8_t i=10; i<=12; i++) { processNoise[i] = dAngBiasSigma; if (!vehicleArmed) { processNoise[i] *= gyroBiasNoiseScaler; } } // if we are yawing rapidly, inhibit yaw gyro bias learning to prevent gyro scale factor errors from corrupting the bias estimate if (highYawRate) { processNoise[12] = 0.0f; P[12][12] = 0.0f; } // scale accel bias noise when disarmed to allow for faster bias estimation // inhibit bias estimation during takeoff with ground effect to prevent bad bias learning if (expectGndEffectTakeoff) { processNoise[13] = 0.0f; } else if (!vehicleArmed) { processNoise[13] = dVelBiasSigma * accelBiasNoiseScaler; } else { processNoise[13] = dVelBiasSigma; } for (uint8_t i=14; i<=15; i++) processNoise[i] = windVelSigma; for (uint8_t i=16; i<=18; i++) processNoise[i] = magEarthSigma; for (uint8_t i=19; i<=21; i++) processNoise[i] = magBodySigma; for (uint8_t i= 0; i<=21; i++) processNoise[i] = sq(processNoise[i]); // set variables used to calculate covariance growth dvx = summedDelVel.x; dvy = summedDelVel.y; dvz = summedDelVel.z; dax = summedDelAng.x; day = summedDelAng.y; daz = summedDelAng.z; q0 = state.quat[0]; q1 = state.quat[1]; q2 = state.quat[2]; q3 = state.quat[3]; dax_b = state.gyro_bias.x; day_b = state.gyro_bias.y; daz_b = state.gyro_bias.z; dvz_b = IMU1_weighting * state.accel_zbias1 + (1.0f - IMU1_weighting) * state.accel_zbias2; _gyrNoise = constrain_float(_gyrNoise, 1e-3f, 5e-2f); daxCov = sq(dt*_gyrNoise); dayCov = sq(dt*_gyrNoise); // Account for 3% scale factor error on Z angular rate. This reduces chance of continuous fast rotations causing loss of yaw reference. dazCov = sq(dt*_gyrNoise) + sq(dt*0.03f*yawRateFilt); _accNoise = constrain_float(_accNoise, 5e-2f, 1.0f); dvxCov = sq(dt*_accNoise); dvyCov = sq(dt*_accNoise); dvzCov = sq(dt*_accNoise); // calculate the predicted covariance due to inertial sensor error propagation SF[0] = dvz - dvz_b; SF[1] = 2*q3*SF[0] + 2*dvx*q1 + 2*dvy*q2; SF[2] = 2*dvx*q3 - 2*q1*SF[0] + 2*dvy*q0; SF[3] = 2*q2*SF[0] + 2*dvx*q0 - 2*dvy*q3; SF[4] = day/2 - day_b/2; SF[5] = daz/2 - daz_b/2; SF[6] = dax/2 - dax_b/2; SF[7] = dax_b/2 - dax/2; SF[8] = daz_b/2 - daz/2; SF[9] = day_b/2 - day/2; SF[10] = 2*q0*SF[0]; SF[11] = q1/2; SF[12] = q2/2; SF[13] = q3/2; SF[14] = 2*dvy*q1; SG[0] = q0/2; SG[1] = sq(q3); SG[2] = sq(q2); SG[3] = sq(q1); SG[4] = sq(q0); SG[5] = 2*q2*q3; SG[6] = 2*q1*q3; SG[7] = 2*q1*q2; SQ[0] = dvzCov*(SG[5] - 2*q0*q1)*(SG[1] - SG[2] - SG[3] + SG[4]) - dvyCov*(SG[5] + 2*q0*q1)*(SG[1] - SG[2] + SG[3] - SG[4]) + dvxCov*(SG[6] - 2*q0*q2)*(SG[7] + 2*q0*q3); SQ[1] = dvzCov*(SG[6] + 2*q0*q2)*(SG[1] - SG[2] - SG[3] + SG[4]) - dvxCov*(SG[6] - 2*q0*q2)*(SG[1] + SG[2] - SG[3] - SG[4]) + dvyCov*(SG[5] + 2*q0*q1)*(SG[7] - 2*q0*q3); SQ[2] = dvzCov*(SG[5] - 2*q0*q1)*(SG[6] + 2*q0*q2) - dvyCov*(SG[7] - 2*q0*q3)*(SG[1] - SG[2] + SG[3] - SG[4]) - dvxCov*(SG[7] + 2*q0*q3)*(SG[1] + SG[2] - SG[3] - SG[4]); SQ[3] = (dayCov*q1*SG[0])/2 - (dazCov*q1*SG[0])/2 - (daxCov*q2*q3)/4; SQ[4] = (dazCov*q2*SG[0])/2 - (daxCov*q2*SG[0])/2 - (dayCov*q1*q3)/4; SQ[5] = (daxCov*q3*SG[0])/2 - (dayCov*q3*SG[0])/2 - (dazCov*q1*q2)/4; SQ[6] = (daxCov*q1*q2)/4 - (dazCov*q3*SG[0])/2 - (dayCov*q1*q2)/4; SQ[7] = (dazCov*q1*q3)/4 - (daxCov*q1*q3)/4 - (dayCov*q2*SG[0])/2; SQ[8] = (dayCov*q2*q3)/4 - (daxCov*q1*SG[0])/2 - (dazCov*q2*q3)/4; SQ[9] = sq(SG[0]); SQ[10] = sq(q1); SPP[0] = SF[10] + SF[14] - 2*dvx*q2; SPP[1] = 2*q2*SF[0] + 2*dvx*q0 - 2*dvy*q3; SPP[2] = 2*dvx*q3 - 2*q1*SF[0] + 2*dvy*q0; SPP[3] = 2*q0*q1 - 2*q2*q3; SPP[4] = 2*q0*q2 + 2*q1*q3; SPP[5] = sq(q0) - sq(q1) - sq(q2) + sq(q3); SPP[6] = SF[13]; SPP[7] = SF[12]; nextP[0][0] = P[0][0] + P[1][0]*SF[7] + P[2][0]*SF[9] + P[3][0]*SF[8] + P[10][0]*SF[11] + P[11][0]*SPP[7] + P[12][0]*SPP[6] + (daxCov*SQ[10])/4 + SF[7]*(P[0][1] + P[1][1]*SF[7] + P[2][1]*SF[9] + P[3][1]*SF[8] + P[10][1]*SF[11] + P[11][1]*SPP[7] + P[12][1]*SPP[6]) + SF[9]*(P[0][2] + P[1][2]*SF[7] + P[2][2]*SF[9] + P[3][2]*SF[8] + P[10][2]*SF[11] + P[11][2]*SPP[7] + P[12][2]*SPP[6]) + SF[8]*(P[0][3] + P[1][3]*SF[7] + P[2][3]*SF[9] + P[3][3]*SF[8] + P[10][3]*SF[11] + P[11][3]*SPP[7] + P[12][3]*SPP[6]) + SF[11]*(P[0][10] + P[1][10]*SF[7] + P[2][10]*SF[9] + P[3][10]*SF[8] + P[10][10]*SF[11] + P[11][10]*SPP[7] + P[12][10]*SPP[6]) + SPP[7]*(P[0][11] + P[1][11]*SF[7] + P[2][11]*SF[9] + P[3][11]*SF[8] + P[10][11]*SF[11] + P[11][11]*SPP[7] + P[12][11]*SPP[6]) + SPP[6]*(P[0][12] + P[1][12]*SF[7] + P[2][12]*SF[9] + P[3][12]*SF[8] + P[10][12]*SF[11] + P[11][12]*SPP[7] + P[12][12]*SPP[6]) + (dayCov*sq(q2))/4 + (dazCov*sq(q3))/4; nextP[0][1] = P[0][1] + SQ[8] + P[1][1]*SF[7] + P[2][1]*SF[9] + P[3][1]*SF[8] + P[10][1]*SF[11] + P[11][1]*SPP[7] + P[12][1]*SPP[6] + SF[6]*(P[0][0] + P[1][0]*SF[7] + P[2][0]*SF[9] + P[3][0]*SF[8] + P[10][0]*SF[11] + P[11][0]*SPP[7] + P[12][0]*SPP[6]) + SF[5]*(P[0][2] + P[1][2]*SF[7] + P[2][2]*SF[9] + P[3][2]*SF[8] + P[10][2]*SF[11] + P[11][2]*SPP[7] + P[12][2]*SPP[6]) + SF[9]*(P[0][3] + P[1][3]*SF[7] + P[2][3]*SF[9] + P[3][3]*SF[8] + P[10][3]*SF[11] + P[11][3]*SPP[7] + P[12][3]*SPP[6]) + SPP[6]*(P[0][11] + P[1][11]*SF[7] + P[2][11]*SF[9] + P[3][11]*SF[8] + P[10][11]*SF[11] + P[11][11]*SPP[7] + P[12][11]*SPP[6]) - SPP[7]*(P[0][12] + P[1][12]*SF[7] + P[2][12]*SF[9] + P[3][12]*SF[8] + P[10][12]*SF[11] + P[11][12]*SPP[7] + P[12][12]*SPP[6]) - (q0*(P[0][10] + P[1][10]*SF[7] + P[2][10]*SF[9] + P[3][10]*SF[8] + P[10][10]*SF[11] + P[11][10]*SPP[7] + P[12][10]*SPP[6]))/2; nextP[0][2] = P[0][2] + SQ[7] + P[1][2]*SF[7] + P[2][2]*SF[9] + P[3][2]*SF[8] + P[10][2]*SF[11] + P[11][2]*SPP[7] + P[12][2]*SPP[6] + SF[4]*(P[0][0] + P[1][0]*SF[7] + P[2][0]*SF[9] + P[3][0]*SF[8] + P[10][0]*SF[11] + P[11][0]*SPP[7] + P[12][0]*SPP[6]) + SF[8]*(P[0][1] + P[1][1]*SF[7] + P[2][1]*SF[9] + P[3][1]*SF[8] + P[10][1]*SF[11] + P[11][1]*SPP[7] + P[12][1]*SPP[6]) + SF[6]*(P[0][3] + P[1][3]*SF[7] + P[2][3]*SF[9] + P[3][3]*SF[8] + P[10][3]*SF[11] + P[11][3]*SPP[7] + P[12][3]*SPP[6]) + SF[11]*(P[0][12] + P[1][12]*SF[7] + P[2][12]*SF[9] + P[3][12]*SF[8] + P[10][12]*SF[11] + P[11][12]*SPP[7] + P[12][12]*SPP[6]) - SPP[6]*(P[0][10] + P[1][10]*SF[7] + P[2][10]*SF[9] + P[3][10]*SF[8] + P[10][10]*SF[11] + P[11][10]*SPP[7] + P[12][10]*SPP[6]) - (q0*(P[0][11] + P[1][11]*SF[7] + P[2][11]*SF[9] + P[3][11]*SF[8] + P[10][11]*SF[11] + P[11][11]*SPP[7] + P[12][11]*SPP[6]))/2; nextP[0][3] = P[0][3] + SQ[6] + P[1][3]*SF[7] + P[2][3]*SF[9] + P[3][3]*SF[8] + P[10][3]*SF[11] + P[11][3]*SPP[7] + P[12][3]*SPP[6] + SF[5]*(P[0][0] + P[1][0]*SF[7] + P[2][0]*SF[9] + P[3][0]*SF[8] + P[10][0]*SF[11] + P[11][0]*SPP[7] + P[12][0]*SPP[6]) + SF[4]*(P[0][1] + P[1][1]*SF[7] + P[2][1]*SF[9] + P[3][1]*SF[8] + P[10][1]*SF[11] + P[11][1]*SPP[7] + P[12][1]*SPP[6]) + SF[7]*(P[0][2] + P[1][2]*SF[7] + P[2][2]*SF[9] + P[3][2]*SF[8] + P[10][2]*SF[11] + P[11][2]*SPP[7] + P[12][2]*SPP[6]) - SF[11]*(P[0][11] + P[1][11]*SF[7] + P[2][11]*SF[9] + P[3][11]*SF[8] + P[10][11]*SF[11] + P[11][11]*SPP[7] + P[12][11]*SPP[6]) + SPP[7]*(P[0][10] + P[1][10]*SF[7] + P[2][10]*SF[9] + P[3][10]*SF[8] + P[10][10]*SF[11] + P[11][10]*SPP[7] + P[12][10]*SPP[6]) - (q0*(P[0][12] + P[1][12]*SF[7] + P[2][12]*SF[9] + P[3][12]*SF[8] + P[10][12]*SF[11] + P[11][12]*SPP[7] + P[12][12]*SPP[6]))/2; nextP[0][4] = P[0][4] + P[1][4]*SF[7] + P[2][4]*SF[9] + P[3][4]*SF[8] + P[10][4]*SF[11] + P[11][4]*SPP[7] + P[12][4]*SPP[6] + SF[3]*(P[0][0] + P[1][0]*SF[7] + P[2][0]*SF[9] + P[3][0]*SF[8] + P[10][0]*SF[11] + P[11][0]*SPP[7] + P[12][0]*SPP[6]) + SF[1]*(P[0][1] + P[1][1]*SF[7] + P[2][1]*SF[9] + P[3][1]*SF[8] + P[10][1]*SF[11] + P[11][1]*SPP[7] + P[12][1]*SPP[6]) + SPP[0]*(P[0][2] + P[1][2]*SF[7] + P[2][2]*SF[9] + P[3][2]*SF[8] + P[10][2]*SF[11] + P[11][2]*SPP[7] + P[12][2]*SPP[6]) - SPP[2]*(P[0][3] + P[1][3]*SF[7] + P[2][3]*SF[9] + P[3][3]*SF[8] + P[10][3]*SF[11] + P[11][3]*SPP[7] + P[12][3]*SPP[6]) - SPP[4]*(P[0][13] + P[1][13]*SF[7] + P[2][13]*SF[9] + P[3][13]*SF[8] + P[10][13]*SF[11] + P[11][13]*SPP[7] + P[12][13]*SPP[6]); nextP[0][5] = P[0][5] + P[1][5]*SF[7] + P[2][5]*SF[9] + P[3][5]*SF[8] + P[10][5]*SF[11] + P[11][5]*SPP[7] + P[12][5]*SPP[6] + SF[2]*(P[0][0] + P[1][0]*SF[7] + P[2][0]*SF[9] + P[3][0]*SF[8] + P[10][0]*SF[11] + P[11][0]*SPP[7] + P[12][0]*SPP[6]) + SF[1]*(P[0][2] + P[1][2]*SF[7] + P[2][2]*SF[9] + P[3][2]*SF[8] + P[10][2]*SF[11] + P[11][2]*SPP[7] + P[12][2]*SPP[6]) + SF[3]*(P[0][3] + P[1][3]*SF[7] + P[2][3]*SF[9] + P[3][3]*SF[8] + P[10][3]*SF[11] + P[11][3]*SPP[7] + P[12][3]*SPP[6]) - SPP[0]*(P[0][1] + P[1][1]*SF[7] + P[2][1]*SF[9] + P[3][1]*SF[8] + P[10][1]*SF[11] + P[11][1]*SPP[7] + P[12][1]*SPP[6]) + SPP[3]*(P[0][13] + P[1][13]*SF[7] + P[2][13]*SF[9] + P[3][13]*SF[8] + P[10][13]*SF[11] + P[11][13]*SPP[7] + P[12][13]*SPP[6]); nextP[0][6] = P[0][6] + P[1][6]*SF[7] + P[2][6]*SF[9] + P[3][6]*SF[8] + P[10][6]*SF[11] + P[11][6]*SPP[7] + P[12][6]*SPP[6] + SF[2]*(P[0][1] + P[1][1]*SF[7] + P[2][1]*SF[9] + P[3][1]*SF[8] + P[10][1]*SF[11] + P[11][1]*SPP[7] + P[12][1]*SPP[6]) + SF[1]*(P[0][3] + P[1][3]*SF[7] + P[2][3]*SF[9] + P[3][3]*SF[8] + P[10][3]*SF[11] + P[11][3]*SPP[7] + P[12][3]*SPP[6]) + SPP[0]*(P[0][0] + P[1][0]*SF[7] + P[2][0]*SF[9] + P[3][0]*SF[8] + P[10][0]*SF[11] + P[11][0]*SPP[7] + P[12][0]*SPP[6]) - SPP[1]*(P[0][2] + P[1][2]*SF[7] + P[2][2]*SF[9] + P[3][2]*SF[8] + P[10][2]*SF[11] + P[11][2]*SPP[7] + P[12][2]*SPP[6]) - (sq(q0) - sq(q1) - sq(q2) + sq(q3))*(P[0][13] + P[1][13]*SF[7] + P[2][13]*SF[9] + P[3][13]*SF[8] + P[10][13]*SF[11] + P[11][13]*SPP[7] + P[12][13]*SPP[6]); nextP[0][7] = P[0][7] + P[1][7]*SF[7] + P[2][7]*SF[9] + P[3][7]*SF[8] + P[10][7]*SF[11] + P[11][7]*SPP[7] + P[12][7]*SPP[6] + dt*(P[0][4] + P[1][4]*SF[7] + P[2][4]*SF[9] + P[3][4]*SF[8] + P[10][4]*SF[11] + P[11][4]*SPP[7] + P[12][4]*SPP[6]); nextP[0][8] = P[0][8] + P[1][8]*SF[7] + P[2][8]*SF[9] + P[3][8]*SF[8] + P[10][8]*SF[11] + P[11][8]*SPP[7] + P[12][8]*SPP[6] + dt*(P[0][5] + P[1][5]*SF[7] + P[2][5]*SF[9] + P[3][5]*SF[8] + P[10][5]*SF[11] + P[11][5]*SPP[7] + P[12][5]*SPP[6]); nextP[0][9] = P[0][9] + P[1][9]*SF[7] + P[2][9]*SF[9] + P[3][9]*SF[8] + P[10][9]*SF[11] + P[11][9]*SPP[7] + P[12][9]*SPP[6] + dt*(P[0][6] + P[1][6]*SF[7] + P[2][6]*SF[9] + P[3][6]*SF[8] + P[10][6]*SF[11] + P[11][6]*SPP[7] + P[12][6]*SPP[6]); nextP[0][10] = P[0][10] + P[1][10]*SF[7] + P[2][10]*SF[9] + P[3][10]*SF[8] + P[10][10]*SF[11] + P[11][10]*SPP[7] + P[12][10]*SPP[6]; nextP[0][11] = P[0][11] + P[1][11]*SF[7] + P[2][11]*SF[9] + P[3][11]*SF[8] + P[10][11]*SF[11] + P[11][11]*SPP[7] + P[12][11]*SPP[6]; nextP[0][12] = P[0][12] + P[1][12]*SF[7] + P[2][12]*SF[9] + P[3][12]*SF[8] + P[10][12]*SF[11] + P[11][12]*SPP[7] + P[12][12]*SPP[6]; nextP[0][13] = P[0][13] + P[1][13]*SF[7] + P[2][13]*SF[9] + P[3][13]*SF[8] + P[10][13]*SF[11] + P[11][13]*SPP[7] + P[12][13]*SPP[6]; nextP[0][14] = P[0][14] + P[1][14]*SF[7] + P[2][14]*SF[9] + P[3][14]*SF[8] + P[10][14]*SF[11] + P[11][14]*SPP[7] + P[12][14]*SPP[6]; nextP[0][15] = P[0][15] + P[1][15]*SF[7] + P[2][15]*SF[9] + P[3][15]*SF[8] + P[10][15]*SF[11] + P[11][15]*SPP[7] + P[12][15]*SPP[6]; nextP[0][16] = P[0][16] + P[1][16]*SF[7] + P[2][16]*SF[9] + P[3][16]*SF[8] + P[10][16]*SF[11] + P[11][16]*SPP[7] + P[12][16]*SPP[6]; nextP[0][17] = P[0][17] + P[1][17]*SF[7] + P[2][17]*SF[9] + P[3][17]*SF[8] + P[10][17]*SF[11] + P[11][17]*SPP[7] + P[12][17]*SPP[6]; nextP[0][18] = P[0][18] + P[1][18]*SF[7] + P[2][18]*SF[9] + P[3][18]*SF[8] + P[10][18]*SF[11] + P[11][18]*SPP[7] + P[12][18]*SPP[6]; nextP[0][19] = P[0][19] + P[1][19]*SF[7] + P[2][19]*SF[9] + P[3][19]*SF[8] + P[10][19]*SF[11] + P[11][19]*SPP[7] + P[12][19]*SPP[6]; nextP[0][20] = P[0][20] + P[1][20]*SF[7] + P[2][20]*SF[9] + P[3][20]*SF[8] + P[10][20]*SF[11] + P[11][20]*SPP[7] + P[12][20]*SPP[6]; nextP[0][21] = P[0][21] + P[1][21]*SF[7] + P[2][21]*SF[9] + P[3][21]*SF[8] + P[10][21]*SF[11] + P[11][21]*SPP[7] + P[12][21]*SPP[6]; nextP[1][0] = P[1][0] + SQ[8] + P[0][0]*SF[6] + P[2][0]*SF[5] + P[3][0]*SF[9] + P[11][0]*SPP[6] - P[12][0]*SPP[7] - (P[10][0]*q0)/2 + SF[7]*(P[1][1] + P[0][1]*SF[6] + P[2][1]*SF[5] + P[3][1]*SF[9] + P[11][1]*SPP[6] - P[12][1]*SPP[7] - (P[10][1]*q0)/2) + SF[9]*(P[1][2] + P[0][2]*SF[6] + P[2][2]*SF[5] + P[3][2]*SF[9] + P[11][2]*SPP[6] - P[12][2]*SPP[7] - (P[10][2]*q0)/2) + SF[8]*(P[1][3] + P[0][3]*SF[6] + P[2][3]*SF[5] + P[3][3]*SF[9] + P[11][3]*SPP[6] - P[12][3]*SPP[7] - (P[10][3]*q0)/2) + SF[11]*(P[1][10] + P[0][10]*SF[6] + P[2][10]*SF[5] + P[3][10]*SF[9] + P[11][10]*SPP[6] - P[12][10]*SPP[7] - (P[10][10]*q0)/2) + SPP[7]*(P[1][11] + P[0][11]*SF[6] + P[2][11]*SF[5] + P[3][11]*SF[9] + P[11][11]*SPP[6] - P[12][11]*SPP[7] - (P[10][11]*q0)/2) + SPP[6]*(P[1][12] + P[0][12]*SF[6] + P[2][12]*SF[5] + P[3][12]*SF[9] + P[11][12]*SPP[6] - P[12][12]*SPP[7] - (P[10][12]*q0)/2); nextP[1][1] = P[1][1] + P[0][1]*SF[6] + P[2][1]*SF[5] + P[3][1]*SF[9] + P[11][1]*SPP[6] - P[12][1]*SPP[7] + daxCov*SQ[9] - (P[10][1]*q0)/2 + SF[6]*(P[1][0] + P[0][0]*SF[6] + P[2][0]*SF[5] + P[3][0]*SF[9] + P[11][0]*SPP[6] - P[12][0]*SPP[7] - (P[10][0]*q0)/2) + SF[5]*(P[1][2] + P[0][2]*SF[6] + P[2][2]*SF[5] + P[3][2]*SF[9] + P[11][2]*SPP[6] - P[12][2]*SPP[7] - (P[10][2]*q0)/2) + SF[9]*(P[1][3] + P[0][3]*SF[6] + P[2][3]*SF[5] + P[3][3]*SF[9] + P[11][3]*SPP[6] - P[12][3]*SPP[7] - (P[10][3]*q0)/2) + SPP[6]*(P[1][11] + P[0][11]*SF[6] + P[2][11]*SF[5] + P[3][11]*SF[9] + P[11][11]*SPP[6] - P[12][11]*SPP[7] - (P[10][11]*q0)/2) - SPP[7]*(P[1][12] + P[0][12]*SF[6] + P[2][12]*SF[5] + P[3][12]*SF[9] + P[11][12]*SPP[6] - P[12][12]*SPP[7] - (P[10][12]*q0)/2) + (dayCov*sq(q3))/4 + (dazCov*sq(q2))/4 - (q0*(P[1][10] + P[0][10]*SF[6] + P[2][10]*SF[5] + P[3][10]*SF[9] + P[11][10]*SPP[6] - P[12][10]*SPP[7] - (P[10][10]*q0)/2))/2; nextP[1][2] = P[1][2] + SQ[5] + P[0][2]*SF[6] + P[2][2]*SF[5] + P[3][2]*SF[9] + P[11][2]*SPP[6] - P[12][2]*SPP[7] - (P[10][2]*q0)/2 + SF[4]*(P[1][0] + P[0][0]*SF[6] + P[2][0]*SF[5] + P[3][0]*SF[9] + P[11][0]*SPP[6] - P[12][0]*SPP[7] - (P[10][0]*q0)/2) + SF[8]*(P[1][1] + P[0][1]*SF[6] + P[2][1]*SF[5] + P[3][1]*SF[9] + P[11][1]*SPP[6] - P[12][1]*SPP[7] - (P[10][1]*q0)/2) + SF[6]*(P[1][3] + P[0][3]*SF[6] + P[2][3]*SF[5] + P[3][3]*SF[9] + P[11][3]*SPP[6] - P[12][3]*SPP[7] - (P[10][3]*q0)/2) + SF[11]*(P[1][12] + P[0][12]*SF[6] + P[2][12]*SF[5] + P[3][12]*SF[9] + P[11][12]*SPP[6] - P[12][12]*SPP[7] - (P[10][12]*q0)/2) - SPP[6]*(P[1][10] + P[0][10]*SF[6] + P[2][10]*SF[5] + P[3][10]*SF[9] + P[11][10]*SPP[6] - P[12][10]*SPP[7] - (P[10][10]*q0)/2) - (q0*(P[1][11] + P[0][11]*SF[6] + P[2][11]*SF[5] + P[3][11]*SF[9] + P[11][11]*SPP[6] - P[12][11]*SPP[7] - (P[10][11]*q0)/2))/2; nextP[1][3] = P[1][3] + SQ[4] + P[0][3]*SF[6] + P[2][3]*SF[5] + P[3][3]*SF[9] + P[11][3]*SPP[6] - P[12][3]*SPP[7] - (P[10][3]*q0)/2 + SF[5]*(P[1][0] + P[0][0]*SF[6] + P[2][0]*SF[5] + P[3][0]*SF[9] + P[11][0]*SPP[6] - P[12][0]*SPP[7] - (P[10][0]*q0)/2) + SF[4]*(P[1][1] + P[0][1]*SF[6] + P[2][1]*SF[5] + P[3][1]*SF[9] + P[11][1]*SPP[6] - P[12][1]*SPP[7] - (P[10][1]*q0)/2) + SF[7]*(P[1][2] + P[0][2]*SF[6] + P[2][2]*SF[5] + P[3][2]*SF[9] + P[11][2]*SPP[6] - P[12][2]*SPP[7] - (P[10][2]*q0)/2) - SF[11]*(P[1][11] + P[0][11]*SF[6] + P[2][11]*SF[5] + P[3][11]*SF[9] + P[11][11]*SPP[6] - P[12][11]*SPP[7] - (P[10][11]*q0)/2) + SPP[7]*(P[1][10] + P[0][10]*SF[6] + P[2][10]*SF[5] + P[3][10]*SF[9] + P[11][10]*SPP[6] - P[12][10]*SPP[7] - (P[10][10]*q0)/2) - (q0*(P[1][12] + P[0][12]*SF[6] + P[2][12]*SF[5] + P[3][12]*SF[9] + P[11][12]*SPP[6] - P[12][12]*SPP[7] - (P[10][12]*q0)/2))/2; nextP[1][4] = P[1][4] + P[0][4]*SF[6] + P[2][4]*SF[5] + P[3][4]*SF[9] + P[11][4]*SPP[6] - P[12][4]*SPP[7] - (P[10][4]*q0)/2 + SF[3]*(P[1][0] + P[0][0]*SF[6] + P[2][0]*SF[5] + P[3][0]*SF[9] + P[11][0]*SPP[6] - P[12][0]*SPP[7] - (P[10][0]*q0)/2) + SF[1]*(P[1][1] + P[0][1]*SF[6] + P[2][1]*SF[5] + P[3][1]*SF[9] + P[11][1]*SPP[6] - P[12][1]*SPP[7] - (P[10][1]*q0)/2) + SPP[0]*(P[1][2] + P[0][2]*SF[6] + P[2][2]*SF[5] + P[3][2]*SF[9] + P[11][2]*SPP[6] - P[12][2]*SPP[7] - (P[10][2]*q0)/2) - SPP[2]*(P[1][3] + P[0][3]*SF[6] + P[2][3]*SF[5] + P[3][3]*SF[9] + P[11][3]*SPP[6] - P[12][3]*SPP[7] - (P[10][3]*q0)/2) - SPP[4]*(P[1][13] + P[0][13]*SF[6] + P[2][13]*SF[5] + P[3][13]*SF[9] + P[11][13]*SPP[6] - P[12][13]*SPP[7] - (P[10][13]*q0)/2); nextP[1][5] = P[1][5] + P[0][5]*SF[6] + P[2][5]*SF[5] + P[3][5]*SF[9] + P[11][5]*SPP[6] - P[12][5]*SPP[7] - (P[10][5]*q0)/2 + SF[2]*(P[1][0] + P[0][0]*SF[6] + P[2][0]*SF[5] + P[3][0]*SF[9] + P[11][0]*SPP[6] - P[12][0]*SPP[7] - (P[10][0]*q0)/2) + SF[1]*(P[1][2] + P[0][2]*SF[6] + P[2][2]*SF[5] + P[3][2]*SF[9] + P[11][2]*SPP[6] - P[12][2]*SPP[7] - (P[10][2]*q0)/2) + SF[3]*(P[1][3] + P[0][3]*SF[6] + P[2][3]*SF[5] + P[3][3]*SF[9] + P[11][3]*SPP[6] - P[12][3]*SPP[7] - (P[10][3]*q0)/2) - SPP[0]*(P[1][1] + P[0][1]*SF[6] + P[2][1]*SF[5] + P[3][1]*SF[9] + P[11][1]*SPP[6] - P[12][1]*SPP[7] - (P[10][1]*q0)/2) + SPP[3]*(P[1][13] + P[0][13]*SF[6] + P[2][13]*SF[5] + P[3][13]*SF[9] + P[11][13]*SPP[6] - P[12][13]*SPP[7] - (P[10][13]*q0)/2); nextP[1][6] = P[1][6] + P[0][6]*SF[6] + P[2][6]*SF[5] + P[3][6]*SF[9] + P[11][6]*SPP[6] - P[12][6]*SPP[7] - (P[10][6]*q0)/2 + SF[2]*(P[1][1] + P[0][1]*SF[6] + P[2][1]*SF[5] + P[3][1]*SF[9] + P[11][1]*SPP[6] - P[12][1]*SPP[7] - (P[10][1]*q0)/2) + SF[1]*(P[1][3] + P[0][3]*SF[6] + P[2][3]*SF[5] + P[3][3]*SF[9] + P[11][3]*SPP[6] - P[12][3]*SPP[7] - (P[10][3]*q0)/2) + SPP[0]*(P[1][0] + P[0][0]*SF[6] + P[2][0]*SF[5] + P[3][0]*SF[9] + P[11][0]*SPP[6] - P[12][0]*SPP[7] - (P[10][0]*q0)/2) - SPP[1]*(P[1][2] + P[0][2]*SF[6] + P[2][2]*SF[5] + P[3][2]*SF[9] + P[11][2]*SPP[6] - P[12][2]*SPP[7] - (P[10][2]*q0)/2) - (sq(q0) - sq(q1) - sq(q2) + sq(q3))*(P[1][13] + P[0][13]*SF[6] + P[2][13]*SF[5] + P[3][13]*SF[9] + P[11][13]*SPP[6] - P[12][13]*SPP[7] - (P[10][13]*q0)/2); nextP[1][7] = P[1][7] + P[0][7]*SF[6] + P[2][7]*SF[5] + P[3][7]*SF[9] + P[11][7]*SPP[6] - P[12][7]*SPP[7] - (P[10][7]*q0)/2 + dt*(P[1][4] + P[0][4]*SF[6] + P[2][4]*SF[5] + P[3][4]*SF[9] + P[11][4]*SPP[6] - P[12][4]*SPP[7] - (P[10][4]*q0)/2); nextP[1][8] = P[1][8] + P[0][8]*SF[6] + P[2][8]*SF[5] + P[3][8]*SF[9] + P[11][8]*SPP[6] - P[12][8]*SPP[7] - (P[10][8]*q0)/2 + dt*(P[1][5] + P[0][5]*SF[6] + P[2][5]*SF[5] + P[3][5]*SF[9] + P[11][5]*SPP[6] - P[12][5]*SPP[7] - (P[10][5]*q0)/2); nextP[1][9] = P[1][9] + P[0][9]*SF[6] + P[2][9]*SF[5] + P[3][9]*SF[9] + P[11][9]*SPP[6] - P[12][9]*SPP[7] - (P[10][9]*q0)/2 + dt*(P[1][6] + P[0][6]*SF[6] + P[2][6]*SF[5] + P[3][6]*SF[9] + P[11][6]*SPP[6] - P[12][6]*SPP[7] - (P[10][6]*q0)/2); nextP[1][10] = P[1][10] + P[0][10]*SF[6] + P[2][10]*SF[5] + P[3][10]*SF[9] + P[11][10]*SPP[6] - P[12][10]*SPP[7] - (P[10][10]*q0)/2; nextP[1][11] = P[1][11] + P[0][11]*SF[6] + P[2][11]*SF[5] + P[3][11]*SF[9] + P[11][11]*SPP[6] - P[12][11]*SPP[7] - (P[10][11]*q0)/2; nextP[1][12] = P[1][12] + P[0][12]*SF[6] + P[2][12]*SF[5] + P[3][12]*SF[9] + P[11][12]*SPP[6] - P[12][12]*SPP[7] - (P[10][12]*q0)/2; nextP[1][13] = P[1][13] + P[0][13]*SF[6] + P[2][13]*SF[5] + P[3][13]*SF[9] + P[11][13]*SPP[6] - P[12][13]*SPP[7] - (P[10][13]*q0)/2; nextP[1][14] = P[1][14] + P[0][14]*SF[6] + P[2][14]*SF[5] + P[3][14]*SF[9] + P[11][14]*SPP[6] - P[12][14]*SPP[7] - (P[10][14]*q0)/2; nextP[1][15] = P[1][15] + P[0][15]*SF[6] + P[2][15]*SF[5] + P[3][15]*SF[9] + P[11][15]*SPP[6] - P[12][15]*SPP[7] - (P[10][15]*q0)/2; nextP[1][16] = P[1][16] + P[0][16]*SF[6] + P[2][16]*SF[5] + P[3][16]*SF[9] + P[11][16]*SPP[6] - P[12][16]*SPP[7] - (P[10][16]*q0)/2; nextP[1][17] = P[1][17] + P[0][17]*SF[6] + P[2][17]*SF[5] + P[3][17]*SF[9] + P[11][17]*SPP[6] - P[12][17]*SPP[7] - (P[10][17]*q0)/2; nextP[1][18] = P[1][18] + P[0][18]*SF[6] + P[2][18]*SF[5] + P[3][18]*SF[9] + P[11][18]*SPP[6] - P[12][18]*SPP[7] - (P[10][18]*q0)/2; nextP[1][19] = P[1][19] + P[0][19]*SF[6] + P[2][19]*SF[5] + P[3][19]*SF[9] + P[11][19]*SPP[6] - P[12][19]*SPP[7] - (P[10][19]*q0)/2; nextP[1][20] = P[1][20] + P[0][20]*SF[6] + P[2][20]*SF[5] + P[3][20]*SF[9] + P[11][20]*SPP[6] - P[12][20]*SPP[7] - (P[10][20]*q0)/2; nextP[1][21] = P[1][21] + P[0][21]*SF[6] + P[2][21]*SF[5] + P[3][21]*SF[9] + P[11][21]*SPP[6] - P[12][21]*SPP[7] - (P[10][21]*q0)/2; nextP[2][0] = P[2][0] + SQ[7] + P[0][0]*SF[4] + P[1][0]*SF[8] + P[3][0]*SF[6] + P[12][0]*SF[11] - P[10][0]*SPP[6] - (P[11][0]*q0)/2 + SF[7]*(P[2][1] + P[0][1]*SF[4] + P[1][1]*SF[8] + P[3][1]*SF[6] + P[12][1]*SF[11] - P[10][1]*SPP[6] - (P[11][1]*q0)/2) + SF[9]*(P[2][2] + P[0][2]*SF[4] + P[1][2]*SF[8] + P[3][2]*SF[6] + P[12][2]*SF[11] - P[10][2]*SPP[6] - (P[11][2]*q0)/2) + SF[8]*(P[2][3] + P[0][3]*SF[4] + P[1][3]*SF[8] + P[3][3]*SF[6] + P[12][3]*SF[11] - P[10][3]*SPP[6] - (P[11][3]*q0)/2) + SF[11]*(P[2][10] + P[0][10]*SF[4] + P[1][10]*SF[8] + P[3][10]*SF[6] + P[12][10]*SF[11] - P[10][10]*SPP[6] - (P[11][10]*q0)/2) + SPP[7]*(P[2][11] + P[0][11]*SF[4] + P[1][11]*SF[8] + P[3][11]*SF[6] + P[12][11]*SF[11] - P[10][11]*SPP[6] - (P[11][11]*q0)/2) + SPP[6]*(P[2][12] + P[0][12]*SF[4] + P[1][12]*SF[8] + P[3][12]*SF[6] + P[12][12]*SF[11] - P[10][12]*SPP[6] - (P[11][12]*q0)/2); nextP[2][1] = P[2][1] + SQ[5] + P[0][1]*SF[4] + P[1][1]*SF[8] + P[3][1]*SF[6] + P[12][1]*SF[11] - P[10][1]*SPP[6] - (P[11][1]*q0)/2 + SF[6]*(P[2][0] + P[0][0]*SF[4] + P[1][0]*SF[8] + P[3][0]*SF[6] + P[12][0]*SF[11] - P[10][0]*SPP[6] - (P[11][0]*q0)/2) + SF[5]*(P[2][2] + P[0][2]*SF[4] + P[1][2]*SF[8] + P[3][2]*SF[6] + P[12][2]*SF[11] - P[10][2]*SPP[6] - (P[11][2]*q0)/2) + SF[9]*(P[2][3] + P[0][3]*SF[4] + P[1][3]*SF[8] + P[3][3]*SF[6] + P[12][3]*SF[11] - P[10][3]*SPP[6] - (P[11][3]*q0)/2) + SPP[6]*(P[2][11] + P[0][11]*SF[4] + P[1][11]*SF[8] + P[3][11]*SF[6] + P[12][11]*SF[11] - P[10][11]*SPP[6] - (P[11][11]*q0)/2) - SPP[7]*(P[2][12] + P[0][12]*SF[4] + P[1][12]*SF[8] + P[3][12]*SF[6] + P[12][12]*SF[11] - P[10][12]*SPP[6] - (P[11][12]*q0)/2) - (q0*(P[2][10] + P[0][10]*SF[4] + P[1][10]*SF[8] + P[3][10]*SF[6] + P[12][10]*SF[11] - P[10][10]*SPP[6] - (P[11][10]*q0)/2))/2; nextP[2][2] = P[2][2] + P[0][2]*SF[4] + P[1][2]*SF[8] + P[3][2]*SF[6] + P[12][2]*SF[11] - P[10][2]*SPP[6] + dayCov*SQ[9] + (dazCov*SQ[10])/4 - (P[11][2]*q0)/2 + SF[4]*(P[2][0] + P[0][0]*SF[4] + P[1][0]*SF[8] + P[3][0]*SF[6] + P[12][0]*SF[11] - P[10][0]*SPP[6] - (P[11][0]*q0)/2) + SF[8]*(P[2][1] + P[0][1]*SF[4] + P[1][1]*SF[8] + P[3][1]*SF[6] + P[12][1]*SF[11] - P[10][1]*SPP[6] - (P[11][1]*q0)/2) + SF[6]*(P[2][3] + P[0][3]*SF[4] + P[1][3]*SF[8] + P[3][3]*SF[6] + P[12][3]*SF[11] - P[10][3]*SPP[6] - (P[11][3]*q0)/2) + SF[11]*(P[2][12] + P[0][12]*SF[4] + P[1][12]*SF[8] + P[3][12]*SF[6] + P[12][12]*SF[11] - P[10][12]*SPP[6] - (P[11][12]*q0)/2) - SPP[6]*(P[2][10] + P[0][10]*SF[4] + P[1][10]*SF[8] + P[3][10]*SF[6] + P[12][10]*SF[11] - P[10][10]*SPP[6] - (P[11][10]*q0)/2) + (daxCov*sq(q3))/4 - (q0*(P[2][11] + P[0][11]*SF[4] + P[1][11]*SF[8] + P[3][11]*SF[6] + P[12][11]*SF[11] - P[10][11]*SPP[6] - (P[11][11]*q0)/2))/2; nextP[2][3] = P[2][3] + SQ[3] + P[0][3]*SF[4] + P[1][3]*SF[8] + P[3][3]*SF[6] + P[12][3]*SF[11] - P[10][3]*SPP[6] - (P[11][3]*q0)/2 + SF[5]*(P[2][0] + P[0][0]*SF[4] + P[1][0]*SF[8] + P[3][0]*SF[6] + P[12][0]*SF[11] - P[10][0]*SPP[6] - (P[11][0]*q0)/2) + SF[4]*(P[2][1] + P[0][1]*SF[4] + P[1][1]*SF[8] + P[3][1]*SF[6] + P[12][1]*SF[11] - P[10][1]*SPP[6] - (P[11][1]*q0)/2) + SF[7]*(P[2][2] + P[0][2]*SF[4] + P[1][2]*SF[8] + P[3][2]*SF[6] + P[12][2]*SF[11] - P[10][2]*SPP[6] - (P[11][2]*q0)/2) - SF[11]*(P[2][11] + P[0][11]*SF[4] + P[1][11]*SF[8] + P[3][11]*SF[6] + P[12][11]*SF[11] - P[10][11]*SPP[6] - (P[11][11]*q0)/2) + SPP[7]*(P[2][10] + P[0][10]*SF[4] + P[1][10]*SF[8] + P[3][10]*SF[6] + P[12][10]*SF[11] - P[10][10]*SPP[6] - (P[11][10]*q0)/2) - (q0*(P[2][12] + P[0][12]*SF[4] + P[1][12]*SF[8] + P[3][12]*SF[6] + P[12][12]*SF[11] - P[10][12]*SPP[6] - (P[11][12]*q0)/2))/2; nextP[2][4] = P[2][4] + P[0][4]*SF[4] + P[1][4]*SF[8] + P[3][4]*SF[6] + P[12][4]*SF[11] - P[10][4]*SPP[6] - (P[11][4]*q0)/2 + SF[3]*(P[2][0] + P[0][0]*SF[4] + P[1][0]*SF[8] + P[3][0]*SF[6] + P[12][0]*SF[11] - P[10][0]*SPP[6] - (P[11][0]*q0)/2) + SF[1]*(P[2][1] + P[0][1]*SF[4] + P[1][1]*SF[8] + P[3][1]*SF[6] + P[12][1]*SF[11] - P[10][1]*SPP[6] - (P[11][1]*q0)/2) + SPP[0]*(P[2][2] + P[0][2]*SF[4] + P[1][2]*SF[8] + P[3][2]*SF[6] + P[12][2]*SF[11] - P[10][2]*SPP[6] - (P[11][2]*q0)/2) - SPP[2]*(P[2][3] + P[0][3]*SF[4] + P[1][3]*SF[8] + P[3][3]*SF[6] + P[12][3]*SF[11] - P[10][3]*SPP[6] - (P[11][3]*q0)/2) - SPP[4]*(P[2][13] + P[0][13]*SF[4] + P[1][13]*SF[8] + P[3][13]*SF[6] + P[12][13]*SF[11] - P[10][13]*SPP[6] - (P[11][13]*q0)/2); nextP[2][5] = P[2][5] + P[0][5]*SF[4] + P[1][5]*SF[8] + P[3][5]*SF[6] + P[12][5]*SF[11] - P[10][5]*SPP[6] - (P[11][5]*q0)/2 + SF[2]*(P[2][0] + P[0][0]*SF[4] + P[1][0]*SF[8] + P[3][0]*SF[6] + P[12][0]*SF[11] - P[10][0]*SPP[6] - (P[11][0]*q0)/2) + SF[1]*(P[2][2] + P[0][2]*SF[4] + P[1][2]*SF[8] + P[3][2]*SF[6] + P[12][2]*SF[11] - P[10][2]*SPP[6] - (P[11][2]*q0)/2) + SF[3]*(P[2][3] + P[0][3]*SF[4] + P[1][3]*SF[8] + P[3][3]*SF[6] + P[12][3]*SF[11] - P[10][3]*SPP[6] - (P[11][3]*q0)/2) - SPP[0]*(P[2][1] + P[0][1]*SF[4] + P[1][1]*SF[8] + P[3][1]*SF[6] + P[12][1]*SF[11] - P[10][1]*SPP[6] - (P[11][1]*q0)/2) + SPP[3]*(P[2][13] + P[0][13]*SF[4] + P[1][13]*SF[8] + P[3][13]*SF[6] + P[12][13]*SF[11] - P[10][13]*SPP[6] - (P[11][13]*q0)/2); nextP[2][6] = P[2][6] + P[0][6]*SF[4] + P[1][6]*SF[8] + P[3][6]*SF[6] + P[12][6]*SF[11] - P[10][6]*SPP[6] - (P[11][6]*q0)/2 + SF[2]*(P[2][1] + P[0][1]*SF[4] + P[1][1]*SF[8] + P[3][1]*SF[6] + P[12][1]*SF[11] - P[10][1]*SPP[6] - (P[11][1]*q0)/2) + SF[1]*(P[2][3] + P[0][3]*SF[4] + P[1][3]*SF[8] + P[3][3]*SF[6] + P[12][3]*SF[11] - P[10][3]*SPP[6] - (P[11][3]*q0)/2) + SPP[0]*(P[2][0] + P[0][0]*SF[4] + P[1][0]*SF[8] + P[3][0]*SF[6] + P[12][0]*SF[11] - P[10][0]*SPP[6] - (P[11][0]*q0)/2) - SPP[1]*(P[2][2] + P[0][2]*SF[4] + P[1][2]*SF[8] + P[3][2]*SF[6] + P[12][2]*SF[11] - P[10][2]*SPP[6] - (P[11][2]*q0)/2) - (sq(q0) - sq(q1) - sq(q2) + sq(q3))*(P[2][13] + P[0][13]*SF[4] + P[1][13]*SF[8] + P[3][13]*SF[6] + P[12][13]*SF[11] - P[10][13]*SPP[6] - (P[11][13]*q0)/2); nextP[2][7] = P[2][7] + P[0][7]*SF[4] + P[1][7]*SF[8] + P[3][7]*SF[6] + P[12][7]*SF[11] - P[10][7]*SPP[6] - (P[11][7]*q0)/2 + dt*(P[2][4] + P[0][4]*SF[4] + P[1][4]*SF[8] + P[3][4]*SF[6] + P[12][4]*SF[11] - P[10][4]*SPP[6] - (P[11][4]*q0)/2); nextP[2][8] = P[2][8] + P[0][8]*SF[4] + P[1][8]*SF[8] + P[3][8]*SF[6] + P[12][8]*SF[11] - P[10][8]*SPP[6] - (P[11][8]*q0)/2 + dt*(P[2][5] + P[0][5]*SF[4] + P[1][5]*SF[8] + P[3][5]*SF[6] + P[12][5]*SF[11] - P[10][5]*SPP[6] - (P[11][5]*q0)/2); nextP[2][9] = P[2][9] + P[0][9]*SF[4] + P[1][9]*SF[8] + P[3][9]*SF[6] + P[12][9]*SF[11] - P[10][9]*SPP[6] - (P[11][9]*q0)/2 + dt*(P[2][6] + P[0][6]*SF[4] + P[1][6]*SF[8] + P[3][6]*SF[6] + P[12][6]*SF[11] - P[10][6]*SPP[6] - (P[11][6]*q0)/2); nextP[2][10] = P[2][10] + P[0][10]*SF[4] + P[1][10]*SF[8] + P[3][10]*SF[6] + P[12][10]*SF[11] - P[10][10]*SPP[6] - (P[11][10]*q0)/2; nextP[2][11] = P[2][11] + P[0][11]*SF[4] + P[1][11]*SF[8] + P[3][11]*SF[6] + P[12][11]*SF[11] - P[10][11]*SPP[6] - (P[11][11]*q0)/2; nextP[2][12] = P[2][12] + P[0][12]*SF[4] + P[1][12]*SF[8] + P[3][12]*SF[6] + P[12][12]*SF[11] - P[10][12]*SPP[6] - (P[11][12]*q0)/2; nextP[2][13] = P[2][13] + P[0][13]*SF[4] + P[1][13]*SF[8] + P[3][13]*SF[6] + P[12][13]*SF[11] - P[10][13]*SPP[6] - (P[11][13]*q0)/2; nextP[2][14] = P[2][14] + P[0][14]*SF[4] + P[1][14]*SF[8] + P[3][14]*SF[6] + P[12][14]*SF[11] - P[10][14]*SPP[6] - (P[11][14]*q0)/2; nextP[2][15] = P[2][15] + P[0][15]*SF[4] + P[1][15]*SF[8] + P[3][15]*SF[6] + P[12][15]*SF[11] - P[10][15]*SPP[6] - (P[11][15]*q0)/2; nextP[2][16] = P[2][16] + P[0][16]*SF[4] + P[1][16]*SF[8] + P[3][16]*SF[6] + P[12][16]*SF[11] - P[10][16]*SPP[6] - (P[11][16]*q0)/2; nextP[2][17] = P[2][17] + P[0][17]*SF[4] + P[1][17]*SF[8] + P[3][17]*SF[6] + P[12][17]*SF[11] - P[10][17]*SPP[6] - (P[11][17]*q0)/2; nextP[2][18] = P[2][18] + P[0][18]*SF[4] + P[1][18]*SF[8] + P[3][18]*SF[6] + P[12][18]*SF[11] - P[10][18]*SPP[6] - (P[11][18]*q0)/2; nextP[2][19] = P[2][19] + P[0][19]*SF[4] + P[1][19]*SF[8] + P[3][19]*SF[6] + P[12][19]*SF[11] - P[10][19]*SPP[6] - (P[11][19]*q0)/2; nextP[2][20] = P[2][20] + P[0][20]*SF[4] + P[1][20]*SF[8] + P[3][20]*SF[6] + P[12][20]*SF[11] - P[10][20]*SPP[6] - (P[11][20]*q0)/2; nextP[2][21] = P[2][21] + P[0][21]*SF[4] + P[1][21]*SF[8] + P[3][21]*SF[6] + P[12][21]*SF[11] - P[10][21]*SPP[6] - (P[11][21]*q0)/2; nextP[3][0] = P[3][0] + SQ[6] + P[0][0]*SF[5] + P[1][0]*SF[4] + P[2][0]*SF[7] - P[11][0]*SF[11] + P[10][0]*SPP[7] - (P[12][0]*q0)/2 + SF[7]*(P[3][1] + P[0][1]*SF[5] + P[1][1]*SF[4] + P[2][1]*SF[7] - P[11][1]*SF[11] + P[10][1]*SPP[7] - (P[12][1]*q0)/2) + SF[9]*(P[3][2] + P[0][2]*SF[5] + P[1][2]*SF[4] + P[2][2]*SF[7] - P[11][2]*SF[11] + P[10][2]*SPP[7] - (P[12][2]*q0)/2) + SF[8]*(P[3][3] + P[0][3]*SF[5] + P[1][3]*SF[4] + P[2][3]*SF[7] - P[11][3]*SF[11] + P[10][3]*SPP[7] - (P[12][3]*q0)/2) + SF[11]*(P[3][10] + P[0][10]*SF[5] + P[1][10]*SF[4] + P[2][10]*SF[7] - P[11][10]*SF[11] + P[10][10]*SPP[7] - (P[12][10]*q0)/2) + SPP[7]*(P[3][11] + P[0][11]*SF[5] + P[1][11]*SF[4] + P[2][11]*SF[7] - P[11][11]*SF[11] + P[10][11]*SPP[7] - (P[12][11]*q0)/2) + SPP[6]*(P[3][12] + P[0][12]*SF[5] + P[1][12]*SF[4] + P[2][12]*SF[7] - P[11][12]*SF[11] + P[10][12]*SPP[7] - (P[12][12]*q0)/2); nextP[3][1] = P[3][1] + SQ[4] + P[0][1]*SF[5] + P[1][1]*SF[4] + P[2][1]*SF[7] - P[11][1]*SF[11] + P[10][1]*SPP[7] - (P[12][1]*q0)/2 + SF[6]*(P[3][0] + P[0][0]*SF[5] + P[1][0]*SF[4] + P[2][0]*SF[7] - P[11][0]*SF[11] + P[10][0]*SPP[7] - (P[12][0]*q0)/2) + SF[5]*(P[3][2] + P[0][2]*SF[5] + P[1][2]*SF[4] + P[2][2]*SF[7] - P[11][2]*SF[11] + P[10][2]*SPP[7] - (P[12][2]*q0)/2) + SF[9]*(P[3][3] + P[0][3]*SF[5] + P[1][3]*SF[4] + P[2][3]*SF[7] - P[11][3]*SF[11] + P[10][3]*SPP[7] - (P[12][3]*q0)/2) + SPP[6]*(P[3][11] + P[0][11]*SF[5] + P[1][11]*SF[4] + P[2][11]*SF[7] - P[11][11]*SF[11] + P[10][11]*SPP[7] - (P[12][11]*q0)/2) - SPP[7]*(P[3][12] + P[0][12]*SF[5] + P[1][12]*SF[4] + P[2][12]*SF[7] - P[11][12]*SF[11] + P[10][12]*SPP[7] - (P[12][12]*q0)/2) - (q0*(P[3][10] + P[0][10]*SF[5] + P[1][10]*SF[4] + P[2][10]*SF[7] - P[11][10]*SF[11] + P[10][10]*SPP[7] - (P[12][10]*q0)/2))/2; nextP[3][2] = P[3][2] + SQ[3] + P[0][2]*SF[5] + P[1][2]*SF[4] + P[2][2]*SF[7] - P[11][2]*SF[11] + P[10][2]*SPP[7] - (P[12][2]*q0)/2 + SF[4]*(P[3][0] + P[0][0]*SF[5] + P[1][0]*SF[4] + P[2][0]*SF[7] - P[11][0]*SF[11] + P[10][0]*SPP[7] - (P[12][0]*q0)/2) + SF[8]*(P[3][1] + P[0][1]*SF[5] + P[1][1]*SF[4] + P[2][1]*SF[7] - P[11][1]*SF[11] + P[10][1]*SPP[7] - (P[12][1]*q0)/2) + SF[6]*(P[3][3] + P[0][3]*SF[5] + P[1][3]*SF[4] + P[2][3]*SF[7] - P[11][3]*SF[11] + P[10][3]*SPP[7] - (P[12][3]*q0)/2) + SF[11]*(P[3][12] + P[0][12]*SF[5] + P[1][12]*SF[4] + P[2][12]*SF[7] - P[11][12]*SF[11] + P[10][12]*SPP[7] - (P[12][12]*q0)/2) - SPP[6]*(P[3][10] + P[0][10]*SF[5] + P[1][10]*SF[4] + P[2][10]*SF[7] - P[11][10]*SF[11] + P[10][10]*SPP[7] - (P[12][10]*q0)/2) - (q0*(P[3][11] + P[0][11]*SF[5] + P[1][11]*SF[4] + P[2][11]*SF[7] - P[11][11]*SF[11] + P[10][11]*SPP[7] - (P[12][11]*q0)/2))/2; nextP[3][3] = P[3][3] + P[0][3]*SF[5] + P[1][3]*SF[4] + P[2][3]*SF[7] - P[11][3]*SF[11] + P[10][3]*SPP[7] + (dayCov*SQ[10])/4 + dazCov*SQ[9] - (P[12][3]*q0)/2 + SF[5]*(P[3][0] + P[0][0]*SF[5] + P[1][0]*SF[4] + P[2][0]*SF[7] - P[11][0]*SF[11] + P[10][0]*SPP[7] - (P[12][0]*q0)/2) + SF[4]*(P[3][1] + P[0][1]*SF[5] + P[1][1]*SF[4] + P[2][1]*SF[7] - P[11][1]*SF[11] + P[10][1]*SPP[7] - (P[12][1]*q0)/2) + SF[7]*(P[3][2] + P[0][2]*SF[5] + P[1][2]*SF[4] + P[2][2]*SF[7] - P[11][2]*SF[11] + P[10][2]*SPP[7] - (P[12][2]*q0)/2) - SF[11]*(P[3][11] + P[0][11]*SF[5] + P[1][11]*SF[4] + P[2][11]*SF[7] - P[11][11]*SF[11] + P[10][11]*SPP[7] - (P[12][11]*q0)/2) + SPP[7]*(P[3][10] + P[0][10]*SF[5] + P[1][10]*SF[4] + P[2][10]*SF[7] - P[11][10]*SF[11] + P[10][10]*SPP[7] - (P[12][10]*q0)/2) + (daxCov*sq(q2))/4 - (q0*(P[3][12] + P[0][12]*SF[5] + P[1][12]*SF[4] + P[2][12]*SF[7] - P[11][12]*SF[11] + P[10][12]*SPP[7] - (P[12][12]*q0)/2))/2; nextP[3][4] = P[3][4] + P[0][4]*SF[5] + P[1][4]*SF[4] + P[2][4]*SF[7] - P[11][4]*SF[11] + P[10][4]*SPP[7] - (P[12][4]*q0)/2 + SF[3]*(P[3][0] + P[0][0]*SF[5] + P[1][0]*SF[4] + P[2][0]*SF[7] - P[11][0]*SF[11] + P[10][0]*SPP[7] - (P[12][0]*q0)/2) + SF[1]*(P[3][1] + P[0][1]*SF[5] + P[1][1]*SF[4] + P[2][1]*SF[7] - P[11][1]*SF[11] + P[10][1]*SPP[7] - (P[12][1]*q0)/2) + SPP[0]*(P[3][2] + P[0][2]*SF[5] + P[1][2]*SF[4] + P[2][2]*SF[7] - P[11][2]*SF[11] + P[10][2]*SPP[7] - (P[12][2]*q0)/2) - SPP[2]*(P[3][3] + P[0][3]*SF[5] + P[1][3]*SF[4] + P[2][3]*SF[7] - P[11][3]*SF[11] + P[10][3]*SPP[7] - (P[12][3]*q0)/2) - SPP[4]*(P[3][13] + P[0][13]*SF[5] + P[1][13]*SF[4] + P[2][13]*SF[7] - P[11][13]*SF[11] + P[10][13]*SPP[7] - (P[12][13]*q0)/2); nextP[3][5] = P[3][5] + P[0][5]*SF[5] + P[1][5]*SF[4] + P[2][5]*SF[7] - P[11][5]*SF[11] + P[10][5]*SPP[7] - (P[12][5]*q0)/2 + SF[2]*(P[3][0] + P[0][0]*SF[5] + P[1][0]*SF[4] + P[2][0]*SF[7] - P[11][0]*SF[11] + P[10][0]*SPP[7] - (P[12][0]*q0)/2) + SF[1]*(P[3][2] + P[0][2]*SF[5] + P[1][2]*SF[4] + P[2][2]*SF[7] - P[11][2]*SF[11] + P[10][2]*SPP[7] - (P[12][2]*q0)/2) + SF[3]*(P[3][3] + P[0][3]*SF[5] + P[1][3]*SF[4] + P[2][3]*SF[7] - P[11][3]*SF[11] + P[10][3]*SPP[7] - (P[12][3]*q0)/2) - SPP[0]*(P[3][1] + P[0][1]*SF[5] + P[1][1]*SF[4] + P[2][1]*SF[7] - P[11][1]*SF[11] + P[10][1]*SPP[7] - (P[12][1]*q0)/2) + SPP[3]*(P[3][13] + P[0][13]*SF[5] + P[1][13]*SF[4] + P[2][13]*SF[7] - P[11][13]*SF[11] + P[10][13]*SPP[7] - (P[12][13]*q0)/2); nextP[3][6] = P[3][6] + P[0][6]*SF[5] + P[1][6]*SF[4] + P[2][6]*SF[7] - P[11][6]*SF[11] + P[10][6]*SPP[7] - (P[12][6]*q0)/2 + SF[2]*(P[3][1] + P[0][1]*SF[5] + P[1][1]*SF[4] + P[2][1]*SF[7] - P[11][1]*SF[11] + P[10][1]*SPP[7] - (P[12][1]*q0)/2) + SF[1]*(P[3][3] + P[0][3]*SF[5] + P[1][3]*SF[4] + P[2][3]*SF[7] - P[11][3]*SF[11] + P[10][3]*SPP[7] - (P[12][3]*q0)/2) + SPP[0]*(P[3][0] + P[0][0]*SF[5] + P[1][0]*SF[4] + P[2][0]*SF[7] - P[11][0]*SF[11] + P[10][0]*SPP[7] - (P[12][0]*q0)/2) - SPP[1]*(P[3][2] + P[0][2]*SF[5] + P[1][2]*SF[4] + P[2][2]*SF[7] - P[11][2]*SF[11] + P[10][2]*SPP[7] - (P[12][2]*q0)/2) - (sq(q0) - sq(q1) - sq(q2) + sq(q3))*(P[3][13] + P[0][13]*SF[5] + P[1][13]*SF[4] + P[2][13]*SF[7] - P[11][13]*SF[11] + P[10][13]*SPP[7] - (P[12][13]*q0)/2); nextP[3][7] = P[3][7] + P[0][7]*SF[5] + P[1][7]*SF[4] + P[2][7]*SF[7] - P[11][7]*SF[11] + P[10][7]*SPP[7] - (P[12][7]*q0)/2 + dt*(P[3][4] + P[0][4]*SF[5] + P[1][4]*SF[4] + P[2][4]*SF[7] - P[11][4]*SF[11] + P[10][4]*SPP[7] - (P[12][4]*q0)/2); nextP[3][8] = P[3][8] + P[0][8]*SF[5] + P[1][8]*SF[4] + P[2][8]*SF[7] - P[11][8]*SF[11] + P[10][8]*SPP[7] - (P[12][8]*q0)/2 + dt*(P[3][5] + P[0][5]*SF[5] + P[1][5]*SF[4] + P[2][5]*SF[7] - P[11][5]*SF[11] + P[10][5]*SPP[7] - (P[12][5]*q0)/2); nextP[3][9] = P[3][9] + P[0][9]*SF[5] + P[1][9]*SF[4] + P[2][9]*SF[7] - P[11][9]*SF[11] + P[10][9]*SPP[7] - (P[12][9]*q0)/2 + dt*(P[3][6] + P[0][6]*SF[5] + P[1][6]*SF[4] + P[2][6]*SF[7] - P[11][6]*SF[11] + P[10][6]*SPP[7] - (P[12][6]*q0)/2); nextP[3][10] = P[3][10] + P[0][10]*SF[5] + P[1][10]*SF[4] + P[2][10]*SF[7] - P[11][10]*SF[11] + P[10][10]*SPP[7] - (P[12][10]*q0)/2; nextP[3][11] = P[3][11] + P[0][11]*SF[5] + P[1][11]*SF[4] + P[2][11]*SF[7] - P[11][11]*SF[11] + P[10][11]*SPP[7] - (P[12][11]*q0)/2; nextP[3][12] = P[3][12] + P[0][12]*SF[5] + P[1][12]*SF[4] + P[2][12]*SF[7] - P[11][12]*SF[11] + P[10][12]*SPP[7] - (P[12][12]*q0)/2; nextP[3][13] = P[3][13] + P[0][13]*SF[5] + P[1][13]*SF[4] + P[2][13]*SF[7] - P[11][13]*SF[11] + P[10][13]*SPP[7] - (P[12][13]*q0)/2; nextP[3][14] = P[3][14] + P[0][14]*SF[5] + P[1][14]*SF[4] + P[2][14]*SF[7] - P[11][14]*SF[11] + P[10][14]*SPP[7] - (P[12][14]*q0)/2; nextP[3][15] = P[3][15] + P[0][15]*SF[5] + P[1][15]*SF[4] + P[2][15]*SF[7] - P[11][15]*SF[11] + P[10][15]*SPP[7] - (P[12][15]*q0)/2; nextP[3][16] = P[3][16] + P[0][16]*SF[5] + P[1][16]*SF[4] + P[2][16]*SF[7] - P[11][16]*SF[11] + P[10][16]*SPP[7] - (P[12][16]*q0)/2; nextP[3][17] = P[3][17] + P[0][17]*SF[5] + P[1][17]*SF[4] + P[2][17]*SF[7] - P[11][17]*SF[11] + P[10][17]*SPP[7] - (P[12][17]*q0)/2; nextP[3][18] = P[3][18] + P[0][18]*SF[5] + P[1][18]*SF[4] + P[2][18]*SF[7] - P[11][18]*SF[11] + P[10][18]*SPP[7] - (P[12][18]*q0)/2; nextP[3][19] = P[3][19] + P[0][19]*SF[5] + P[1][19]*SF[4] + P[2][19]*SF[7] - P[11][19]*SF[11] + P[10][19]*SPP[7] - (P[12][19]*q0)/2; nextP[3][20] = P[3][20] + P[0][20]*SF[5] + P[1][20]*SF[4] + P[2][20]*SF[7] - P[11][20]*SF[11] + P[10][20]*SPP[7] - (P[12][20]*q0)/2; nextP[3][21] = P[3][21] + P[0][21]*SF[5] + P[1][21]*SF[4] + P[2][21]*SF[7] - P[11][21]*SF[11] + P[10][21]*SPP[7] - (P[12][21]*q0)/2; nextP[4][0] = P[4][0] + P[0][0]*SF[3] + P[1][0]*SF[1] + P[2][0]*SPP[0] - P[3][0]*SPP[2] - P[13][0]*SPP[4] + SF[7]*(P[4][1] + P[0][1]*SF[3] + P[1][1]*SF[1] + P[2][1]*SPP[0] - P[3][1]*SPP[2] - P[13][1]*SPP[4]) + SF[9]*(P[4][2] + P[0][2]*SF[3] + P[1][2]*SF[1] + P[2][2]*SPP[0] - P[3][2]*SPP[2] - P[13][2]*SPP[4]) + SF[8]*(P[4][3] + P[0][3]*SF[3] + P[1][3]*SF[1] + P[2][3]*SPP[0] - P[3][3]*SPP[2] - P[13][3]*SPP[4]) + SF[11]*(P[4][10] + P[0][10]*SF[3] + P[1][10]*SF[1] + P[2][10]*SPP[0] - P[3][10]*SPP[2] - P[13][10]*SPP[4]) + SPP[7]*(P[4][11] + P[0][11]*SF[3] + P[1][11]*SF[1] + P[2][11]*SPP[0] - P[3][11]*SPP[2] - P[13][11]*SPP[4]) + SPP[6]*(P[4][12] + P[0][12]*SF[3] + P[1][12]*SF[1] + P[2][12]*SPP[0] - P[3][12]*SPP[2] - P[13][12]*SPP[4]); nextP[4][1] = P[4][1] + P[0][1]*SF[3] + P[1][1]*SF[1] + P[2][1]*SPP[0] - P[3][1]*SPP[2] - P[13][1]*SPP[4] + SF[6]*(P[4][0] + P[0][0]*SF[3] + P[1][0]*SF[1] + P[2][0]*SPP[0] - P[3][0]*SPP[2] - P[13][0]*SPP[4]) + SF[5]*(P[4][2] + P[0][2]*SF[3] + P[1][2]*SF[1] + P[2][2]*SPP[0] - P[3][2]*SPP[2] - P[13][2]*SPP[4]) + SF[9]*(P[4][3] + P[0][3]*SF[3] + P[1][3]*SF[1] + P[2][3]*SPP[0] - P[3][3]*SPP[2] - P[13][3]*SPP[4]) + SPP[6]*(P[4][11] + P[0][11]*SF[3] + P[1][11]*SF[1] + P[2][11]*SPP[0] - P[3][11]*SPP[2] - P[13][11]*SPP[4]) - SPP[7]*(P[4][12] + P[0][12]*SF[3] + P[1][12]*SF[1] + P[2][12]*SPP[0] - P[3][12]*SPP[2] - P[13][12]*SPP[4]) - (q0*(P[4][10] + P[0][10]*SF[3] + P[1][10]*SF[1] + P[2][10]*SPP[0] - P[3][10]*SPP[2] - P[13][10]*SPP[4]))/2; nextP[4][2] = P[4][2] + P[0][2]*SF[3] + P[1][2]*SF[1] + P[2][2]*SPP[0] - P[3][2]*SPP[2] - P[13][2]*SPP[4] + SF[4]*(P[4][0] + P[0][0]*SF[3] + P[1][0]*SF[1] + P[2][0]*SPP[0] - P[3][0]*SPP[2] - P[13][0]*SPP[4]) + SF[8]*(P[4][1] + P[0][1]*SF[3] + P[1][1]*SF[1] + P[2][1]*SPP[0] - P[3][1]*SPP[2] - P[13][1]*SPP[4]) + SF[6]*(P[4][3] + P[0][3]*SF[3] + P[1][3]*SF[1] + P[2][3]*SPP[0] - P[3][3]*SPP[2] - P[13][3]*SPP[4]) + SF[11]*(P[4][12] + P[0][12]*SF[3] + P[1][12]*SF[1] + P[2][12]*SPP[0] - P[3][12]*SPP[2] - P[13][12]*SPP[4]) - SPP[6]*(P[4][10] + P[0][10]*SF[3] + P[1][10]*SF[1] + P[2][10]*SPP[0] - P[3][10]*SPP[2] - P[13][10]*SPP[4]) - (q0*(P[4][11] + P[0][11]*SF[3] + P[1][11]*SF[1] + P[2][11]*SPP[0] - P[3][11]*SPP[2] - P[13][11]*SPP[4]))/2; nextP[4][3] = P[4][3] + P[0][3]*SF[3] + P[1][3]*SF[1] + P[2][3]*SPP[0] - P[3][3]*SPP[2] - P[13][3]*SPP[4] + SF[5]*(P[4][0] + P[0][0]*SF[3] + P[1][0]*SF[1] + P[2][0]*SPP[0] - P[3][0]*SPP[2] - P[13][0]*SPP[4]) + SF[4]*(P[4][1] + P[0][1]*SF[3] + P[1][1]*SF[1] + P[2][1]*SPP[0] - P[3][1]*SPP[2] - P[13][1]*SPP[4]) + SF[7]*(P[4][2] + P[0][2]*SF[3] + P[1][2]*SF[1] + P[2][2]*SPP[0] - P[3][2]*SPP[2] - P[13][2]*SPP[4]) - SF[11]*(P[4][11] + P[0][11]*SF[3] + P[1][11]*SF[1] + P[2][11]*SPP[0] - P[3][11]*SPP[2] - P[13][11]*SPP[4]) + SPP[7]*(P[4][10] + P[0][10]*SF[3] + P[1][10]*SF[1] + P[2][10]*SPP[0] - P[3][10]*SPP[2] - P[13][10]*SPP[4]) - (q0*(P[4][12] + P[0][12]*SF[3] + P[1][12]*SF[1] + P[2][12]*SPP[0] - P[3][12]*SPP[2] - P[13][12]*SPP[4]))/2; nextP[4][4] = P[4][4] + P[0][4]*SF[3] + P[1][4]*SF[1] + P[2][4]*SPP[0] - P[3][4]*SPP[2] - P[13][4]*SPP[4] + dvyCov*sq(SG[7] - 2*q0*q3) + dvzCov*sq(SG[6] + 2*q0*q2) + SF[3]*(P[4][0] + P[0][0]*SF[3] + P[1][0]*SF[1] + P[2][0]*SPP[0] - P[3][0]*SPP[2] - P[13][0]*SPP[4]) + SF[1]*(P[4][1] + P[0][1]*SF[3] + P[1][1]*SF[1] + P[2][1]*SPP[0] - P[3][1]*SPP[2] - P[13][1]*SPP[4]) + SPP[0]*(P[4][2] + P[0][2]*SF[3] + P[1][2]*SF[1] + P[2][2]*SPP[0] - P[3][2]*SPP[2] - P[13][2]*SPP[4]) - SPP[2]*(P[4][3] + P[0][3]*SF[3] + P[1][3]*SF[1] + P[2][3]*SPP[0] - P[3][3]*SPP[2] - P[13][3]*SPP[4]) - SPP[4]*(P[4][13] + P[0][13]*SF[3] + P[1][13]*SF[1] + P[2][13]*SPP[0] - P[3][13]*SPP[2] - P[13][13]*SPP[4]) + dvxCov*sq(SG[1] + SG[2] - SG[3] - SG[4]); nextP[4][5] = P[4][5] + SQ[2] + P[0][5]*SF[3] + P[1][5]*SF[1] + P[2][5]*SPP[0] - P[3][5]*SPP[2] - P[13][5]*SPP[4] + SF[2]*(P[4][0] + P[0][0]*SF[3] + P[1][0]*SF[1] + P[2][0]*SPP[0] - P[3][0]*SPP[2] - P[13][0]*SPP[4]) + SF[1]*(P[4][2] + P[0][2]*SF[3] + P[1][2]*SF[1] + P[2][2]*SPP[0] - P[3][2]*SPP[2] - P[13][2]*SPP[4]) + SF[3]*(P[4][3] + P[0][3]*SF[3] + P[1][3]*SF[1] + P[2][3]*SPP[0] - P[3][3]*SPP[2] - P[13][3]*SPP[4]) - SPP[0]*(P[4][1] + P[0][1]*SF[3] + P[1][1]*SF[1] + P[2][1]*SPP[0] - P[3][1]*SPP[2] - P[13][1]*SPP[4]) + SPP[3]*(P[4][13] + P[0][13]*SF[3] + P[1][13]*SF[1] + P[2][13]*SPP[0] - P[3][13]*SPP[2] - P[13][13]*SPP[4]); nextP[4][6] = P[4][6] + SQ[1] + P[0][6]*SF[3] + P[1][6]*SF[1] + P[2][6]*SPP[0] - P[3][6]*SPP[2] - P[13][6]*SPP[4] + SF[2]*(P[4][1] + P[0][1]*SF[3] + P[1][1]*SF[1] + P[2][1]*SPP[0] - P[3][1]*SPP[2] - P[13][1]*SPP[4]) + SF[1]*(P[4][3] + P[0][3]*SF[3] + P[1][3]*SF[1] + P[2][3]*SPP[0] - P[3][3]*SPP[2] - P[13][3]*SPP[4]) + SPP[0]*(P[4][0] + P[0][0]*SF[3] + P[1][0]*SF[1] + P[2][0]*SPP[0] - P[3][0]*SPP[2] - P[13][0]*SPP[4]) - SPP[1]*(P[4][2] + P[0][2]*SF[3] + P[1][2]*SF[1] + P[2][2]*SPP[0] - P[3][2]*SPP[2] - P[13][2]*SPP[4]) - (sq(q0) - sq(q1) - sq(q2) + sq(q3))*(P[4][13] + P[0][13]*SF[3] + P[1][13]*SF[1] + P[2][13]*SPP[0] - P[3][13]*SPP[2] - P[13][13]*SPP[4]); nextP[4][7] = P[4][7] + P[0][7]*SF[3] + P[1][7]*SF[1] + P[2][7]*SPP[0] - P[3][7]*SPP[2] - P[13][7]*SPP[4] + dt*(P[4][4] + P[0][4]*SF[3] + P[1][4]*SF[1] + P[2][4]*SPP[0] - P[3][4]*SPP[2] - P[13][4]*SPP[4]); nextP[4][8] = P[4][8] + P[0][8]*SF[3] + P[1][8]*SF[1] + P[2][8]*SPP[0] - P[3][8]*SPP[2] - P[13][8]*SPP[4] + dt*(P[4][5] + P[0][5]*SF[3] + P[1][5]*SF[1] + P[2][5]*SPP[0] - P[3][5]*SPP[2] - P[13][5]*SPP[4]); nextP[4][9] = P[4][9] + P[0][9]*SF[3] + P[1][9]*SF[1] + P[2][9]*SPP[0] - P[3][9]*SPP[2] - P[13][9]*SPP[4] + dt*(P[4][6] + P[0][6]*SF[3] + P[1][6]*SF[1] + P[2][6]*SPP[0] - P[3][6]*SPP[2] - P[13][6]*SPP[4]); nextP[4][10] = P[4][10] + P[0][10]*SF[3] + P[1][10]*SF[1] + P[2][10]*SPP[0] - P[3][10]*SPP[2] - P[13][10]*SPP[4]; nextP[4][11] = P[4][11] + P[0][11]*SF[3] + P[1][11]*SF[1] + P[2][11]*SPP[0] - P[3][11]*SPP[2] - P[13][11]*SPP[4]; nextP[4][12] = P[4][12] + P[0][12]*SF[3] + P[1][12]*SF[1] + P[2][12]*SPP[0] - P[3][12]*SPP[2] - P[13][12]*SPP[4]; nextP[4][13] = P[4][13] + P[0][13]*SF[3] + P[1][13]*SF[1] + P[2][13]*SPP[0] - P[3][13]*SPP[2] - P[13][13]*SPP[4]; nextP[4][14] = P[4][14] + P[0][14]*SF[3] + P[1][14]*SF[1] + P[2][14]*SPP[0] - P[3][14]*SPP[2] - P[13][14]*SPP[4]; nextP[4][15] = P[4][15] + P[0][15]*SF[3] + P[1][15]*SF[1] + P[2][15]*SPP[0] - P[3][15]*SPP[2] - P[13][15]*SPP[4]; nextP[4][16] = P[4][16] + P[0][16]*SF[3] + P[1][16]*SF[1] + P[2][16]*SPP[0] - P[3][16]*SPP[2] - P[13][16]*SPP[4]; nextP[4][17] = P[4][17] + P[0][17]*SF[3] + P[1][17]*SF[1] + P[2][17]*SPP[0] - P[3][17]*SPP[2] - P[13][17]*SPP[4]; nextP[4][18] = P[4][18] + P[0][18]*SF[3] + P[1][18]*SF[1] + P[2][18]*SPP[0] - P[3][18]*SPP[2] - P[13][18]*SPP[4]; nextP[4][19] = P[4][19] + P[0][19]*SF[3] + P[1][19]*SF[1] + P[2][19]*SPP[0] - P[3][19]*SPP[2] - P[13][19]*SPP[4]; nextP[4][20] = P[4][20] + P[0][20]*SF[3] + P[1][20]*SF[1] + P[2][20]*SPP[0] - P[3][20]*SPP[2] - P[13][20]*SPP[4]; nextP[4][21] = P[4][21] + P[0][21]*SF[3] + P[1][21]*SF[1] + P[2][21]*SPP[0] - P[3][21]*SPP[2] - P[13][21]*SPP[4]; nextP[5][0] = P[5][0] + P[0][0]*SF[2] + P[2][0]*SF[1] + P[3][0]*SF[3] - P[1][0]*SPP[0] + P[13][0]*SPP[3] + SF[7]*(P[5][1] + P[0][1]*SF[2] + P[2][1]*SF[1] + P[3][1]*SF[3] - P[1][1]*SPP[0] + P[13][1]*SPP[3]) + SF[9]*(P[5][2] + P[0][2]*SF[2] + P[2][2]*SF[1] + P[3][2]*SF[3] - P[1][2]*SPP[0] + P[13][2]*SPP[3]) + SF[8]*(P[5][3] + P[0][3]*SF[2] + P[2][3]*SF[1] + P[3][3]*SF[3] - P[1][3]*SPP[0] + P[13][3]*SPP[3]) + SF[11]*(P[5][10] + P[0][10]*SF[2] + P[2][10]*SF[1] + P[3][10]*SF[3] - P[1][10]*SPP[0] + P[13][10]*SPP[3]) + SPP[7]*(P[5][11] + P[0][11]*SF[2] + P[2][11]*SF[1] + P[3][11]*SF[3] - P[1][11]*SPP[0] + P[13][11]*SPP[3]) + SPP[6]*(P[5][12] + P[0][12]*SF[2] + P[2][12]*SF[1] + P[3][12]*SF[3] - P[1][12]*SPP[0] + P[13][12]*SPP[3]); nextP[5][1] = P[5][1] + P[0][1]*SF[2] + P[2][1]*SF[1] + P[3][1]*SF[3] - P[1][1]*SPP[0] + P[13][1]*SPP[3] + SF[6]*(P[5][0] + P[0][0]*SF[2] + P[2][0]*SF[1] + P[3][0]*SF[3] - P[1][0]*SPP[0] + P[13][0]*SPP[3]) + SF[5]*(P[5][2] + P[0][2]*SF[2] + P[2][2]*SF[1] + P[3][2]*SF[3] - P[1][2]*SPP[0] + P[13][2]*SPP[3]) + SF[9]*(P[5][3] + P[0][3]*SF[2] + P[2][3]*SF[1] + P[3][3]*SF[3] - P[1][3]*SPP[0] + P[13][3]*SPP[3]) + SPP[6]*(P[5][11] + P[0][11]*SF[2] + P[2][11]*SF[1] + P[3][11]*SF[3] - P[1][11]*SPP[0] + P[13][11]*SPP[3]) - SPP[7]*(P[5][12] + P[0][12]*SF[2] + P[2][12]*SF[1] + P[3][12]*SF[3] - P[1][12]*SPP[0] + P[13][12]*SPP[3]) - (q0*(P[5][10] + P[0][10]*SF[2] + P[2][10]*SF[1] + P[3][10]*SF[3] - P[1][10]*SPP[0] + P[13][10]*SPP[3]))/2; nextP[5][2] = P[5][2] + P[0][2]*SF[2] + P[2][2]*SF[1] + P[3][2]*SF[3] - P[1][2]*SPP[0] + P[13][2]*SPP[3] + SF[4]*(P[5][0] + P[0][0]*SF[2] + P[2][0]*SF[1] + P[3][0]*SF[3] - P[1][0]*SPP[0] + P[13][0]*SPP[3]) + SF[8]*(P[5][1] + P[0][1]*SF[2] + P[2][1]*SF[1] + P[3][1]*SF[3] - P[1][1]*SPP[0] + P[13][1]*SPP[3]) + SF[6]*(P[5][3] + P[0][3]*SF[2] + P[2][3]*SF[1] + P[3][3]*SF[3] - P[1][3]*SPP[0] + P[13][3]*SPP[3]) + SF[11]*(P[5][12] + P[0][12]*SF[2] + P[2][12]*SF[1] + P[3][12]*SF[3] - P[1][12]*SPP[0] + P[13][12]*SPP[3]) - SPP[6]*(P[5][10] + P[0][10]*SF[2] + P[2][10]*SF[1] + P[3][10]*SF[3] - P[1][10]*SPP[0] + P[13][10]*SPP[3]) - (q0*(P[5][11] + P[0][11]*SF[2] + P[2][11]*SF[1] + P[3][11]*SF[3] - P[1][11]*SPP[0] + P[13][11]*SPP[3]))/2; nextP[5][3] = P[5][3] + P[0][3]*SF[2] + P[2][3]*SF[1] + P[3][3]*SF[3] - P[1][3]*SPP[0] + P[13][3]*SPP[3] + SF[5]*(P[5][0] + P[0][0]*SF[2] + P[2][0]*SF[1] + P[3][0]*SF[3] - P[1][0]*SPP[0] + P[13][0]*SPP[3]) + SF[4]*(P[5][1] + P[0][1]*SF[2] + P[2][1]*SF[1] + P[3][1]*SF[3] - P[1][1]*SPP[0] + P[13][1]*SPP[3]) + SF[7]*(P[5][2] + P[0][2]*SF[2] + P[2][2]*SF[1] + P[3][2]*SF[3] - P[1][2]*SPP[0] + P[13][2]*SPP[3]) - SF[11]*(P[5][11] + P[0][11]*SF[2] + P[2][11]*SF[1] + P[3][11]*SF[3] - P[1][11]*SPP[0] + P[13][11]*SPP[3]) + SPP[7]*(P[5][10] + P[0][10]*SF[2] + P[2][10]*SF[1] + P[3][10]*SF[3] - P[1][10]*SPP[0] + P[13][10]*SPP[3]) - (q0*(P[5][12] + P[0][12]*SF[2] + P[2][12]*SF[1] + P[3][12]*SF[3] - P[1][12]*SPP[0] + P[13][12]*SPP[3]))/2; nextP[5][4] = P[5][4] + SQ[2] + P[0][4]*SF[2] + P[2][4]*SF[1] + P[3][4]*SF[3] - P[1][4]*SPP[0] + P[13][4]*SPP[3] + SF[3]*(P[5][0] + P[0][0]*SF[2] + P[2][0]*SF[1] + P[3][0]*SF[3] - P[1][0]*SPP[0] + P[13][0]*SPP[3]) + SF[1]*(P[5][1] + P[0][1]*SF[2] + P[2][1]*SF[1] + P[3][1]*SF[3] - P[1][1]*SPP[0] + P[13][1]*SPP[3]) + SPP[0]*(P[5][2] + P[0][2]*SF[2] + P[2][2]*SF[1] + P[3][2]*SF[3] - P[1][2]*SPP[0] + P[13][2]*SPP[3]) - SPP[2]*(P[5][3] + P[0][3]*SF[2] + P[2][3]*SF[1] + P[3][3]*SF[3] - P[1][3]*SPP[0] + P[13][3]*SPP[3]) - SPP[4]*(P[5][13] + P[0][13]*SF[2] + P[2][13]*SF[1] + P[3][13]*SF[3] - P[1][13]*SPP[0] + P[13][13]*SPP[3]); nextP[5][5] = P[5][5] + P[0][5]*SF[2] + P[2][5]*SF[1] + P[3][5]*SF[3] - P[1][5]*SPP[0] + P[13][5]*SPP[3] + dvxCov*sq(SG[7] + 2*q0*q3) + dvzCov*sq(SG[5] - 2*q0*q1) + SF[2]*(P[5][0] + P[0][0]*SF[2] + P[2][0]*SF[1] + P[3][0]*SF[3] - P[1][0]*SPP[0] + P[13][0]*SPP[3]) + SF[1]*(P[5][2] + P[0][2]*SF[2] + P[2][2]*SF[1] + P[3][2]*SF[3] - P[1][2]*SPP[0] + P[13][2]*SPP[3]) + SF[3]*(P[5][3] + P[0][3]*SF[2] + P[2][3]*SF[1] + P[3][3]*SF[3] - P[1][3]*SPP[0] + P[13][3]*SPP[3]) - SPP[0]*(P[5][1] + P[0][1]*SF[2] + P[2][1]*SF[1] + P[3][1]*SF[3] - P[1][1]*SPP[0] + P[13][1]*SPP[3]) + SPP[3]*(P[5][13] + P[0][13]*SF[2] + P[2][13]*SF[1] + P[3][13]*SF[3] - P[1][13]*SPP[0] + P[13][13]*SPP[3]) + dvyCov*sq(SG[1] - SG[2] + SG[3] - SG[4]); nextP[5][6] = P[5][6] + SQ[0] + P[0][6]*SF[2] + P[2][6]*SF[1] + P[3][6]*SF[3] - P[1][6]*SPP[0] + P[13][6]*SPP[3] + SF[2]*(P[5][1] + P[0][1]*SF[2] + P[2][1]*SF[1] + P[3][1]*SF[3] - P[1][1]*SPP[0] + P[13][1]*SPP[3]) + SF[1]*(P[5][3] + P[0][3]*SF[2] + P[2][3]*SF[1] + P[3][3]*SF[3] - P[1][3]*SPP[0] + P[13][3]*SPP[3]) + SPP[0]*(P[5][0] + P[0][0]*SF[2] + P[2][0]*SF[1] + P[3][0]*SF[3] - P[1][0]*SPP[0] + P[13][0]*SPP[3]) - SPP[1]*(P[5][2] + P[0][2]*SF[2] + P[2][2]*SF[1] + P[3][2]*SF[3] - P[1][2]*SPP[0] + P[13][2]*SPP[3]) - (sq(q0) - sq(q1) - sq(q2) + sq(q3))*(P[5][13] + P[0][13]*SF[2] + P[2][13]*SF[1] + P[3][13]*SF[3] - P[1][13]*SPP[0] + P[13][13]*SPP[3]); nextP[5][7] = P[5][7] + P[0][7]*SF[2] + P[2][7]*SF[1] + P[3][7]*SF[3] - P[1][7]*SPP[0] + P[13][7]*SPP[3] + dt*(P[5][4] + P[0][4]*SF[2] + P[2][4]*SF[1] + P[3][4]*SF[3] - P[1][4]*SPP[0] + P[13][4]*SPP[3]); nextP[5][8] = P[5][8] + P[0][8]*SF[2] + P[2][8]*SF[1] + P[3][8]*SF[3] - P[1][8]*SPP[0] + P[13][8]*SPP[3] + dt*(P[5][5] + P[0][5]*SF[2] + P[2][5]*SF[1] + P[3][5]*SF[3] - P[1][5]*SPP[0] + P[13][5]*SPP[3]); nextP[5][9] = P[5][9] + P[0][9]*SF[2] + P[2][9]*SF[1] + P[3][9]*SF[3] - P[1][9]*SPP[0] + P[13][9]*SPP[3] + dt*(P[5][6] + P[0][6]*SF[2] + P[2][6]*SF[1] + P[3][6]*SF[3] - P[1][6]*SPP[0] + P[13][6]*SPP[3]); nextP[5][10] = P[5][10] + P[0][10]*SF[2] + P[2][10]*SF[1] + P[3][10]*SF[3] - P[1][10]*SPP[0] + P[13][10]*SPP[3]; nextP[5][11] = P[5][11] + P[0][11]*SF[2] + P[2][11]*SF[1] + P[3][11]*SF[3] - P[1][11]*SPP[0] + P[13][11]*SPP[3]; nextP[5][12] = P[5][12] + P[0][12]*SF[2] + P[2][12]*SF[1] + P[3][12]*SF[3] - P[1][12]*SPP[0] + P[13][12]*SPP[3]; nextP[5][13] = P[5][13] + P[0][13]*SF[2] + P[2][13]*SF[1] + P[3][13]*SF[3] - P[1][13]*SPP[0] + P[13][13]*SPP[3]; nextP[5][14] = P[5][14] + P[0][14]*SF[2] + P[2][14]*SF[1] + P[3][14]*SF[3] - P[1][14]*SPP[0] + P[13][14]*SPP[3]; nextP[5][15] = P[5][15] + P[0][15]*SF[2] + P[2][15]*SF[1] + P[3][15]*SF[3] - P[1][15]*SPP[0] + P[13][15]*SPP[3]; nextP[5][16] = P[5][16] + P[0][16]*SF[2] + P[2][16]*SF[1] + P[3][16]*SF[3] - P[1][16]*SPP[0] + P[13][16]*SPP[3]; nextP[5][17] = P[5][17] + P[0][17]*SF[2] + P[2][17]*SF[1] + P[3][17]*SF[3] - P[1][17]*SPP[0] + P[13][17]*SPP[3]; nextP[5][18] = P[5][18] + P[0][18]*SF[2] + P[2][18]*SF[1] + P[3][18]*SF[3] - P[1][18]*SPP[0] + P[13][18]*SPP[3]; nextP[5][19] = P[5][19] + P[0][19]*SF[2] + P[2][19]*SF[1] + P[3][19]*SF[3] - P[1][19]*SPP[0] + P[13][19]*SPP[3]; nextP[5][20] = P[5][20] + P[0][20]*SF[2] + P[2][20]*SF[1] + P[3][20]*SF[3] - P[1][20]*SPP[0] + P[13][20]*SPP[3]; nextP[5][21] = P[5][21] + P[0][21]*SF[2] + P[2][21]*SF[1] + P[3][21]*SF[3] - P[1][21]*SPP[0] + P[13][21]*SPP[3]; nextP[6][0] = P[6][0] + P[1][0]*SF[2] + P[3][0]*SF[1] + P[0][0]*SPP[0] - P[2][0]*SPP[1] - P[13][0]*(sq(q0) - sq(q1) - sq(q2) + sq(q3)) + SF[7]*(P[6][1] + P[1][1]*SF[2] + P[3][1]*SF[1] + P[0][1]*SPP[0] - P[2][1]*SPP[1] - P[13][1]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SF[9]*(P[6][2] + P[1][2]*SF[2] + P[3][2]*SF[1] + P[0][2]*SPP[0] - P[2][2]*SPP[1] - P[13][2]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SF[8]*(P[6][3] + P[1][3]*SF[2] + P[3][3]*SF[1] + P[0][3]*SPP[0] - P[2][3]*SPP[1] - P[13][3]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SF[11]*(P[6][10] + P[1][10]*SF[2] + P[3][10]*SF[1] + P[0][10]*SPP[0] - P[2][10]*SPP[1] - P[13][10]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SPP[7]*(P[6][11] + P[1][11]*SF[2] + P[3][11]*SF[1] + P[0][11]*SPP[0] - P[2][11]*SPP[1] - P[13][11]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SPP[6]*(P[6][12] + P[1][12]*SF[2] + P[3][12]*SF[1] + P[0][12]*SPP[0] - P[2][12]*SPP[1] - P[13][12]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))); nextP[6][1] = P[6][1] + P[1][1]*SF[2] + P[3][1]*SF[1] + P[0][1]*SPP[0] - P[2][1]*SPP[1] - P[13][1]*(sq(q0) - sq(q1) - sq(q2) + sq(q3)) + SF[6]*(P[6][0] + P[1][0]*SF[2] + P[3][0]*SF[1] + P[0][0]*SPP[0] - P[2][0]*SPP[1] - P[13][0]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SF[5]*(P[6][2] + P[1][2]*SF[2] + P[3][2]*SF[1] + P[0][2]*SPP[0] - P[2][2]*SPP[1] - P[13][2]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SF[9]*(P[6][3] + P[1][3]*SF[2] + P[3][3]*SF[1] + P[0][3]*SPP[0] - P[2][3]*SPP[1] - P[13][3]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SPP[6]*(P[6][11] + P[1][11]*SF[2] + P[3][11]*SF[1] + P[0][11]*SPP[0] - P[2][11]*SPP[1] - P[13][11]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) - SPP[7]*(P[6][12] + P[1][12]*SF[2] + P[3][12]*SF[1] + P[0][12]*SPP[0] - P[2][12]*SPP[1] - P[13][12]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) - (q0*(P[6][10] + P[1][10]*SF[2] + P[3][10]*SF[1] + P[0][10]*SPP[0] - P[2][10]*SPP[1] - P[13][10]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))))/2; nextP[6][2] = P[6][2] + P[1][2]*SF[2] + P[3][2]*SF[1] + P[0][2]*SPP[0] - P[2][2]*SPP[1] - P[13][2]*(sq(q0) - sq(q1) - sq(q2) + sq(q3)) + SF[4]*(P[6][0] + P[1][0]*SF[2] + P[3][0]*SF[1] + P[0][0]*SPP[0] - P[2][0]*SPP[1] - P[13][0]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SF[8]*(P[6][1] + P[1][1]*SF[2] + P[3][1]*SF[1] + P[0][1]*SPP[0] - P[2][1]*SPP[1] - P[13][1]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SF[6]*(P[6][3] + P[1][3]*SF[2] + P[3][3]*SF[1] + P[0][3]*SPP[0] - P[2][3]*SPP[1] - P[13][3]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SF[11]*(P[6][12] + P[1][12]*SF[2] + P[3][12]*SF[1] + P[0][12]*SPP[0] - P[2][12]*SPP[1] - P[13][12]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) - SPP[6]*(P[6][10] + P[1][10]*SF[2] + P[3][10]*SF[1] + P[0][10]*SPP[0] - P[2][10]*SPP[1] - P[13][10]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) - (q0*(P[6][11] + P[1][11]*SF[2] + P[3][11]*SF[1] + P[0][11]*SPP[0] - P[2][11]*SPP[1] - P[13][11]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))))/2; nextP[6][3] = P[6][3] + P[1][3]*SF[2] + P[3][3]*SF[1] + P[0][3]*SPP[0] - P[2][3]*SPP[1] - P[13][3]*(sq(q0) - sq(q1) - sq(q2) + sq(q3)) + SF[5]*(P[6][0] + P[1][0]*SF[2] + P[3][0]*SF[1] + P[0][0]*SPP[0] - P[2][0]*SPP[1] - P[13][0]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SF[4]*(P[6][1] + P[1][1]*SF[2] + P[3][1]*SF[1] + P[0][1]*SPP[0] - P[2][1]*SPP[1] - P[13][1]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SF[7]*(P[6][2] + P[1][2]*SF[2] + P[3][2]*SF[1] + P[0][2]*SPP[0] - P[2][2]*SPP[1] - P[13][2]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) - SF[11]*(P[6][11] + P[1][11]*SF[2] + P[3][11]*SF[1] + P[0][11]*SPP[0] - P[2][11]*SPP[1] - P[13][11]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SPP[7]*(P[6][10] + P[1][10]*SF[2] + P[3][10]*SF[1] + P[0][10]*SPP[0] - P[2][10]*SPP[1] - P[13][10]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) - (q0*(P[6][12] + P[1][12]*SF[2] + P[3][12]*SF[1] + P[0][12]*SPP[0] - P[2][12]*SPP[1] - P[13][12]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))))/2; nextP[6][4] = P[6][4] + SQ[1] + P[1][4]*SF[2] + P[3][4]*SF[1] + P[0][4]*SPP[0] - P[2][4]*SPP[1] - P[13][4]*(sq(q0) - sq(q1) - sq(q2) + sq(q3)) + SF[3]*(P[6][0] + P[1][0]*SF[2] + P[3][0]*SF[1] + P[0][0]*SPP[0] - P[2][0]*SPP[1] - P[13][0]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SF[1]*(P[6][1] + P[1][1]*SF[2] + P[3][1]*SF[1] + P[0][1]*SPP[0] - P[2][1]*SPP[1] - P[13][1]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SPP[0]*(P[6][2] + P[1][2]*SF[2] + P[3][2]*SF[1] + P[0][2]*SPP[0] - P[2][2]*SPP[1] - P[13][2]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) - SPP[2]*(P[6][3] + P[1][3]*SF[2] + P[3][3]*SF[1] + P[0][3]*SPP[0] - P[2][3]*SPP[1] - P[13][3]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) - SPP[4]*(P[6][13] + P[1][13]*SF[2] + P[3][13]*SF[1] + P[0][13]*SPP[0] - P[2][13]*SPP[1] - P[13][13]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))); nextP[6][5] = P[6][5] + SQ[0] + P[1][5]*SF[2] + P[3][5]*SF[1] + P[0][5]*SPP[0] - P[2][5]*SPP[1] - P[13][5]*(sq(q0) - sq(q1) - sq(q2) + sq(q3)) + SF[2]*(P[6][0] + P[1][0]*SF[2] + P[3][0]*SF[1] + P[0][0]*SPP[0] - P[2][0]*SPP[1] - P[13][0]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SF[1]*(P[6][2] + P[1][2]*SF[2] + P[3][2]*SF[1] + P[0][2]*SPP[0] - P[2][2]*SPP[1] - P[13][2]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SF[3]*(P[6][3] + P[1][3]*SF[2] + P[3][3]*SF[1] + P[0][3]*SPP[0] - P[2][3]*SPP[1] - P[13][3]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) - SPP[0]*(P[6][1] + P[1][1]*SF[2] + P[3][1]*SF[1] + P[0][1]*SPP[0] - P[2][1]*SPP[1] - P[13][1]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SPP[3]*(P[6][13] + P[1][13]*SF[2] + P[3][13]*SF[1] + P[0][13]*SPP[0] - P[2][13]*SPP[1] - P[13][13]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))); nextP[6][6] = P[6][6] + P[1][6]*SF[2] + P[3][6]*SF[1] + P[0][6]*SPP[0] - P[2][6]*SPP[1] - P[13][6]*(sq(q0) - sq(q1) - sq(q2) + sq(q3)) + dvxCov*sq(SG[6] - 2*q0*q2) + dvyCov*sq(SG[5] + 2*q0*q1) - SPP[5]*(P[6][13] + P[1][13]*SF[2] + P[3][13]*SF[1] + P[0][13]*SPP[0] - P[2][13]*SPP[1] - P[13][13]*SPP[5]) + SF[2]*(P[6][1] + P[1][1]*SF[2] + P[3][1]*SF[1] + P[0][1]*SPP[0] - P[2][1]*SPP[1] - P[13][1]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SF[1]*(P[6][3] + P[1][3]*SF[2] + P[3][3]*SF[1] + P[0][3]*SPP[0] - P[2][3]*SPP[1] - P[13][3]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + SPP[0]*(P[6][0] + P[1][0]*SF[2] + P[3][0]*SF[1] + P[0][0]*SPP[0] - P[2][0]*SPP[1] - P[13][0]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) - SPP[1]*(P[6][2] + P[1][2]*SF[2] + P[3][2]*SF[1] + P[0][2]*SPP[0] - P[2][2]*SPP[1] - P[13][2]*(sq(q0) - sq(q1) - sq(q2) + sq(q3))) + dvzCov*sq(SG[1] - SG[2] - SG[3] + SG[4]); nextP[6][7] = P[6][7] + P[1][7]*SF[2] + P[3][7]*SF[1] + P[0][7]*SPP[0] - P[2][7]*SPP[1] - P[13][7]*SPP[5] + dt*(P[6][4] + P[1][4]*SF[2] + P[3][4]*SF[1] + P[0][4]*SPP[0] - P[2][4]*SPP[1] - P[13][4]*SPP[5]); nextP[6][8] = P[6][8] + P[1][8]*SF[2] + P[3][8]*SF[1] + P[0][8]*SPP[0] - P[2][8]*SPP[1] - P[13][8]*SPP[5] + dt*(P[6][5] + P[1][5]*SF[2] + P[3][5]*SF[1] + P[0][5]*SPP[0] - P[2][5]*SPP[1] - P[13][5]*SPP[5]); nextP[6][9] = P[6][9] + P[1][9]*SF[2] + P[3][9]*SF[1] + P[0][9]*SPP[0] - P[2][9]*SPP[1] - P[13][9]*SPP[5] + dt*(P[6][6] + P[1][6]*SF[2] + P[3][6]*SF[1] + P[0][6]*SPP[0] - P[2][6]*SPP[1] - P[13][6]*SPP[5]); nextP[6][10] = P[6][10] + P[1][10]*SF[2] + P[3][10]*SF[1] + P[0][10]*SPP[0] - P[2][10]*SPP[1] - P[13][10]*SPP[5]; nextP[6][11] = P[6][11] + P[1][11]*SF[2] + P[3][11]*SF[1] + P[0][11]*SPP[0] - P[2][11]*SPP[1] - P[13][11]*SPP[5]; nextP[6][12] = P[6][12] + P[1][12]*SF[2] + P[3][12]*SF[1] + P[0][12]*SPP[0] - P[2][12]*SPP[1] - P[13][12]*SPP[5]; nextP[6][13] = P[6][13] + P[1][13]*SF[2] + P[3][13]*SF[1] + P[0][13]*SPP[0] - P[2][13]*SPP[1] - P[13][13]*SPP[5]; nextP[6][14] = P[6][14] + P[1][14]*SF[2] + P[3][14]*SF[1] + P[0][14]*SPP[0] - P[2][14]*SPP[1] - P[13][14]*SPP[5]; nextP[6][15] = P[6][15] + P[1][15]*SF[2] + P[3][15]*SF[1] + P[0][15]*SPP[0] - P[2][15]*SPP[1] - P[13][15]*SPP[5]; nextP[6][16] = P[6][16] + P[1][16]*SF[2] + P[3][16]*SF[1] + P[0][16]*SPP[0] - P[2][16]*SPP[1] - P[13][16]*SPP[5]; nextP[6][17] = P[6][17] + P[1][17]*SF[2] + P[3][17]*SF[1] + P[0][17]*SPP[0] - P[2][17]*SPP[1] - P[13][17]*SPP[5]; nextP[6][18] = P[6][18] + P[1][18]*SF[2] + P[3][18]*SF[1] + P[0][18]*SPP[0] - P[2][18]*SPP[1] - P[13][18]*SPP[5]; nextP[6][19] = P[6][19] + P[1][19]*SF[2] + P[3][19]*SF[1] + P[0][19]*SPP[0] - P[2][19]*SPP[1] - P[13][19]*SPP[5]; nextP[6][20] = P[6][20] + P[1][20]*SF[2] + P[3][20]*SF[1] + P[0][20]*SPP[0] - P[2][20]*SPP[1] - P[13][20]*SPP[5]; nextP[6][21] = P[6][21] + P[1][21]*SF[2] + P[3][21]*SF[1] + P[0][21]*SPP[0] - P[2][21]*SPP[1] - P[13][21]*SPP[5]; nextP[7][0] = P[7][0] + P[4][0]*dt + SF[7]*(P[7][1] + P[4][1]*dt) + SF[9]*(P[7][2] + P[4][2]*dt) + SF[8]*(P[7][3] + P[4][3]*dt) + SF[11]*(P[7][10] + P[4][10]*dt) + SPP[7]*(P[7][11] + P[4][11]*dt) + SPP[6]*(P[7][12] + P[4][12]*dt); nextP[7][1] = P[7][1] + P[4][1]*dt + SF[6]*(P[7][0] + P[4][0]*dt) + SF[5]*(P[7][2] + P[4][2]*dt) + SF[9]*(P[7][3] + P[4][3]*dt) + SPP[6]*(P[7][11] + P[4][11]*dt) - SPP[7]*(P[7][12] + P[4][12]*dt) - (q0*(P[7][10] + P[4][10]*dt))/2; nextP[7][2] = P[7][2] + P[4][2]*dt + SF[4]*(P[7][0] + P[4][0]*dt) + SF[8]*(P[7][1] + P[4][1]*dt) + SF[6]*(P[7][3] + P[4][3]*dt) + SF[11]*(P[7][12] + P[4][12]*dt) - SPP[6]*(P[7][10] + P[4][10]*dt) - (q0*(P[7][11] + P[4][11]*dt))/2; nextP[7][3] = P[7][3] + P[4][3]*dt + SF[5]*(P[7][0] + P[4][0]*dt) + SF[4]*(P[7][1] + P[4][1]*dt) + SF[7]*(P[7][2] + P[4][2]*dt) - SF[11]*(P[7][11] + P[4][11]*dt) + SPP[7]*(P[7][10] + P[4][10]*dt) - (q0*(P[7][12] + P[4][12]*dt))/2; nextP[7][4] = P[7][4] + P[4][4]*dt + SF[1]*(P[7][1] + P[4][1]*dt) + SF[3]*(P[7][0] + P[4][0]*dt) + SPP[0]*(P[7][2] + P[4][2]*dt) - SPP[2]*(P[7][3] + P[4][3]*dt) - SPP[4]*(P[7][13] + P[4][13]*dt); nextP[7][5] = P[7][5] + P[4][5]*dt + SF[2]*(P[7][0] + P[4][0]*dt) + SF[1]*(P[7][2] + P[4][2]*dt) + SF[3]*(P[7][3] + P[4][3]*dt) - SPP[0]*(P[7][1] + P[4][1]*dt) + SPP[3]*(P[7][13] + P[4][13]*dt); nextP[7][6] = P[7][6] + P[4][6]*dt + SF[2]*(P[7][1] + P[4][1]*dt) + SF[1]*(P[7][3] + P[4][3]*dt) + SPP[0]*(P[7][0] + P[4][0]*dt) - SPP[1]*(P[7][2] + P[4][2]*dt) - SPP[5]*(P[7][13] + P[4][13]*dt); nextP[7][7] = P[7][7] + P[4][7]*dt + dt*(P[7][4] + P[4][4]*dt); nextP[7][8] = P[7][8] + P[4][8]*dt + dt*(P[7][5] + P[4][5]*dt); nextP[7][9] = P[7][9] + P[4][9]*dt + dt*(P[7][6] + P[4][6]*dt); nextP[7][10] = P[7][10] + P[4][10]*dt; nextP[7][11] = P[7][11] + P[4][11]*dt; nextP[7][12] = P[7][12] + P[4][12]*dt; nextP[7][13] = P[7][13] + P[4][13]*dt; nextP[7][14] = P[7][14] + P[4][14]*dt; nextP[7][15] = P[7][15] + P[4][15]*dt; nextP[7][16] = P[7][16] + P[4][16]*dt; nextP[7][17] = P[7][17] + P[4][17]*dt; nextP[7][18] = P[7][18] + P[4][18]*dt; nextP[7][19] = P[7][19] + P[4][19]*dt; nextP[7][20] = P[7][20] + P[4][20]*dt; nextP[7][21] = P[7][21] + P[4][21]*dt; nextP[8][0] = P[8][0] + P[5][0]*dt + SF[7]*(P[8][1] + P[5][1]*dt) + SF[9]*(P[8][2] + P[5][2]*dt) + SF[8]*(P[8][3] + P[5][3]*dt) + SF[11]*(P[8][10] + P[5][10]*dt) + SPP[7]*(P[8][11] + P[5][11]*dt) + SPP[6]*(P[8][12] + P[5][12]*dt); nextP[8][1] = P[8][1] + P[5][1]*dt + SF[6]*(P[8][0] + P[5][0]*dt) + SF[5]*(P[8][2] + P[5][2]*dt) + SF[9]*(P[8][3] + P[5][3]*dt) + SPP[6]*(P[8][11] + P[5][11]*dt) - SPP[7]*(P[8][12] + P[5][12]*dt) - (q0*(P[8][10] + P[5][10]*dt))/2; nextP[8][2] = P[8][2] + P[5][2]*dt + SF[4]*(P[8][0] + P[5][0]*dt) + SF[8]*(P[8][1] + P[5][1]*dt) + SF[6]*(P[8][3] + P[5][3]*dt) + SF[11]*(P[8][12] + P[5][12]*dt) - SPP[6]*(P[8][10] + P[5][10]*dt) - (q0*(P[8][11] + P[5][11]*dt))/2; nextP[8][3] = P[8][3] + P[5][3]*dt + SF[5]*(P[8][0] + P[5][0]*dt) + SF[4]*(P[8][1] + P[5][1]*dt) + SF[7]*(P[8][2] + P[5][2]*dt) - SF[11]*(P[8][11] + P[5][11]*dt) + SPP[7]*(P[8][10] + P[5][10]*dt) - (q0*(P[8][12] + P[5][12]*dt))/2; nextP[8][4] = P[8][4] + P[5][4]*dt + SF[1]*(P[8][1] + P[5][1]*dt) + SF[3]*(P[8][0] + P[5][0]*dt) + SPP[0]*(P[8][2] + P[5][2]*dt) - SPP[2]*(P[8][3] + P[5][3]*dt) - SPP[4]*(P[8][13] + P[5][13]*dt); nextP[8][5] = P[8][5] + P[5][5]*dt + SF[2]*(P[8][0] + P[5][0]*dt) + SF[1]*(P[8][2] + P[5][2]*dt) + SF[3]*(P[8][3] + P[5][3]*dt) - SPP[0]*(P[8][1] + P[5][1]*dt) + SPP[3]*(P[8][13] + P[5][13]*dt); nextP[8][6] = P[8][6] + P[5][6]*dt + SF[2]*(P[8][1] + P[5][1]*dt) + SF[1]*(P[8][3] + P[5][3]*dt) + SPP[0]*(P[8][0] + P[5][0]*dt) - SPP[1]*(P[8][2] + P[5][2]*dt) - SPP[5]*(P[8][13] + P[5][13]*dt); nextP[8][7] = P[8][7] + P[5][7]*dt + dt*(P[8][4] + P[5][4]*dt); nextP[8][8] = P[8][8] + P[5][8]*dt + dt*(P[8][5] + P[5][5]*dt); nextP[8][9] = P[8][9] + P[5][9]*dt + dt*(P[8][6] + P[5][6]*dt); nextP[8][10] = P[8][10] + P[5][10]*dt; nextP[8][11] = P[8][11] + P[5][11]*dt; nextP[8][12] = P[8][12] + P[5][12]*dt; nextP[8][13] = P[8][13] + P[5][13]*dt; nextP[8][14] = P[8][14] + P[5][14]*dt; nextP[8][15] = P[8][15] + P[5][15]*dt; nextP[8][16] = P[8][16] + P[5][16]*dt; nextP[8][17] = P[8][17] + P[5][17]*dt; nextP[8][18] = P[8][18] + P[5][18]*dt; nextP[8][19] = P[8][19] + P[5][19]*dt; nextP[8][20] = P[8][20] + P[5][20]*dt; nextP[8][21] = P[8][21] + P[5][21]*dt; nextP[9][0] = P[9][0] + P[6][0]*dt + SF[7]*(P[9][1] + P[6][1]*dt) + SF[9]*(P[9][2] + P[6][2]*dt) + SF[8]*(P[9][3] + P[6][3]*dt) + SF[11]*(P[9][10] + P[6][10]*dt) + SPP[7]*(P[9][11] + P[6][11]*dt) + SPP[6]*(P[9][12] + P[6][12]*dt); nextP[9][1] = P[9][1] + P[6][1]*dt + SF[6]*(P[9][0] + P[6][0]*dt) + SF[5]*(P[9][2] + P[6][2]*dt) + SF[9]*(P[9][3] + P[6][3]*dt) + SPP[6]*(P[9][11] + P[6][11]*dt) - SPP[7]*(P[9][12] + P[6][12]*dt) - (q0*(P[9][10] + P[6][10]*dt))/2; nextP[9][2] = P[9][2] + P[6][2]*dt + SF[4]*(P[9][0] + P[6][0]*dt) + SF[8]*(P[9][1] + P[6][1]*dt) + SF[6]*(P[9][3] + P[6][3]*dt) + SF[11]*(P[9][12] + P[6][12]*dt) - SPP[6]*(P[9][10] + P[6][10]*dt) - (q0*(P[9][11] + P[6][11]*dt))/2; nextP[9][3] = P[9][3] + P[6][3]*dt + SF[5]*(P[9][0] + P[6][0]*dt) + SF[4]*(P[9][1] + P[6][1]*dt) + SF[7]*(P[9][2] + P[6][2]*dt) - SF[11]*(P[9][11] + P[6][11]*dt) + SPP[7]*(P[9][10] + P[6][10]*dt) - (q0*(P[9][12] + P[6][12]*dt))/2; nextP[9][4] = P[9][4] + P[6][4]*dt + SF[1]*(P[9][1] + P[6][1]*dt) + SF[3]*(P[9][0] + P[6][0]*dt) + SPP[0]*(P[9][2] + P[6][2]*dt) - SPP[2]*(P[9][3] + P[6][3]*dt) - SPP[4]*(P[9][13] + P[6][13]*dt); nextP[9][5] = P[9][5] + P[6][5]*dt + SF[2]*(P[9][0] + P[6][0]*dt) + SF[1]*(P[9][2] + P[6][2]*dt) + SF[3]*(P[9][3] + P[6][3]*dt) - SPP[0]*(P[9][1] + P[6][1]*dt) + SPP[3]*(P[9][13] + P[6][13]*dt); nextP[9][6] = P[9][6] + P[6][6]*dt + SF[2]*(P[9][1] + P[6][1]*dt) + SF[1]*(P[9][3] + P[6][3]*dt) + SPP[0]*(P[9][0] + P[6][0]*dt) - SPP[1]*(P[9][2] + P[6][2]*dt) - SPP[5]*(P[9][13] + P[6][13]*dt); nextP[9][7] = P[9][7] + P[6][7]*dt + dt*(P[9][4] + P[6][4]*dt); nextP[9][8] = P[9][8] + P[6][8]*dt + dt*(P[9][5] + P[6][5]*dt); nextP[9][9] = P[9][9] + P[6][9]*dt + dt*(P[9][6] + P[6][6]*dt); nextP[9][10] = P[9][10] + P[6][10]*dt; nextP[9][11] = P[9][11] + P[6][11]*dt; nextP[9][12] = P[9][12] + P[6][12]*dt; nextP[9][13] = P[9][13] + P[6][13]*dt; nextP[9][14] = P[9][14] + P[6][14]*dt; nextP[9][15] = P[9][15] + P[6][15]*dt; nextP[9][16] = P[9][16] + P[6][16]*dt; nextP[9][17] = P[9][17] + P[6][17]*dt; nextP[9][18] = P[9][18] + P[6][18]*dt; nextP[9][19] = P[9][19] + P[6][19]*dt; nextP[9][20] = P[9][20] + P[6][20]*dt; nextP[9][21] = P[9][21] + P[6][21]*dt; nextP[10][0] = P[10][0] + P[10][1]*SF[7] + P[10][2]*SF[9] + P[10][3]*SF[8] + P[10][10]*SF[11] + P[10][11]*SPP[7] + P[10][12]*SPP[6]; nextP[10][1] = P[10][1] + P[10][0]*SF[6] + P[10][2]*SF[5] + P[10][3]*SF[9] + P[10][11]*SPP[6] - P[10][12]*SPP[7] - (P[10][10]*q0)/2; nextP[10][2] = P[10][2] + P[10][0]*SF[4] + P[10][1]*SF[8] + P[10][3]*SF[6] + P[10][12]*SF[11] - P[10][10]*SPP[6] - (P[10][11]*q0)/2; nextP[10][3] = P[10][3] + P[10][0]*SF[5] + P[10][1]*SF[4] + P[10][2]*SF[7] - P[10][11]*SF[11] + P[10][10]*SPP[7] - (P[10][12]*q0)/2; nextP[10][4] = P[10][4] + P[10][1]*SF[1] + P[10][0]*SF[3] + P[10][2]*SPP[0] - P[10][3]*SPP[2] - P[10][13]*SPP[4]; nextP[10][5] = P[10][5] + P[10][0]*SF[2] + P[10][2]*SF[1] + P[10][3]*SF[3] - P[10][1]*SPP[0] + P[10][13]*SPP[3]; nextP[10][6] = P[10][6] + P[10][1]*SF[2] + P[10][3]*SF[1] + P[10][0]*SPP[0] - P[10][2]*SPP[1] - P[10][13]*SPP[5]; nextP[10][7] = P[10][7] + P[10][4]*dt; nextP[10][8] = P[10][8] + P[10][5]*dt; nextP[10][9] = P[10][9] + P[10][6]*dt; nextP[10][10] = P[10][10]; nextP[10][11] = P[10][11]; nextP[10][12] = P[10][12]; nextP[10][13] = P[10][13]; nextP[10][14] = P[10][14]; nextP[10][15] = P[10][15]; nextP[10][16] = P[10][16]; nextP[10][17] = P[10][17]; nextP[10][18] = P[10][18]; nextP[10][19] = P[10][19]; nextP[10][20] = P[10][20]; nextP[10][21] = P[10][21]; nextP[11][0] = P[11][0] + P[11][1]*SF[7] + P[11][2]*SF[9] + P[11][3]*SF[8] + P[11][10]*SF[11] + P[11][11]*SPP[7] + P[11][12]*SPP[6]; nextP[11][1] = P[11][1] + P[11][0]*SF[6] + P[11][2]*SF[5] + P[11][3]*SF[9] + P[11][11]*SPP[6] - P[11][12]*SPP[7] - (P[11][10]*q0)/2; nextP[11][2] = P[11][2] + P[11][0]*SF[4] + P[11][1]*SF[8] + P[11][3]*SF[6] + P[11][12]*SF[11] - P[11][10]*SPP[6] - (P[11][11]*q0)/2; nextP[11][3] = P[11][3] + P[11][0]*SF[5] + P[11][1]*SF[4] + P[11][2]*SF[7] - P[11][11]*SF[11] + P[11][10]*SPP[7] - (P[11][12]*q0)/2; nextP[11][4] = P[11][4] + P[11][1]*SF[1] + P[11][0]*SF[3] + P[11][2]*SPP[0] - P[11][3]*SPP[2] - P[11][13]*SPP[4]; nextP[11][5] = P[11][5] + P[11][0]*SF[2] + P[11][2]*SF[1] + P[11][3]*SF[3] - P[11][1]*SPP[0] + P[11][13]*SPP[3]; nextP[11][6] = P[11][6] + P[11][1]*SF[2] + P[11][3]*SF[1] + P[11][0]*SPP[0] - P[11][2]*SPP[1] - P[11][13]*SPP[5]; nextP[11][7] = P[11][7] + P[11][4]*dt; nextP[11][8] = P[11][8] + P[11][5]*dt; nextP[11][9] = P[11][9] + P[11][6]*dt; nextP[11][10] = P[11][10]; nextP[11][11] = P[11][11]; nextP[11][12] = P[11][12]; nextP[11][13] = P[11][13]; nextP[11][14] = P[11][14]; nextP[11][15] = P[11][15]; nextP[11][16] = P[11][16]; nextP[11][17] = P[11][17]; nextP[11][18] = P[11][18]; nextP[11][19] = P[11][19]; nextP[11][20] = P[11][20]; nextP[11][21] = P[11][21]; nextP[12][0] = P[12][0] + P[12][1]*SF[7] + P[12][2]*SF[9] + P[12][3]*SF[8] + P[12][10]*SF[11] + P[12][11]*SPP[7] + P[12][12]*SPP[6]; nextP[12][1] = P[12][1] + P[12][0]*SF[6] + P[12][2]*SF[5] + P[12][3]*SF[9] + P[12][11]*SPP[6] - P[12][12]*SPP[7] - (P[12][10]*q0)/2; nextP[12][2] = P[12][2] + P[12][0]*SF[4] + P[12][1]*SF[8] + P[12][3]*SF[6] + P[12][12]*SF[11] - P[12][10]*SPP[6] - (P[12][11]*q0)/2; nextP[12][3] = P[12][3] + P[12][0]*SF[5] + P[12][1]*SF[4] + P[12][2]*SF[7] - P[12][11]*SF[11] + P[12][10]*SPP[7] - (P[12][12]*q0)/2; nextP[12][4] = P[12][4] + P[12][1]*SF[1] + P[12][0]*SF[3] + P[12][2]*SPP[0] - P[12][3]*SPP[2] - P[12][13]*SPP[4]; nextP[12][5] = P[12][5] + P[12][0]*SF[2] + P[12][2]*SF[1] + P[12][3]*SF[3] - P[12][1]*SPP[0] + P[12][13]*SPP[3]; nextP[12][6] = P[12][6] + P[12][1]*SF[2] + P[12][3]*SF[1] + P[12][0]*SPP[0] - P[12][2]*SPP[1] - P[12][13]*SPP[5]; nextP[12][7] = P[12][7] + P[12][4]*dt; nextP[12][8] = P[12][8] + P[12][5]*dt; nextP[12][9] = P[12][9] + P[12][6]*dt; nextP[12][10] = P[12][10]; nextP[12][11] = P[12][11]; nextP[12][12] = P[12][12]; nextP[12][13] = P[12][13]; nextP[12][14] = P[12][14]; nextP[12][15] = P[12][15]; nextP[12][16] = P[12][16]; nextP[12][17] = P[12][17]; nextP[12][18] = P[12][18]; nextP[12][19] = P[12][19]; nextP[12][20] = P[12][20]; nextP[12][21] = P[12][21]; nextP[13][0] = P[13][0] + P[13][1]*SF[7] + P[13][2]*SF[9] + P[13][3]*SF[8] + P[13][10]*SF[11] + P[13][11]*SPP[7] + P[13][12]*SPP[6]; nextP[13][1] = P[13][1] + P[13][0]*SF[6] + P[13][2]*SF[5] + P[13][3]*SF[9] + P[13][11]*SPP[6] - P[13][12]*SPP[7] - (P[13][10]*q0)/2; nextP[13][2] = P[13][2] + P[13][0]*SF[4] + P[13][1]*SF[8] + P[13][3]*SF[6] + P[13][12]*SF[11] - P[13][10]*SPP[6] - (P[13][11]*q0)/2; nextP[13][3] = P[13][3] + P[13][0]*SF[5] + P[13][1]*SF[4] + P[13][2]*SF[7] - P[13][11]*SF[11] + P[13][10]*SPP[7] - (P[13][12]*q0)/2; nextP[13][4] = P[13][4] + P[13][1]*SF[1] + P[13][0]*SF[3] + P[13][2]*SPP[0] - P[13][3]*SPP[2] - P[13][13]*SPP[4]; nextP[13][5] = P[13][5] + P[13][0]*SF[2] + P[13][2]*SF[1] + P[13][3]*SF[3] - P[13][1]*SPP[0] + P[13][13]*SPP[3]; nextP[13][6] = P[13][6] + P[13][1]*SF[2] + P[13][3]*SF[1] + P[13][0]*SPP[0] - P[13][2]*SPP[1] - P[13][13]*SPP[5]; nextP[13][7] = P[13][7] + P[13][4]*dt; nextP[13][8] = P[13][8] + P[13][5]*dt; nextP[13][9] = P[13][9] + P[13][6]*dt; nextP[13][10] = P[13][10]; nextP[13][11] = P[13][11]; nextP[13][12] = P[13][12]; nextP[13][13] = P[13][13]; nextP[13][14] = P[13][14]; nextP[13][15] = P[13][15]; nextP[13][16] = P[13][16]; nextP[13][17] = P[13][17]; nextP[13][18] = P[13][18]; nextP[13][19] = P[13][19]; nextP[13][20] = P[13][20]; nextP[13][21] = P[13][21]; nextP[14][0] = P[14][0] + P[14][1]*SF[7] + P[14][2]*SF[9] + P[14][3]*SF[8] + P[14][10]*SF[11] + P[14][11]*SPP[7] + P[14][12]*SPP[6]; nextP[14][1] = P[14][1] + P[14][0]*SF[6] + P[14][2]*SF[5] + P[14][3]*SF[9] + P[14][11]*SPP[6] - P[14][12]*SPP[7] - (P[14][10]*q0)/2; nextP[14][2] = P[14][2] + P[14][0]*SF[4] + P[14][1]*SF[8] + P[14][3]*SF[6] + P[14][12]*SF[11] - P[14][10]*SPP[6] - (P[14][11]*q0)/2; nextP[14][3] = P[14][3] + P[14][0]*SF[5] + P[14][1]*SF[4] + P[14][2]*SF[7] - P[14][11]*SF[11] + P[14][10]*SPP[7] - (P[14][12]*q0)/2; nextP[14][4] = P[14][4] + P[14][1]*SF[1] + P[14][0]*SF[3] + P[14][2]*SPP[0] - P[14][3]*SPP[2] - P[14][13]*SPP[4]; nextP[14][5] = P[14][5] + P[14][0]*SF[2] + P[14][2]*SF[1] + P[14][3]*SF[3] - P[14][1]*SPP[0] + P[14][13]*SPP[3]; nextP[14][6] = P[14][6] + P[14][1]*SF[2] + P[14][3]*SF[1] + P[14][0]*SPP[0] - P[14][2]*SPP[1] - P[14][13]*SPP[5]; nextP[14][7] = P[14][7] + P[14][4]*dt; nextP[14][8] = P[14][8] + P[14][5]*dt; nextP[14][9] = P[14][9] + P[14][6]*dt; nextP[14][10] = P[14][10]; nextP[14][11] = P[14][11]; nextP[14][12] = P[14][12]; nextP[14][13] = P[14][13]; nextP[14][14] = P[14][14]; nextP[14][15] = P[14][15]; nextP[14][16] = P[14][16]; nextP[14][17] = P[14][17]; nextP[14][18] = P[14][18]; nextP[14][19] = P[14][19]; nextP[14][20] = P[14][20]; nextP[14][21] = P[14][21]; nextP[15][0] = P[15][0] + P[15][1]*SF[7] + P[15][2]*SF[9] + P[15][3]*SF[8] + P[15][10]*SF[11] + P[15][11]*SPP[7] + P[15][12]*SPP[6]; nextP[15][1] = P[15][1] + P[15][0]*SF[6] + P[15][2]*SF[5] + P[15][3]*SF[9] + P[15][11]*SPP[6] - P[15][12]*SPP[7] - (P[15][10]*q0)/2; nextP[15][2] = P[15][2] + P[15][0]*SF[4] + P[15][1]*SF[8] + P[15][3]*SF[6] + P[15][12]*SF[11] - P[15][10]*SPP[6] - (P[15][11]*q0)/2; nextP[15][3] = P[15][3] + P[15][0]*SF[5] + P[15][1]*SF[4] + P[15][2]*SF[7] - P[15][11]*SF[11] + P[15][10]*SPP[7] - (P[15][12]*q0)/2; nextP[15][4] = P[15][4] + P[15][1]*SF[1] + P[15][0]*SF[3] + P[15][2]*SPP[0] - P[15][3]*SPP[2] - P[15][13]*SPP[4]; nextP[15][5] = P[15][5] + P[15][0]*SF[2] + P[15][2]*SF[1] + P[15][3]*SF[3] - P[15][1]*SPP[0] + P[15][13]*SPP[3]; nextP[15][6] = P[15][6] + P[15][1]*SF[2] + P[15][3]*SF[1] + P[15][0]*SPP[0] - P[15][2]*SPP[1] - P[15][13]*SPP[5]; nextP[15][7] = P[15][7] + P[15][4]*dt; nextP[15][8] = P[15][8] + P[15][5]*dt; nextP[15][9] = P[15][9] + P[15][6]*dt; nextP[15][10] = P[15][10]; nextP[15][11] = P[15][11]; nextP[15][12] = P[15][12]; nextP[15][13] = P[15][13]; nextP[15][14] = P[15][14]; nextP[15][15] = P[15][15]; nextP[15][16] = P[15][16]; nextP[15][17] = P[15][17]; nextP[15][18] = P[15][18]; nextP[15][19] = P[15][19]; nextP[15][20] = P[15][20]; nextP[15][21] = P[15][21]; nextP[16][0] = P[16][0] + P[16][1]*SF[7] + P[16][2]*SF[9] + P[16][3]*SF[8] + P[16][10]*SF[11] + P[16][11]*SPP[7] + P[16][12]*SPP[6]; nextP[16][1] = P[16][1] + P[16][0]*SF[6] + P[16][2]*SF[5] + P[16][3]*SF[9] + P[16][11]*SPP[6] - P[16][12]*SPP[7] - (P[16][10]*q0)/2; nextP[16][2] = P[16][2] + P[16][0]*SF[4] + P[16][1]*SF[8] + P[16][3]*SF[6] + P[16][12]*SF[11] - P[16][10]*SPP[6] - (P[16][11]*q0)/2; nextP[16][3] = P[16][3] + P[16][0]*SF[5] + P[16][1]*SF[4] + P[16][2]*SF[7] - P[16][11]*SF[11] + P[16][10]*SPP[7] - (P[16][12]*q0)/2; nextP[16][4] = P[16][4] + P[16][1]*SF[1] + P[16][0]*SF[3] + P[16][2]*SPP[0] - P[16][3]*SPP[2] - P[16][13]*SPP[4]; nextP[16][5] = P[16][5] + P[16][0]*SF[2] + P[16][2]*SF[1] + P[16][3]*SF[3] - P[16][1]*SPP[0] + P[16][13]*SPP[3]; nextP[16][6] = P[16][6] + P[16][1]*SF[2] + P[16][3]*SF[1] + P[16][0]*SPP[0] - P[16][2]*SPP[1] - P[16][13]*SPP[5]; nextP[16][7] = P[16][7] + P[16][4]*dt; nextP[16][8] = P[16][8] + P[16][5]*dt; nextP[16][9] = P[16][9] + P[16][6]*dt; nextP[16][10] = P[16][10]; nextP[16][11] = P[16][11]; nextP[16][12] = P[16][12]; nextP[16][13] = P[16][13]; nextP[16][14] = P[16][14]; nextP[16][15] = P[16][15]; nextP[16][16] = P[16][16]; nextP[16][17] = P[16][17]; nextP[16][18] = P[16][18]; nextP[16][19] = P[16][19]; nextP[16][20] = P[16][20]; nextP[16][21] = P[16][21]; nextP[17][0] = P[17][0] + P[17][1]*SF[7] + P[17][2]*SF[9] + P[17][3]*SF[8] + P[17][10]*SF[11] + P[17][11]*SPP[7] + P[17][12]*SPP[6]; nextP[17][1] = P[17][1] + P[17][0]*SF[6] + P[17][2]*SF[5] + P[17][3]*SF[9] + P[17][11]*SPP[6] - P[17][12]*SPP[7] - (P[17][10]*q0)/2; nextP[17][2] = P[17][2] + P[17][0]*SF[4] + P[17][1]*SF[8] + P[17][3]*SF[6] + P[17][12]*SF[11] - P[17][10]*SPP[6] - (P[17][11]*q0)/2; nextP[17][3] = P[17][3] + P[17][0]*SF[5] + P[17][1]*SF[4] + P[17][2]*SF[7] - P[17][11]*SF[11] + P[17][10]*SPP[7] - (P[17][12]*q0)/2; nextP[17][4] = P[17][4] + P[17][1]*SF[1] + P[17][0]*SF[3] + P[17][2]*SPP[0] - P[17][3]*SPP[2] - P[17][13]*SPP[4]; nextP[17][5] = P[17][5] + P[17][0]*SF[2] + P[17][2]*SF[1] + P[17][3]*SF[3] - P[17][1]*SPP[0] + P[17][13]*SPP[3]; nextP[17][6] = P[17][6] + P[17][1]*SF[2] + P[17][3]*SF[1] + P[17][0]*SPP[0] - P[17][2]*SPP[1] - P[17][13]*SPP[5]; nextP[17][7] = P[17][7] + P[17][4]*dt; nextP[17][8] = P[17][8] + P[17][5]*dt; nextP[17][9] = P[17][9] + P[17][6]*dt; nextP[17][10] = P[17][10]; nextP[17][11] = P[17][11]; nextP[17][12] = P[17][12]; nextP[17][13] = P[17][13]; nextP[17][14] = P[17][14]; nextP[17][15] = P[17][15]; nextP[17][16] = P[17][16]; nextP[17][17] = P[17][17]; nextP[17][18] = P[17][18]; nextP[17][19] = P[17][19]; nextP[17][20] = P[17][20]; nextP[17][21] = P[17][21]; nextP[18][0] = P[18][0] + P[18][1]*SF[7] + P[18][2]*SF[9] + P[18][3]*SF[8] + P[18][10]*SF[11] + P[18][11]*SPP[7] + P[18][12]*SPP[6]; nextP[18][1] = P[18][1] + P[18][0]*SF[6] + P[18][2]*SF[5] + P[18][3]*SF[9] + P[18][11]*SPP[6] - P[18][12]*SPP[7] - (P[18][10]*q0)/2; nextP[18][2] = P[18][2] + P[18][0]*SF[4] + P[18][1]*SF[8] + P[18][3]*SF[6] + P[18][12]*SF[11] - P[18][10]*SPP[6] - (P[18][11]*q0)/2; nextP[18][3] = P[18][3] + P[18][0]*SF[5] + P[18][1]*SF[4] + P[18][2]*SF[7] - P[18][11]*SF[11] + P[18][10]*SPP[7] - (P[18][12]*q0)/2; nextP[18][4] = P[18][4] + P[18][1]*SF[1] + P[18][0]*SF[3] + P[18][2]*SPP[0] - P[18][3]*SPP[2] - P[18][13]*SPP[4]; nextP[18][5] = P[18][5] + P[18][0]*SF[2] + P[18][2]*SF[1] + P[18][3]*SF[3] - P[18][1]*SPP[0] + P[18][13]*SPP[3]; nextP[18][6] = P[18][6] + P[18][1]*SF[2] + P[18][3]*SF[1] + P[18][0]*SPP[0] - P[18][2]*SPP[1] - P[18][13]*SPP[5]; nextP[18][7] = P[18][7] + P[18][4]*dt; nextP[18][8] = P[18][8] + P[18][5]*dt; nextP[18][9] = P[18][9] + P[18][6]*dt; nextP[18][10] = P[18][10]; nextP[18][11] = P[18][11]; nextP[18][12] = P[18][12]; nextP[18][13] = P[18][13]; nextP[18][14] = P[18][14]; nextP[18][15] = P[18][15]; nextP[18][16] = P[18][16]; nextP[18][17] = P[18][17]; nextP[18][18] = P[18][18]; nextP[18][19] = P[18][19]; nextP[18][20] = P[18][20]; nextP[18][21] = P[18][21]; nextP[19][0] = P[19][0] + P[19][1]*SF[7] + P[19][2]*SF[9] + P[19][3]*SF[8] + P[19][10]*SF[11] + P[19][11]*SPP[7] + P[19][12]*SPP[6]; nextP[19][1] = P[19][1] + P[19][0]*SF[6] + P[19][2]*SF[5] + P[19][3]*SF[9] + P[19][11]*SPP[6] - P[19][12]*SPP[7] - (P[19][10]*q0)/2; nextP[19][2] = P[19][2] + P[19][0]*SF[4] + P[19][1]*SF[8] + P[19][3]*SF[6] + P[19][12]*SF[11] - P[19][10]*SPP[6] - (P[19][11]*q0)/2; nextP[19][3] = P[19][3] + P[19][0]*SF[5] + P[19][1]*SF[4] + P[19][2]*SF[7] - P[19][11]*SF[11] + P[19][10]*SPP[7] - (P[19][12]*q0)/2; nextP[19][4] = P[19][4] + P[19][1]*SF[1] + P[19][0]*SF[3] + P[19][2]*SPP[0] - P[19][3]*SPP[2] - P[19][13]*SPP[4]; nextP[19][5] = P[19][5] + P[19][0]*SF[2] + P[19][2]*SF[1] + P[19][3]*SF[3] - P[19][1]*SPP[0] + P[19][13]*SPP[3]; nextP[19][6] = P[19][6] + P[19][1]*SF[2] + P[19][3]*SF[1] + P[19][0]*SPP[0] - P[19][2]*SPP[1] - P[19][13]*SPP[5]; nextP[19][7] = P[19][7] + P[19][4]*dt; nextP[19][8] = P[19][8] + P[19][5]*dt; nextP[19][9] = P[19][9] + P[19][6]*dt; nextP[19][10] = P[19][10]; nextP[19][11] = P[19][11]; nextP[19][12] = P[19][12]; nextP[19][13] = P[19][13]; nextP[19][14] = P[19][14]; nextP[19][15] = P[19][15]; nextP[19][16] = P[19][16]; nextP[19][17] = P[19][17]; nextP[19][18] = P[19][18]; nextP[19][19] = P[19][19]; nextP[19][20] = P[19][20]; nextP[19][21] = P[19][21]; nextP[20][0] = P[20][0] + P[20][1]*SF[7] + P[20][2]*SF[9] + P[20][3]*SF[8] + P[20][10]*SF[11] + P[20][11]*SPP[7] + P[20][12]*SPP[6]; nextP[20][1] = P[20][1] + P[20][0]*SF[6] + P[20][2]*SF[5] + P[20][3]*SF[9] + P[20][11]*SPP[6] - P[20][12]*SPP[7] - (P[20][10]*q0)/2; nextP[20][2] = P[20][2] + P[20][0]*SF[4] + P[20][1]*SF[8] + P[20][3]*SF[6] + P[20][12]*SF[11] - P[20][10]*SPP[6] - (P[20][11]*q0)/2; nextP[20][3] = P[20][3] + P[20][0]*SF[5] + P[20][1]*SF[4] + P[20][2]*SF[7] - P[20][11]*SF[11] + P[20][10]*SPP[7] - (P[20][12]*q0)/2; nextP[20][4] = P[20][4] + P[20][1]*SF[1] + P[20][0]*SF[3] + P[20][2]*SPP[0] - P[20][3]*SPP[2] - P[20][13]*SPP[4]; nextP[20][5] = P[20][5] + P[20][0]*SF[2] + P[20][2]*SF[1] + P[20][3]*SF[3] - P[20][1]*SPP[0] + P[20][13]*SPP[3]; nextP[20][6] = P[20][6] + P[20][1]*SF[2] + P[20][3]*SF[1] + P[20][0]*SPP[0] - P[20][2]*SPP[1] - P[20][13]*SPP[5]; nextP[20][7] = P[20][7] + P[20][4]*dt; nextP[20][8] = P[20][8] + P[20][5]*dt; nextP[20][9] = P[20][9] + P[20][6]*dt; nextP[20][10] = P[20][10]; nextP[20][11] = P[20][11]; nextP[20][12] = P[20][12]; nextP[20][13] = P[20][13]; nextP[20][14] = P[20][14]; nextP[20][15] = P[20][15]; nextP[20][16] = P[20][16]; nextP[20][17] = P[20][17]; nextP[20][18] = P[20][18]; nextP[20][19] = P[20][19]; nextP[20][20] = P[20][20]; nextP[20][21] = P[20][21]; nextP[21][0] = P[21][0] + P[21][1]*SF[7] + P[21][2]*SF[9] + P[21][3]*SF[8] + P[21][10]*SF[11] + P[21][11]*SPP[7] + P[21][12]*SPP[6]; nextP[21][1] = P[21][1] + P[21][0]*SF[6] + P[21][2]*SF[5] + P[21][3]*SF[9] + P[21][11]*SPP[6] - P[21][12]*SPP[7] - (P[21][10]*q0)/2; nextP[21][2] = P[21][2] + P[21][0]*SF[4] + P[21][1]*SF[8] + P[21][3]*SF[6] + P[21][12]*SF[11] - P[21][10]*SPP[6] - (P[21][11]*q0)/2; nextP[21][3] = P[21][3] + P[21][0]*SF[5] + P[21][1]*SF[4] + P[21][2]*SF[7] - P[21][11]*SF[11] + P[21][10]*SPP[7] - (P[21][12]*q0)/2; nextP[21][4] = P[21][4] + P[21][1]*SF[1] + P[21][0]*SF[3] + P[21][2]*SPP[0] - P[21][3]*SPP[2] - P[21][13]*SPP[4]; nextP[21][5] = P[21][5] + P[21][0]*SF[2] + P[21][2]*SF[1] + P[21][3]*SF[3] - P[21][1]*SPP[0] + P[21][13]*SPP[3]; nextP[21][6] = P[21][6] + P[21][1]*SF[2] + P[21][3]*SF[1] + P[21][0]*SPP[0] - P[21][2]*SPP[1] - P[21][13]*SPP[5]; nextP[21][7] = P[21][7] + P[21][4]*dt; nextP[21][8] = P[21][8] + P[21][5]*dt; nextP[21][9] = P[21][9] + P[21][6]*dt; nextP[21][10] = P[21][10]; nextP[21][11] = P[21][11]; nextP[21][12] = P[21][12]; nextP[21][13] = P[21][13]; nextP[21][14] = P[21][14]; nextP[21][15] = P[21][15]; nextP[21][16] = P[21][16]; nextP[21][17] = P[21][17]; nextP[21][18] = P[21][18]; nextP[21][19] = P[21][19]; nextP[21][20] = P[21][20]; nextP[21][21] = P[21][21]; // add the general state process noise variances for (uint8_t i=0; i<= 21; i++) { nextP[i][i] = nextP[i][i] + processNoise[i]; } // if the total position variance exceeds 1e4 (100m), then stop covariance // growth by setting the predicted to the previous values // This prevent an ill conditioned matrix from occurring for long periods // without GPS if ((P[7][7] + P[8][8]) > 1e4f) { for (uint8_t i=7; i<=8; i++) { for (uint8_t j=0; j<=21; j++) { nextP[i][j] = P[i][j]; nextP[j][i] = P[j][i]; } } } // copy covariances to output and fix numerical errors CopyAndFixCovariances(); // constrain diagonals to prevent ill-conditioning ConstrainVariances(); // set the flag to indicate that covariance prediction has been performed and reset the increments used by the covariance prediction covPredStep = true; summedDelAng.zero(); summedDelVel.zero(); dt = 0.0f; perf_end(_perf_CovariancePrediction); } // fuse selected position, velocity and height measurements void NavEKF::FuseVelPosNED() { // start performance timer perf_begin(_perf_FuseVelPosNED); // health is set bad until test passed velHealth = false; posHealth = false; hgtHealth = false; // declare variables used to check measurement errors Vector3f velInnov; Vector3f velInnov1; Vector3f velInnov2; // declare variables used to control access to arrays bool fuseData[6] = {false,false,false,false,false,false}; uint8_t stateIndex; uint8_t obsIndex; // declare variables used by state and covariance update calculations float posErr; Vector6 R_OBS; // Measurement variances used for fusion Vector6 R_OBS_DATA_CHECKS; // Measurement variances used for data checks only Vector6 observation; float SK; // perform sequential fusion of GPS measurements. This assumes that the // errors in the different velocity and position components are // uncorrelated which is not true, however in the absence of covariance // data from the GPS receiver it is the only assumption we can make // so we might as well take advantage of the computational efficiencies // associated with sequential fusion if (fuseVelData || fusePosData || fuseHgtData) { // if constant position or constant velocity mode use the current states to calculate the predicted // measurement rather than use states from a previous time. We need to do this // because there may be no stored states due to lack of real measurements. if (constPosMode) { statesAtPosTime = state; } else if (constVelMode) { statesAtVelTime = state; } // set the GPS data timeout depending on whether airspeed data is present uint32_t gpsRetryTime; if (useAirspeed()) gpsRetryTime = gpsRetryTimeUseTAS; else gpsRetryTime = gpsRetryTimeNoTAS; // form the observation vector and zero velocity and horizontal position observations if in constant position mode // If in constant velocity mode, hold the last known horizontal velocity vector if (!constPosMode && !constVelMode) { observation[0] = velNED.x + gpsVelGlitchOffset.x; observation[1] = velNED.y + gpsVelGlitchOffset.y; observation[2] = velNED.z; observation[3] = gpsPosNE.x + gpsPosGlitchOffsetNE.x; observation[4] = gpsPosNE.y + gpsPosGlitchOffsetNE.y; } else if (constPosMode){ for (uint8_t i=0; i<=4; i++) observation[i] = 0.0f; } else if (constVelMode) { observation[0] = heldVelNE.x; observation[1] = heldVelNE.y; for (uint8_t i=2; i<=4; i++) observation[i] = 0.0f; } observation[5] = -hgtMea; // calculate additional error in GPS position caused by manoeuvring posErr = gpsPosVarAccScale * accNavMag; // estimate the GPS Velocity, GPS horiz position and height measurement variances. // if the GPS is able to report a speed error, we use it to adjust the observation noise for GPS velocity // otherwise we scale it using manoeuvre acceleration if (gpsSpdAccuracy > 0.0f) { // use GPS receivers reported speed accuracy - floor at value set by gps noise parameter R_OBS[0] = sq(constrain_float(gpsSpdAccuracy, _gpsHorizVelNoise, 50.0f)); R_OBS[2] = sq(constrain_float(gpsSpdAccuracy, _gpsVertVelNoise, 50.0f)); } else { // calculate additional error in GPS velocity caused by manoeuvring R_OBS[0] = sq(constrain_float(_gpsHorizVelNoise, 0.05f, 5.0f)) + sq(gpsNEVelVarAccScale * accNavMag); R_OBS[2] = sq(constrain_float(_gpsVertVelNoise, 0.05f, 5.0f)) + sq(gpsDVelVarAccScale * accNavMag); } R_OBS[1] = R_OBS[0]; R_OBS[3] = sq(constrain_float(_gpsHorizPosNoise, 0.1f, 10.0f)) + sq(posErr); R_OBS[4] = R_OBS[3]; R_OBS[5] = sq(constrain_float(_baroAltNoise, 0.1f, 10.0f)); // reduce weighting (increase observation noise) on baro if we are likely to be in ground effect if ((getTakeoffExpected() || getTouchdownExpected()) && vehicleArmed) { R_OBS[5] *= gndEffectBaroScaler; } // For data integrity checks we use the same measurement variances as used to calculate the Kalman gains for all measurements except GPS horizontal velocity // For horizontal GPs velocity we don't want the acceptance radius to increase with reported GPS accuracy so we use a value based on best GPs perfomrance // plus a margin for manoeuvres. It is better to reject GPS horizontal velocity errors early for (uint8_t i=0; i<=1; i++) R_OBS_DATA_CHECKS[i] = sq(constrain_float(_gpsHorizVelNoise, 0.05f, 5.0f)) + sq(gpsNEVelVarAccScale * accNavMag); for (uint8_t i=2; i<=5; i++) R_OBS_DATA_CHECKS[i] = R_OBS[i]; // if vertical GPS velocity data is being used, check to see if the GPS vertical velocity and barometer // innovations have the same sign and are outside limits. If so, then it is likely aliasing is affecting // the accelerometers and we should disable the GPS and barometer innovation consistency checks. if (useGpsVertVel && fuseVelData && (imuSampleTime_ms - lastHgtMeasTime) < (2 * msecHgtAvg)) { // calculate innovations for height and vertical GPS vel measurements float hgtErr = statesAtHgtTime.position.z - observation[5]; float velDErr = statesAtVelTime.velocity.z - observation[2]; // check if they are the same sign and both more than 3-sigma out of bounds if ((hgtErr*velDErr > 0.0f) && (sq(hgtErr) > 9.0f * (P[9][9] + R_OBS_DATA_CHECKS[5])) && (sq(velDErr) > 9.0f * (P[6][6] + R_OBS_DATA_CHECKS[2]))) { badIMUdata = true; } else { badIMUdata = false; } } // calculate innovations and check GPS data validity using an innovation consistency check // test position measurements if (fusePosData) { // test horizontal position measurements innovVelPos[3] = statesAtPosTime.position.x - observation[3]; innovVelPos[4] = statesAtPosTime.position.y - observation[4]; varInnovVelPos[3] = P[7][7] + R_OBS_DATA_CHECKS[3]; varInnovVelPos[4] = P[8][8] + R_OBS_DATA_CHECKS[4]; // apply an innovation consistency threshold test, but don't fail if bad IMU data // calculate max valid position innovation squared based on a maximum horizontal inertial nav accel error and GPS noise parameter // max inertial nav error is scaled with horizontal g to allow for increased errors when manoeuvring float accelScale = (1.0f + 0.1f * accNavMag); float maxPosInnov2 = sq(_gpsPosInnovGate * _gpsHorizPosNoise) + sq(0.005f * accelScale * float(_gpsGlitchAccelMax) * sq(0.001f * float(imuSampleTime_ms - lastPosPassTime))); posTestRatio = (sq(innovVelPos[3]) + sq(innovVelPos[4])) / maxPosInnov2; posHealth = ((posTestRatio < 1.0f) || badIMUdata); // declare a timeout condition if we have been too long without data or not aiding posTimeout = (((imuSampleTime_ms - lastPosPassTime) > gpsRetryTime) || PV_AidingMode == AID_NONE); // use position data if healthy, timed out, or in constant position mode if (posHealth || posTimeout || constPosMode) { posHealth = true; // only reset the failed time and do glitch timeout checks if we are doing full aiding if (PV_AidingMode == AID_ABSOLUTE) { lastPosPassTime = imuSampleTime_ms; // if timed out or outside the specified glitch radius, increment the offset applied to GPS data to compensate for large GPS position jumps if (posTimeout || (maxPosInnov2 > sq(float(_gpsGlitchRadiusMax)))) { gpsPosGlitchOffsetNE.x += innovVelPos[3]; gpsPosGlitchOffsetNE.y += innovVelPos[4]; // limit the radius of the offset and decay the offset to zero radially decayGpsOffset(); // reset the position to the current GPS position which will include the glitch correction offset ResetPosition(); // reset the velocity to the GPS velocity ResetVelocity(); // don't fuse data on this time step fusePosData = false; // record the fail time lastPosFailTime = imuSampleTime_ms; // Reset the normalised innovation to avoid false failing the bad position fusion test posTestRatio = 0.0f; } } } else { posHealth = false; } } // test velocity measurements if (fuseVelData) { // test velocity measurements uint8_t imax = 2; if (_fusionModeGPS == 1 || constVelMode) { imax = 1; } float K1 = 0; // innovation to error ratio for IMU1 float K2 = 0; // innovation to error ratio for IMU2 float innovVelSumSq = 0; // sum of squares of velocity innovations float varVelSum = 0; // sum of velocity innovation variances for (uint8_t i = 0; i<=imax; i++) { // velocity states start at index 4 stateIndex = i + 4; // calculate innovations using blended and single IMU predicted states velInnov[i] = statesAtVelTime.velocity[i] - observation[i]; // blended velInnov1[i] = statesAtVelTime.vel1[i] - observation[i]; // IMU1 velInnov2[i] = statesAtVelTime.vel2[i] - observation[i]; // IMU2 // calculate innovation variance varInnovVelPos[i] = P[stateIndex][stateIndex] + R_OBS_DATA_CHECKS[i]; // calculate error weightings for single IMU velocity states using // observation error to normalise float R_hgt; if (i == 2) { R_hgt = sq(constrain_float(_gpsVertVelNoise, 0.05f, 5.0f)); } else { R_hgt = sq(constrain_float(_gpsHorizVelNoise, 0.05f, 5.0f)); } K1 += R_hgt / (R_hgt + sq(velInnov1[i])); K2 += R_hgt / (R_hgt + sq(velInnov2[i])); // sum the innovation and innovation variances innovVelSumSq += sq(velInnov[i]); varVelSum += varInnovVelPos[i]; } // calculate weighting used by fuseVelPosNED to do IMU accel data blending // this is used to detect and compensate for aliasing errors with the accelerometers // provide for a first order lowpass filter to reduce noise on the weighting if required // set weighting to 0.5 when on ground to allow more rapid learning of bias errors without 'ringing' in bias estimates if (vehicleArmed) { IMU1_weighting = 1.0f * (K1 / (K1 + K2)) + 0.0f * IMU1_weighting; // filter currently inactive } else { IMU1_weighting = 0.5f; } // If either of the IMU's has experienced clipping within the last two filter time constants (approx 0.4 seconds) we apply a hard switch away from that sensor // to the IMU with the lower if (clipRateFilt1 > 0.1f || clipRateFilt2 > 0.1f) { if (clipRateFilt1 > clipRateFilt2) { IMU1_weighting = 0.0f; } else { IMU1_weighting = 1.0f; } } // apply an innovation consistency threshold test, but don't fail if bad IMU data // calculate the test ratio velTestRatio = innovVelSumSq / (varVelSum * sq(_gpsVelInnovGate)); // fail if the ratio is greater than 1 velHealth = ((velTestRatio < 1.0f) || badIMUdata); // declare a timeout if we have not fused velocity data for too long or not aiding velTimeout = (((imuSampleTime_ms - lastVelPassTime) > gpsRetryTime) || PV_AidingMode == AID_NONE); // if data is healthy or in constant velocity mode we fuse it if (velHealth || velTimeout || constVelMode) { velHealth = true; // restart the timeout count lastVelPassTime = imuSampleTime_ms; } else if (velTimeout && !posHealth && PV_AidingMode == AID_ABSOLUTE) { // if data is not healthy and timed out and position is unhealthy and we are using aiding, we reset the velocity, but do not fuse data on this time step ResetVelocity(); fuseVelData = false; } else { // if data is unhealthy and position is healthy, we do not fuse it velHealth = false; } } // test height measurements if (fuseHgtData) { // calculate height innovations innovVelPos[5] = statesAtHgtTime.position.z - observation[5]; varInnovVelPos[5] = P[9][9] + R_OBS_DATA_CHECKS[5]; // calculate the innovation consistency test ratio hgtTestRatio = sq(innovVelPos[5]) / (sq(_hgtInnovGate) * varInnovVelPos[5]); // fail if the ratio is > 1, but don't fail if bad IMU data hgtHealth = ((hgtTestRatio < 1.0f) || badIMUdata); hgtTimeout = (imuSampleTime_ms - lastHgtPassTime) > hgtRetryTime; // Fuse height data if healthy or timed out or in constant position mode if (hgtHealth || hgtTimeout || constPosMode) { hgtHealth = true; lastHgtPassTime = imuSampleTime_ms; // if timed out, reset the height, but do not fuse data on this time step if (hgtTimeout) { ResetHeight(); fuseHgtData = false; } } else { hgtHealth = false; } } // set range for sequential fusion of velocity and position measurements depending on which data is available and its health if (fuseVelData && useGpsVertVel && velHealth && !constPosMode && PV_AidingMode == AID_ABSOLUTE) { fuseData[0] = true; fuseData[1] = true; fuseData[2] = true; } if (fuseVelData && _fusionModeGPS == 1 && velHealth && !constPosMode && PV_AidingMode == AID_ABSOLUTE) { fuseData[0] = true; fuseData[1] = true; } if ((fusePosData && posHealth && PV_AidingMode == AID_ABSOLUTE) || constPosMode) { fuseData[3] = true; fuseData[4] = true; } if ((fuseHgtData && hgtHealth) || constPosMode) { fuseData[5] = true; } if (constVelMode) { fuseData[0] = true; fuseData[1] = true; } // fuse measurements sequentially for (obsIndex=0; obsIndex<=5; obsIndex++) { if (fuseData[obsIndex]) { stateIndex = 4 + obsIndex; // calculate the measurement innovation, using states from a different time coordinate if fusing height data // adjust scaling on GPS measurement noise variances if not enough satellites if (obsIndex <= 2) { innovVelPos[obsIndex] = statesAtVelTime.velocity[obsIndex] - observation[obsIndex]; R_OBS[obsIndex] *= sq(gpsNoiseScaler); } else if (obsIndex == 3 || obsIndex == 4) { innovVelPos[obsIndex] = statesAtPosTime.position[obsIndex-3] - observation[obsIndex]; R_OBS[obsIndex] *= sq(gpsNoiseScaler); } else { innovVelPos[obsIndex] = statesAtHgtTime.position[obsIndex-3] - observation[obsIndex]; if (obsIndex == 5) { static const float gndMaxBaroErr = 4.0f; static const float gndBaroInnovFloor = -0.5f; if(getTouchdownExpected()) { // when a touchdown is expected, floor the barometer innovation at gndBaroInnovFloor // constrain the correction between 0 and gndBaroInnovFloor+gndMaxBaroErr // this function looks like this: // |/ //---------|--------- // ____/| // / | // / | innovVelPos[5] += constrain_float(-innovVelPos[5]+gndBaroInnovFloor, 0.0f, gndBaroInnovFloor+gndMaxBaroErr); } } } // calculate the Kalman gain and calculate innovation variances varInnovVelPos[obsIndex] = P[stateIndex][stateIndex] + R_OBS[obsIndex]; SK = 1.0f/varInnovVelPos[obsIndex]; for (uint8_t i= 0; i<=12; i++) { Kfusion[i] = P[i][stateIndex]*SK; } // Only height and height rate observations are used to update z accel bias estimate // Protect Kalman gain from ill-conditioning // Don't update Z accel bias if off-level by greater than 60 degrees to avoid scale factor error effects // Don't update if we are taking off with ground effect if ((obsIndex == 5 || obsIndex == 2) && prevTnb.c.z > 0.5f && !getTakeoffExpected()) { Kfusion[13] = constrain_float(P[13][stateIndex]*SK,-1.0f,0.0f); } else { Kfusion[13] = 0.0f; } // inhibit wind state estimation by setting Kalman gains to zero if (!inhibitWindStates) { Kfusion[14] = P[14][stateIndex]*SK; Kfusion[15] = P[15][stateIndex]*SK; } else { Kfusion[14] = 0.0f; Kfusion[15] = 0.0f; } // inhibit magnetic field state estimation by setting Kalman gains to zero if (!inhibitMagStates) { for (uint8_t i = 16; i<=21; i++) { Kfusion[i] = P[i][stateIndex]*SK; } } else { for (uint8_t i = 16; i<=21; i++) { Kfusion[i] = 0.0f; } } // Set the Kalman gain values for the single IMU states Kfusion[26] = Kfusion[9]; // IMU1 posD Kfusion[30] = Kfusion[9]; // IMU2 posD for (uint8_t i = 0; i<=2; i++) { Kfusion[i+23] = Kfusion[i+4]; // IMU1 velNED Kfusion[i+27] = Kfusion[i+4]; // IMU2 velNED } // Don't update Z accel bias values if we have clipping // we achieve this by setting the corresponding Kalman gains to zero if (clipRateFilt1 < 0.1f && clipRateFilt2 < 0.1f) { // no clipping Kfusion[22] = Kfusion[13]; } else if (clipRateFilt1 >0.1f && clipRateFilt2 > 0.1f) { // both clipping; Kfusion[22] = Kfusion[13] = 0.0f; } else if (clipRateFilt1 > clipRateFilt2) { // IMU1 clipping Kfusion[22] = Kfusion[13]; Kfusion[13] = 0.0f; } else { // IMU2 clipping Kfusion[22] = 0.0f; } // Correct states that have been predicted using single (not blended) IMU data if (obsIndex == 5){ // Calculate height measurement innovations using single IMU states float hgtInnov1 = statesAtHgtTime.posD1 - observation[obsIndex]; float hgtInnov2 = statesAtHgtTime.posD2 - observation[obsIndex]; if (vehicleArmed) { // Correct single IMU prediction states using height measurement, limiting rate of change of bias to 0.005 m/s3 float correctionLimit = 0.005f * dtIMUavg * dtVelPos; state.accel_zbias1 -= constrain_float(Kfusion[13] * hgtInnov1, -correctionLimit, correctionLimit); // IMU1 Z accel bias state.accel_zbias2 -= constrain_float(Kfusion[22] * hgtInnov2, -correctionLimit, correctionLimit); // IMU2 Z accel bias } else { // When disarmed, do not rate limit accel bias learning state.accel_zbias1 -= Kfusion[13] * hgtInnov1; // IMU1 Z accel bias state.accel_zbias2 -= Kfusion[22] * hgtInnov2; // IMU2 Z accel bias } for (uint8_t i = 23; i<=26; i++) { states[i] = states[i] - Kfusion[i] * hgtInnov1; // IMU1 velNED,posD } for (uint8_t i = 27; i<=30; i++) { states[i] = states[i] - Kfusion[i] * hgtInnov2; // IMU2 velNED,posD } } else if (obsIndex == 0 || obsIndex == 1 || obsIndex == 2) { // Correct single IMU prediction states using velocity measurements for (uint8_t i = 23; i<=26; i++) { states[i] = states[i] - Kfusion[i] * velInnov1[obsIndex]; // IMU1 velNED,posD } for (uint8_t i = 27; i<=30; i++) { states[i] = states[i] - Kfusion[i] * velInnov2[obsIndex]; // IMU2 velNED,posD } } // calculate state corrections and re-normalise the quaternions for states predicted using the blended IMU data // attitude, velocity and position corrections are spread across multiple prediction cycles between now // and the anticipated time for the next measurement. // Don't spread quaternion corrections if total angle change across predicted interval is going to exceed 0.1 rad // Don't apply corrections to Z bias state as this has been done already as part of the single IMU calculations bool highRates = ((gpsUpdateCountMax * correctedDelAng.length()) > 0.1f); for (uint8_t i = 0; i<=21; i++) { if (i != 13) { if ((i <= 3 && highRates) || i >= 10 || constPosMode || constVelMode) { states[i] = states[i] - Kfusion[i] * innovVelPos[obsIndex]; } else { if (obsIndex == 5) { hgtIncrStateDelta[i] -= Kfusion[i] * innovVelPos[obsIndex] * hgtUpdateCountMaxInv; } else { gpsIncrStateDelta[i] -= Kfusion[i] * innovVelPos[obsIndex] * gpsUpdateCountMaxInv; } } } } state.quat.normalize(); // update the covariance - take advantage of direct observation of a single state at index = stateIndex to reduce computations // this is a numerically optimised implementation of standard equation P = (I - K*H)*P; for (uint8_t i= 0; i<=21; i++) { for (uint8_t j= 0; j<=21; j++) { KHP[i][j] = Kfusion[i] * P[stateIndex][j]; } } for (uint8_t i= 0; i<=21; i++) { for (uint8_t j= 0; j<=21; j++) { P[i][j] = P[i][j] - KHP[i][j]; } } } } } // force the covariance matrix to be symmetrical and limit the variances to prevent ill-condiioning. ForceSymmetry(); ConstrainVariances(); // stop performance timer perf_end(_perf_FuseVelPosNED); } // fuse magnetometer measurements and apply innovation consistency checks // fuse each axis on consecutive time steps to spread computional load void NavEKF::FuseMagnetometer() { // declarations ftype &q0 = mag_state.q0; ftype &q1 = mag_state.q1; ftype &q2 = mag_state.q2; ftype &q3 = mag_state.q3; ftype &magN = mag_state.magN; ftype &magE = mag_state.magE; ftype &magD = mag_state.magD; ftype &magXbias = mag_state.magXbias; ftype &magYbias = mag_state.magYbias; ftype &magZbias = mag_state.magZbias; uint8_t &obsIndex = mag_state.obsIndex; Matrix3f &DCM = mag_state.DCM; Vector3f &MagPred = mag_state.MagPred; ftype &R_MAG = mag_state.R_MAG; ftype *SH_MAG = &mag_state.SH_MAG[0]; Vector22 H_MAG; Vector6 SK_MX; Vector6 SK_MY; Vector6 SK_MZ; // perform sequential fusion of magnetometer measurements. // this assumes that the errors in the different components are // uncorrelated which is not true, however in the absence of covariance // data fit is the only assumption we can make // so we might as well take advantage of the computational efficiencies // associated with sequential fusion // calculate observation jacobians and Kalman gains if (obsIndex == 0) { // copy required states to local variable names q0 = statesAtMagMeasTime.quat[0]; q1 = statesAtMagMeasTime.quat[1]; q2 = statesAtMagMeasTime.quat[2]; q3 = statesAtMagMeasTime.quat[3]; magN = statesAtMagMeasTime.earth_magfield[0]; magE = statesAtMagMeasTime.earth_magfield[1]; magD = statesAtMagMeasTime.earth_magfield[2]; magXbias = statesAtMagMeasTime.body_magfield[0]; magYbias = statesAtMagMeasTime.body_magfield[1]; magZbias = statesAtMagMeasTime.body_magfield[2]; // rotate predicted earth components into body axes and calculate // predicted measurements DCM[0][0] = q0*q0 + q1*q1 - q2*q2 - q3*q3; DCM[0][1] = 2*(q1*q2 + q0*q3); DCM[0][2] = 2*(q1*q3-q0*q2); DCM[1][0] = 2*(q1*q2 - q0*q3); DCM[1][1] = q0*q0 - q1*q1 + q2*q2 - q3*q3; DCM[1][2] = 2*(q2*q3 + q0*q1); DCM[2][0] = 2*(q1*q3 + q0*q2); DCM[2][1] = 2*(q2*q3 - q0*q1); DCM[2][2] = q0*q0 - q1*q1 - q2*q2 + q3*q3; MagPred[0] = DCM[0][0]*magN + DCM[0][1]*magE + DCM[0][2]*magD + magXbias; MagPred[1] = DCM[1][0]*magN + DCM[1][1]*magE + DCM[1][2]*magD + magYbias; MagPred[2] = DCM[2][0]*magN + DCM[2][1]*magE + DCM[2][2]*magD + magZbias; // scale magnetometer observation error with total angular rate R_MAG = sq(constrain_float(_magNoise, 0.01f, 0.5f)) + sq(magVarRateScale*dAngIMU.length() / dtIMUavg); // calculate observation jacobians SH_MAG[0] = 2*magD*q3 + 2*magE*q2 + 2*magN*q1; SH_MAG[1] = 2*magD*q0 - 2*magE*q1 + 2*magN*q2; SH_MAG[2] = 2*magD*q1 + 2*magE*q0 - 2*magN*q3; SH_MAG[3] = sq(q3); SH_MAG[4] = sq(q2); SH_MAG[5] = sq(q1); SH_MAG[6] = sq(q0); SH_MAG[7] = 2*magN*q0; SH_MAG[8] = 2*magE*q3; for (uint8_t i=0; i<=21; i++) H_MAG[i] = 0; H_MAG[0] = SH_MAG[7] + SH_MAG[8] - 2*magD*q2; H_MAG[1] = SH_MAG[0]; H_MAG[2] = 2*magE*q1 - 2*magD*q0 - 2*magN*q2; H_MAG[3] = SH_MAG[2]; H_MAG[16] = SH_MAG[5] - SH_MAG[4] - SH_MAG[3] + SH_MAG[6]; H_MAG[17] = 2*q0*q3 + 2*q1*q2; H_MAG[18] = 2*q1*q3 - 2*q0*q2; H_MAG[19] = 1; // calculate Kalman gain float temp = (P[19][19] + R_MAG + P[1][19]*SH_MAG[0] + P[3][19]*SH_MAG[2] - P[16][19]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) - (2*magD*q0 - 2*magE*q1 + 2*magN*q2)*(P[19][2] + P[1][2]*SH_MAG[0] + P[3][2]*SH_MAG[2] - P[16][2]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[17][2]*(2*q0*q3 + 2*q1*q2) - P[18][2]*(2*q0*q2 - 2*q1*q3) - P[2][2]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + P[0][2]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + (SH_MAG[7] + SH_MAG[8] - 2*magD*q2)*(P[19][0] + P[1][0]*SH_MAG[0] + P[3][0]*SH_MAG[2] - P[16][0]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[17][0]*(2*q0*q3 + 2*q1*q2) - P[18][0]*(2*q0*q2 - 2*q1*q3) - P[2][0]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + P[0][0]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + SH_MAG[0]*(P[19][1] + P[1][1]*SH_MAG[0] + P[3][1]*SH_MAG[2] - P[16][1]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[17][1]*(2*q0*q3 + 2*q1*q2) - P[18][1]*(2*q0*q2 - 2*q1*q3) - P[2][1]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + P[0][1]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + SH_MAG[2]*(P[19][3] + P[1][3]*SH_MAG[0] + P[3][3]*SH_MAG[2] - P[16][3]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[17][3]*(2*q0*q3 + 2*q1*q2) - P[18][3]*(2*q0*q2 - 2*q1*q3) - P[2][3]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + P[0][3]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) - (SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6])*(P[19][16] + P[1][16]*SH_MAG[0] + P[3][16]*SH_MAG[2] - P[16][16]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[17][16]*(2*q0*q3 + 2*q1*q2) - P[18][16]*(2*q0*q2 - 2*q1*q3) - P[2][16]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + P[0][16]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + P[17][19]*(2*q0*q3 + 2*q1*q2) - P[18][19]*(2*q0*q2 - 2*q1*q3) - P[2][19]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + (2*q0*q3 + 2*q1*q2)*(P[19][17] + P[1][17]*SH_MAG[0] + P[3][17]*SH_MAG[2] - P[16][17]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[17][17]*(2*q0*q3 + 2*q1*q2) - P[18][17]*(2*q0*q2 - 2*q1*q3) - P[2][17]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + P[0][17]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) - (2*q0*q2 - 2*q1*q3)*(P[19][18] + P[1][18]*SH_MAG[0] + P[3][18]*SH_MAG[2] - P[16][18]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[17][18]*(2*q0*q3 + 2*q1*q2) - P[18][18]*(2*q0*q2 - 2*q1*q3) - P[2][18]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + P[0][18]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + P[0][19]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)); if (temp >= R_MAG) { SK_MX[0] = 1.0f / temp; faultStatus.bad_xmag = false; } else { // the calculation is badly conditioned, so we cannot perform fusion on this step // we reset the covariance matrix and try again next measurement CovarianceInit(); obsIndex = 1; faultStatus.bad_xmag = true; return; } SK_MX[1] = SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]; SK_MX[2] = 2*magD*q0 - 2*magE*q1 + 2*magN*q2; SK_MX[3] = SH_MAG[7] + SH_MAG[8] - 2*magD*q2; SK_MX[4] = 2*q0*q2 - 2*q1*q3; SK_MX[5] = 2*q0*q3 + 2*q1*q2; Kfusion[0] = SK_MX[0]*(P[0][19] + P[0][1]*SH_MAG[0] + P[0][3]*SH_MAG[2] + P[0][0]*SK_MX[3] - P[0][2]*SK_MX[2] - P[0][16]*SK_MX[1] + P[0][17]*SK_MX[5] - P[0][18]*SK_MX[4]); Kfusion[1] = SK_MX[0]*(P[1][19] + P[1][1]*SH_MAG[0] + P[1][3]*SH_MAG[2] + P[1][0]*SK_MX[3] - P[1][2]*SK_MX[2] - P[1][16]*SK_MX[1] + P[1][17]*SK_MX[5] - P[1][18]*SK_MX[4]); Kfusion[2] = SK_MX[0]*(P[2][19] + P[2][1]*SH_MAG[0] + P[2][3]*SH_MAG[2] + P[2][0]*SK_MX[3] - P[2][2]*SK_MX[2] - P[2][16]*SK_MX[1] + P[2][17]*SK_MX[5] - P[2][18]*SK_MX[4]); Kfusion[3] = SK_MX[0]*(P[3][19] + P[3][1]*SH_MAG[0] + P[3][3]*SH_MAG[2] + P[3][0]*SK_MX[3] - P[3][2]*SK_MX[2] - P[3][16]*SK_MX[1] + P[3][17]*SK_MX[5] - P[3][18]*SK_MX[4]); Kfusion[4] = SK_MX[0]*(P[4][19] + P[4][1]*SH_MAG[0] + P[4][3]*SH_MAG[2] + P[4][0]*SK_MX[3] - P[4][2]*SK_MX[2] - P[4][16]*SK_MX[1] + P[4][17]*SK_MX[5] - P[4][18]*SK_MX[4]); Kfusion[5] = SK_MX[0]*(P[5][19] + P[5][1]*SH_MAG[0] + P[5][3]*SH_MAG[2] + P[5][0]*SK_MX[3] - P[5][2]*SK_MX[2] - P[5][16]*SK_MX[1] + P[5][17]*SK_MX[5] - P[5][18]*SK_MX[4]); Kfusion[6] = SK_MX[0]*(P[6][19] + P[6][1]*SH_MAG[0] + P[6][3]*SH_MAG[2] + P[6][0]*SK_MX[3] - P[6][2]*SK_MX[2] - P[6][16]*SK_MX[1] + P[6][17]*SK_MX[5] - P[6][18]*SK_MX[4]); Kfusion[7] = SK_MX[0]*(P[7][19] + P[7][1]*SH_MAG[0] + P[7][3]*SH_MAG[2] + P[7][0]*SK_MX[3] - P[7][2]*SK_MX[2] - P[7][16]*SK_MX[1] + P[7][17]*SK_MX[5] - P[7][18]*SK_MX[4]); Kfusion[8] = SK_MX[0]*(P[8][19] + P[8][1]*SH_MAG[0] + P[8][3]*SH_MAG[2] + P[8][0]*SK_MX[3] - P[8][2]*SK_MX[2] - P[8][16]*SK_MX[1] + P[8][17]*SK_MX[5] - P[8][18]*SK_MX[4]); Kfusion[9] = SK_MX[0]*(P[9][19] + P[9][1]*SH_MAG[0] + P[9][3]*SH_MAG[2] + P[9][0]*SK_MX[3] - P[9][2]*SK_MX[2] - P[9][16]*SK_MX[1] + P[9][17]*SK_MX[5] - P[9][18]*SK_MX[4]); Kfusion[10] = SK_MX[0]*(P[10][19] + P[10][1]*SH_MAG[0] + P[10][3]*SH_MAG[2] + P[10][0]*SK_MX[3] - P[10][2]*SK_MX[2] - P[10][16]*SK_MX[1] + P[10][17]*SK_MX[5] - P[10][18]*SK_MX[4]); Kfusion[11] = SK_MX[0]*(P[11][19] + P[11][1]*SH_MAG[0] + P[11][3]*SH_MAG[2] + P[11][0]*SK_MX[3] - P[11][2]*SK_MX[2] - P[11][16]*SK_MX[1] + P[11][17]*SK_MX[5] - P[11][18]*SK_MX[4]); Kfusion[12] = SK_MX[0]*(P[12][19] + P[12][1]*SH_MAG[0] + P[12][3]*SH_MAG[2] + P[12][0]*SK_MX[3] - P[12][2]*SK_MX[2] - P[12][16]*SK_MX[1] + P[12][17]*SK_MX[5] - P[12][18]*SK_MX[4]); // this term has been zeroed to improve stability of the Z accel bias Kfusion[13] = 0.0f;//SK_MX[0]*(P[13][19] + P[13][1]*SH_MAG[0] + P[13][3]*SH_MAG[2] + P[13][0]*SK_MX[3] - P[13][2]*SK_MX[2] - P[13][16]*SK_MX[1] + P[13][17]*SK_MX[5] - P[13][18]*SK_MX[4]); // zero Kalman gains to inhibit wind state estimation if (!inhibitWindStates) { Kfusion[14] = SK_MX[0]*(P[14][19] + P[14][1]*SH_MAG[0] + P[14][3]*SH_MAG[2] + P[14][0]*SK_MX[3] - P[14][2]*SK_MX[2] - P[14][16]*SK_MX[1] + P[14][17]*SK_MX[5] - P[14][18]*SK_MX[4]); Kfusion[15] = SK_MX[0]*(P[15][19] + P[15][1]*SH_MAG[0] + P[15][3]*SH_MAG[2] + P[15][0]*SK_MX[3] - P[15][2]*SK_MX[2] - P[15][16]*SK_MX[1] + P[15][17]*SK_MX[5] - P[15][18]*SK_MX[4]); } else { Kfusion[14] = 0.0f; Kfusion[15] = 0.0f; } // zero Kalman gains to inhibit magnetic field state estimation if (!inhibitMagStates) { Kfusion[16] = SK_MX[0]*(P[16][19] + P[16][1]*SH_MAG[0] + P[16][3]*SH_MAG[2] + P[16][0]*SK_MX[3] - P[16][2]*SK_MX[2] - P[16][16]*SK_MX[1] + P[16][17]*SK_MX[5] - P[16][18]*SK_MX[4]); Kfusion[17] = SK_MX[0]*(P[17][19] + P[17][1]*SH_MAG[0] + P[17][3]*SH_MAG[2] + P[17][0]*SK_MX[3] - P[17][2]*SK_MX[2] - P[17][16]*SK_MX[1] + P[17][17]*SK_MX[5] - P[17][18]*SK_MX[4]); Kfusion[18] = SK_MX[0]*(P[18][19] + P[18][1]*SH_MAG[0] + P[18][3]*SH_MAG[2] + P[18][0]*SK_MX[3] - P[18][2]*SK_MX[2] - P[18][16]*SK_MX[1] + P[18][17]*SK_MX[5] - P[18][18]*SK_MX[4]); Kfusion[19] = SK_MX[0]*(P[19][19] + P[19][1]*SH_MAG[0] + P[19][3]*SH_MAG[2] + P[19][0]*SK_MX[3] - P[19][2]*SK_MX[2] - P[19][16]*SK_MX[1] + P[19][17]*SK_MX[5] - P[19][18]*SK_MX[4]); Kfusion[20] = SK_MX[0]*(P[20][19] + P[20][1]*SH_MAG[0] + P[20][3]*SH_MAG[2] + P[20][0]*SK_MX[3] - P[20][2]*SK_MX[2] - P[20][16]*SK_MX[1] + P[20][17]*SK_MX[5] - P[20][18]*SK_MX[4]); Kfusion[21] = SK_MX[0]*(P[21][19] + P[21][1]*SH_MAG[0] + P[21][3]*SH_MAG[2] + P[21][0]*SK_MX[3] - P[21][2]*SK_MX[2] - P[21][16]*SK_MX[1] + P[21][17]*SK_MX[5] - P[21][18]*SK_MX[4]); } else { for (uint8_t i=16; i<=21; i++) { Kfusion[i] = 0.0f; } } // calculate the observation innovation variance varInnovMag[0] = 1.0f/SK_MX[0]; // reset the observation index to 0 (we start by fusing the X measurement) obsIndex = 0; // set flags to indicate to other processes that fusion has been performed and is required on the next frame // this can be used by other fusion processes to avoid fusing on the same frame as this expensive step magFusePerformed = true; magFuseRequired = true; } else if (obsIndex == 1) // we are now fusing the Y measurement { // calculate observation jacobians for (uint8_t i=0; i<=21; i++) H_MAG[i] = 0; H_MAG[0] = SH_MAG[2]; H_MAG[1] = SH_MAG[1]; H_MAG[2] = SH_MAG[0]; H_MAG[3] = 2*magD*q2 - SH_MAG[8] - SH_MAG[7]; H_MAG[16] = 2*q1*q2 - 2*q0*q3; H_MAG[17] = SH_MAG[4] - SH_MAG[3] - SH_MAG[5] + SH_MAG[6]; H_MAG[18] = 2*q0*q1 + 2*q2*q3; H_MAG[20] = 1; // calculate Kalman gain float temp = (P[20][20] + R_MAG + P[0][20]*SH_MAG[2] + P[1][20]*SH_MAG[1] + P[2][20]*SH_MAG[0] - P[17][20]*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - (2*q0*q3 - 2*q1*q2)*(P[20][16] + P[0][16]*SH_MAG[2] + P[1][16]*SH_MAG[1] + P[2][16]*SH_MAG[0] - P[17][16]*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P[16][16]*(2*q0*q3 - 2*q1*q2) + P[18][16]*(2*q0*q1 + 2*q2*q3) - P[3][16]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + (2*q0*q1 + 2*q2*q3)*(P[20][18] + P[0][18]*SH_MAG[2] + P[1][18]*SH_MAG[1] + P[2][18]*SH_MAG[0] - P[17][18]*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P[16][18]*(2*q0*q3 - 2*q1*q2) + P[18][18]*(2*q0*q1 + 2*q2*q3) - P[3][18]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) - (SH_MAG[7] + SH_MAG[8] - 2*magD*q2)*(P[20][3] + P[0][3]*SH_MAG[2] + P[1][3]*SH_MAG[1] + P[2][3]*SH_MAG[0] - P[17][3]*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P[16][3]*(2*q0*q3 - 2*q1*q2) + P[18][3]*(2*q0*q1 + 2*q2*q3) - P[3][3]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) - P[16][20]*(2*q0*q3 - 2*q1*q2) + P[18][20]*(2*q0*q1 + 2*q2*q3) + SH_MAG[2]*(P[20][0] + P[0][0]*SH_MAG[2] + P[1][0]*SH_MAG[1] + P[2][0]*SH_MAG[0] - P[17][0]*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P[16][0]*(2*q0*q3 - 2*q1*q2) + P[18][0]*(2*q0*q1 + 2*q2*q3) - P[3][0]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + SH_MAG[1]*(P[20][1] + P[0][1]*SH_MAG[2] + P[1][1]*SH_MAG[1] + P[2][1]*SH_MAG[0] - P[17][1]*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P[16][1]*(2*q0*q3 - 2*q1*q2) + P[18][1]*(2*q0*q1 + 2*q2*q3) - P[3][1]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + SH_MAG[0]*(P[20][2] + P[0][2]*SH_MAG[2] + P[1][2]*SH_MAG[1] + P[2][2]*SH_MAG[0] - P[17][2]*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P[16][2]*(2*q0*q3 - 2*q1*q2) + P[18][2]*(2*q0*q1 + 2*q2*q3) - P[3][2]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) - (SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6])*(P[20][17] + P[0][17]*SH_MAG[2] + P[1][17]*SH_MAG[1] + P[2][17]*SH_MAG[0] - P[17][17]*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P[16][17]*(2*q0*q3 - 2*q1*q2) + P[18][17]*(2*q0*q1 + 2*q2*q3) - P[3][17]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) - P[3][20]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)); if (temp >= R_MAG) { SK_MY[0] = 1.0f / temp; faultStatus.bad_ymag = false; } else { // the calculation is badly conditioned, so we cannot perform fusion on this step // we reset the covariance matrix and try again next measurement CovarianceInit(); obsIndex = 2; faultStatus.bad_ymag = true; return; } SK_MY[1] = SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]; SK_MY[2] = SH_MAG[7] + SH_MAG[8] - 2*magD*q2; SK_MY[3] = 2*q0*q3 - 2*q1*q2; SK_MY[4] = 2*q0*q1 + 2*q2*q3; Kfusion[0] = SK_MY[0]*(P[0][20] + P[0][0]*SH_MAG[2] + P[0][1]*SH_MAG[1] + P[0][2]*SH_MAG[0] - P[0][3]*SK_MY[2] - P[0][17]*SK_MY[1] - P[0][16]*SK_MY[3] + P[0][18]*SK_MY[4]); Kfusion[1] = SK_MY[0]*(P[1][20] + P[1][0]*SH_MAG[2] + P[1][1]*SH_MAG[1] + P[1][2]*SH_MAG[0] - P[1][3]*SK_MY[2] - P[1][17]*SK_MY[1] - P[1][16]*SK_MY[3] + P[1][18]*SK_MY[4]); Kfusion[2] = SK_MY[0]*(P[2][20] + P[2][0]*SH_MAG[2] + P[2][1]*SH_MAG[1] + P[2][2]*SH_MAG[0] - P[2][3]*SK_MY[2] - P[2][17]*SK_MY[1] - P[2][16]*SK_MY[3] + P[2][18]*SK_MY[4]); Kfusion[3] = SK_MY[0]*(P[3][20] + P[3][0]*SH_MAG[2] + P[3][1]*SH_MAG[1] + P[3][2]*SH_MAG[0] - P[3][3]*SK_MY[2] - P[3][17]*SK_MY[1] - P[3][16]*SK_MY[3] + P[3][18]*SK_MY[4]); Kfusion[4] = SK_MY[0]*(P[4][20] + P[4][0]*SH_MAG[2] + P[4][1]*SH_MAG[1] + P[4][2]*SH_MAG[0] - P[4][3]*SK_MY[2] - P[4][17]*SK_MY[1] - P[4][16]*SK_MY[3] + P[4][18]*SK_MY[4]); Kfusion[5] = SK_MY[0]*(P[5][20] + P[5][0]*SH_MAG[2] + P[5][1]*SH_MAG[1] + P[5][2]*SH_MAG[0] - P[5][3]*SK_MY[2] - P[5][17]*SK_MY[1] - P[5][16]*SK_MY[3] + P[5][18]*SK_MY[4]); Kfusion[6] = SK_MY[0]*(P[6][20] + P[6][0]*SH_MAG[2] + P[6][1]*SH_MAG[1] + P[6][2]*SH_MAG[0] - P[6][3]*SK_MY[2] - P[6][17]*SK_MY[1] - P[6][16]*SK_MY[3] + P[6][18]*SK_MY[4]); Kfusion[7] = SK_MY[0]*(P[7][20] + P[7][0]*SH_MAG[2] + P[7][1]*SH_MAG[1] + P[7][2]*SH_MAG[0] - P[7][3]*SK_MY[2] - P[7][17]*SK_MY[1] - P[7][16]*SK_MY[3] + P[7][18]*SK_MY[4]); Kfusion[8] = SK_MY[0]*(P[8][20] + P[8][0]*SH_MAG[2] + P[8][1]*SH_MAG[1] + P[8][2]*SH_MAG[0] - P[8][3]*SK_MY[2] - P[8][17]*SK_MY[1] - P[8][16]*SK_MY[3] + P[8][18]*SK_MY[4]); Kfusion[9] = SK_MY[0]*(P[9][20] + P[9][0]*SH_MAG[2] + P[9][1]*SH_MAG[1] + P[9][2]*SH_MAG[0] - P[9][3]*SK_MY[2] - P[9][17]*SK_MY[1] - P[9][16]*SK_MY[3] + P[9][18]*SK_MY[4]); Kfusion[10] = SK_MY[0]*(P[10][20] + P[10][0]*SH_MAG[2] + P[10][1]*SH_MAG[1] + P[10][2]*SH_MAG[0] - P[10][3]*SK_MY[2] - P[10][17]*SK_MY[1] - P[10][16]*SK_MY[3] + P[10][18]*SK_MY[4]); Kfusion[11] = SK_MY[0]*(P[11][20] + P[11][0]*SH_MAG[2] + P[11][1]*SH_MAG[1] + P[11][2]*SH_MAG[0] - P[11][3]*SK_MY[2] - P[11][17]*SK_MY[1] - P[11][16]*SK_MY[3] + P[11][18]*SK_MY[4]); Kfusion[12] = SK_MY[0]*(P[12][20] + P[12][0]*SH_MAG[2] + P[12][1]*SH_MAG[1] + P[12][2]*SH_MAG[0] - P[12][3]*SK_MY[2] - P[12][17]*SK_MY[1] - P[12][16]*SK_MY[3] + P[12][18]*SK_MY[4]); // this term has been zeroed to improve stability of the Z accel bias Kfusion[13] = 0.0f;//SK_MY[0]*(P[13][20] + P[13][0]*SH_MAG[2] + P[13][1]*SH_MAG[1] + P[13][2]*SH_MAG[0] - P[13][3]*SK_MY[2] - P[13][17]*SK_MY[1] - P[13][16]*SK_MY[3] + P[13][18]*SK_MY[4]); // zero Kalman gains to inhibit wind state estimation if (!inhibitWindStates) { Kfusion[14] = SK_MY[0]*(P[14][20] + P[14][0]*SH_MAG[2] + P[14][1]*SH_MAG[1] + P[14][2]*SH_MAG[0] - P[14][3]*SK_MY[2] - P[14][17]*SK_MY[1] - P[14][16]*SK_MY[3] + P[14][18]*SK_MY[4]); Kfusion[15] = SK_MY[0]*(P[15][20] + P[15][0]*SH_MAG[2] + P[15][1]*SH_MAG[1] + P[15][2]*SH_MAG[0] - P[15][3]*SK_MY[2] - P[15][17]*SK_MY[1] - P[15][16]*SK_MY[3] + P[15][18]*SK_MY[4]); } else { Kfusion[14] = 0.0f; Kfusion[15] = 0.0f; } // zero Kalman gains to inhibit magnetic field state estimation if (!inhibitMagStates) { Kfusion[16] = SK_MY[0]*(P[16][20] + P[16][0]*SH_MAG[2] + P[16][1]*SH_MAG[1] + P[16][2]*SH_MAG[0] - P[16][3]*SK_MY[2] - P[16][17]*SK_MY[1] - P[16][16]*SK_MY[3] + P[16][18]*SK_MY[4]); Kfusion[17] = SK_MY[0]*(P[17][20] + P[17][0]*SH_MAG[2] + P[17][1]*SH_MAG[1] + P[17][2]*SH_MAG[0] - P[17][3]*SK_MY[2] - P[17][17]*SK_MY[1] - P[17][16]*SK_MY[3] + P[17][18]*SK_MY[4]); Kfusion[18] = SK_MY[0]*(P[18][20] + P[18][0]*SH_MAG[2] + P[18][1]*SH_MAG[1] + P[18][2]*SH_MAG[0] - P[18][3]*SK_MY[2] - P[18][17]*SK_MY[1] - P[18][16]*SK_MY[3] + P[18][18]*SK_MY[4]); Kfusion[19] = SK_MY[0]*(P[19][20] + P[19][0]*SH_MAG[2] + P[19][1]*SH_MAG[1] + P[19][2]*SH_MAG[0] - P[19][3]*SK_MY[2] - P[19][17]*SK_MY[1] - P[19][16]*SK_MY[3] + P[19][18]*SK_MY[4]); Kfusion[20] = SK_MY[0]*(P[20][20] + P[20][0]*SH_MAG[2] + P[20][1]*SH_MAG[1] + P[20][2]*SH_MAG[0] - P[20][3]*SK_MY[2] - P[20][17]*SK_MY[1] - P[20][16]*SK_MY[3] + P[20][18]*SK_MY[4]); Kfusion[21] = SK_MY[0]*(P[21][20] + P[21][0]*SH_MAG[2] + P[21][1]*SH_MAG[1] + P[21][2]*SH_MAG[0] - P[21][3]*SK_MY[2] - P[21][17]*SK_MY[1] - P[21][16]*SK_MY[3] + P[21][18]*SK_MY[4]); } else { for (uint8_t i=16; i<=21; i++) { Kfusion[i] = 0.0f; } } // calculate the observation innovation variance varInnovMag[1] = 1.0f/SK_MY[0]; // set flags to indicate to other processes that fusion has been performede and is required on the next frame // this can be used by other fusion processes to avoid fusing on the same frame as this expensive step magFusePerformed = true; magFuseRequired = true; } else if (obsIndex == 2) // we are now fusing the Z measurement { // calculate observation jacobians for (uint8_t i=0; i<=21; i++) H_MAG[i] = 0; H_MAG[0] = SH_MAG[1]; H_MAG[1] = 2*magN*q3 - 2*magE*q0 - 2*magD*q1; H_MAG[2] = SH_MAG[7] + SH_MAG[8] - 2*magD*q2; H_MAG[3] = SH_MAG[0]; H_MAG[16] = 2*q0*q2 + 2*q1*q3; H_MAG[17] = 2*q2*q3 - 2*q0*q1; H_MAG[18] = SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]; H_MAG[21] = 1; // calculate Kalman gain float temp = (P[21][21] + R_MAG + P[0][21]*SH_MAG[1] + P[3][21]*SH_MAG[0] + P[18][21]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) - (2*magD*q1 + 2*magE*q0 - 2*magN*q3)*(P[21][1] + P[0][1]*SH_MAG[1] + P[3][1]*SH_MAG[0] + P[18][1]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P[16][1]*(2*q0*q2 + 2*q1*q3) - P[17][1]*(2*q0*q1 - 2*q2*q3) - P[1][1]*(2*magD*q1 + 2*magE*q0 - 2*magN*q3) + P[2][1]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + (SH_MAG[7] + SH_MAG[8] - 2*magD*q2)*(P[21][2] + P[0][2]*SH_MAG[1] + P[3][2]*SH_MAG[0] + P[18][2]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P[16][2]*(2*q0*q2 + 2*q1*q3) - P[17][2]*(2*q0*q1 - 2*q2*q3) - P[1][2]*(2*magD*q1 + 2*magE*q0 - 2*magN*q3) + P[2][2]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + SH_MAG[1]*(P[21][0] + P[0][0]*SH_MAG[1] + P[3][0]*SH_MAG[0] + P[18][0]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P[16][0]*(2*q0*q2 + 2*q1*q3) - P[17][0]*(2*q0*q1 - 2*q2*q3) - P[1][0]*(2*magD*q1 + 2*magE*q0 - 2*magN*q3) + P[2][0]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + SH_MAG[0]*(P[21][3] + P[0][3]*SH_MAG[1] + P[3][3]*SH_MAG[0] + P[18][3]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P[16][3]*(2*q0*q2 + 2*q1*q3) - P[17][3]*(2*q0*q1 - 2*q2*q3) - P[1][3]*(2*magD*q1 + 2*magE*q0 - 2*magN*q3) + P[2][3]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + (SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6])*(P[21][18] + P[0][18]*SH_MAG[1] + P[3][18]*SH_MAG[0] + P[18][18]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P[16][18]*(2*q0*q2 + 2*q1*q3) - P[17][18]*(2*q0*q1 - 2*q2*q3) - P[1][18]*(2*magD*q1 + 2*magE*q0 - 2*magN*q3) + P[2][18]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + P[16][21]*(2*q0*q2 + 2*q1*q3) - P[17][21]*(2*q0*q1 - 2*q2*q3) - P[1][21]*(2*magD*q1 + 2*magE*q0 - 2*magN*q3) + (2*q0*q2 + 2*q1*q3)*(P[21][16] + P[0][16]*SH_MAG[1] + P[3][16]*SH_MAG[0] + P[18][16]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P[16][16]*(2*q0*q2 + 2*q1*q3) - P[17][16]*(2*q0*q1 - 2*q2*q3) - P[1][16]*(2*magD*q1 + 2*magE*q0 - 2*magN*q3) + P[2][16]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) - (2*q0*q1 - 2*q2*q3)*(P[21][17] + P[0][17]*SH_MAG[1] + P[3][17]*SH_MAG[0] + P[18][17]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P[16][17]*(2*q0*q2 + 2*q1*q3) - P[17][17]*(2*q0*q1 - 2*q2*q3) - P[1][17]*(2*magD*q1 + 2*magE*q0 - 2*magN*q3) + P[2][17]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + P[2][21]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)); if (temp >= R_MAG) { SK_MZ[0] = 1.0f / temp; faultStatus.bad_zmag = false; } else { // the calculation is badly conditioned, so we cannot perform fusion on this step // we reset the covariance matrix and try again next measurement CovarianceInit(); obsIndex = 3; faultStatus.bad_zmag = true; return; } SK_MZ[1] = SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]; SK_MZ[2] = 2*magD*q1 + 2*magE*q0 - 2*magN*q3; SK_MZ[3] = SH_MAG[7] + SH_MAG[8] - 2*magD*q2; SK_MZ[4] = 2*q0*q1 - 2*q2*q3; SK_MZ[5] = 2*q0*q2 + 2*q1*q3; Kfusion[0] = SK_MZ[0]*(P[0][21] + P[0][0]*SH_MAG[1] + P[0][3]*SH_MAG[0] - P[0][1]*SK_MZ[2] + P[0][2]*SK_MZ[3] + P[0][18]*SK_MZ[1] + P[0][16]*SK_MZ[5] - P[0][17]*SK_MZ[4]); Kfusion[1] = SK_MZ[0]*(P[1][21] + P[1][0]*SH_MAG[1] + P[1][3]*SH_MAG[0] - P[1][1]*SK_MZ[2] + P[1][2]*SK_MZ[3] + P[1][18]*SK_MZ[1] + P[1][16]*SK_MZ[5] - P[1][17]*SK_MZ[4]); Kfusion[2] = SK_MZ[0]*(P[2][21] + P[2][0]*SH_MAG[1] + P[2][3]*SH_MAG[0] - P[2][1]*SK_MZ[2] + P[2][2]*SK_MZ[3] + P[2][18]*SK_MZ[1] + P[2][16]*SK_MZ[5] - P[2][17]*SK_MZ[4]); Kfusion[3] = SK_MZ[0]*(P[3][21] + P[3][0]*SH_MAG[1] + P[3][3]*SH_MAG[0] - P[3][1]*SK_MZ[2] + P[3][2]*SK_MZ[3] + P[3][18]*SK_MZ[1] + P[3][16]*SK_MZ[5] - P[3][17]*SK_MZ[4]); Kfusion[4] = SK_MZ[0]*(P[4][21] + P[4][0]*SH_MAG[1] + P[4][3]*SH_MAG[0] - P[4][1]*SK_MZ[2] + P[4][2]*SK_MZ[3] + P[4][18]*SK_MZ[1] + P[4][16]*SK_MZ[5] - P[4][17]*SK_MZ[4]); Kfusion[5] = SK_MZ[0]*(P[5][21] + P[5][0]*SH_MAG[1] + P[5][3]*SH_MAG[0] - P[5][1]*SK_MZ[2] + P[5][2]*SK_MZ[3] + P[5][18]*SK_MZ[1] + P[5][16]*SK_MZ[5] - P[5][17]*SK_MZ[4]); Kfusion[6] = SK_MZ[0]*(P[6][21] + P[6][0]*SH_MAG[1] + P[6][3]*SH_MAG[0] - P[6][1]*SK_MZ[2] + P[6][2]*SK_MZ[3] + P[6][18]*SK_MZ[1] + P[6][16]*SK_MZ[5] - P[6][17]*SK_MZ[4]); Kfusion[7] = SK_MZ[0]*(P[7][21] + P[7][0]*SH_MAG[1] + P[7][3]*SH_MAG[0] - P[7][1]*SK_MZ[2] + P[7][2]*SK_MZ[3] + P[7][18]*SK_MZ[1] + P[7][16]*SK_MZ[5] - P[7][17]*SK_MZ[4]); Kfusion[8] = SK_MZ[0]*(P[8][21] + P[8][0]*SH_MAG[1] + P[8][3]*SH_MAG[0] - P[8][1]*SK_MZ[2] + P[8][2]*SK_MZ[3] + P[8][18]*SK_MZ[1] + P[8][16]*SK_MZ[5] - P[8][17]*SK_MZ[4]); Kfusion[9] = SK_MZ[0]*(P[9][21] + P[9][0]*SH_MAG[1] + P[9][3]*SH_MAG[0] - P[9][1]*SK_MZ[2] + P[9][2]*SK_MZ[3] + P[9][18]*SK_MZ[1] + P[9][16]*SK_MZ[5] - P[9][17]*SK_MZ[4]); Kfusion[10] = SK_MZ[0]*(P[10][21] + P[10][0]*SH_MAG[1] + P[10][3]*SH_MAG[0] - P[10][1]*SK_MZ[2] + P[10][2]*SK_MZ[3] + P[10][18]*SK_MZ[1] + P[10][16]*SK_MZ[5] - P[10][17]*SK_MZ[4]); Kfusion[11] = SK_MZ[0]*(P[11][21] + P[11][0]*SH_MAG[1] + P[11][3]*SH_MAG[0] - P[11][1]*SK_MZ[2] + P[11][2]*SK_MZ[3] + P[11][18]*SK_MZ[1] + P[11][16]*SK_MZ[5] - P[11][17]*SK_MZ[4]); Kfusion[12] = SK_MZ[0]*(P[12][21] + P[12][0]*SH_MAG[1] + P[12][3]*SH_MAG[0] - P[12][1]*SK_MZ[2] + P[12][2]*SK_MZ[3] + P[12][18]*SK_MZ[1] + P[12][16]*SK_MZ[5] - P[12][17]*SK_MZ[4]); // this term has been zeroed to improve stability of the Z accel bias Kfusion[13] = 0.0f;//SK_MZ[0]*(P[13][21] + P[13][0]*SH_MAG[1] + P[13][3]*SH_MAG[0] - P[13][1]*SK_MZ[2] + P[13][2]*SK_MZ[3] + P[13][18]*SK_MZ[1] + P[13][16]*SK_MZ[5] - P[13][17]*SK_MZ[4]); // zero Kalman gains to inhibit wind state estimation if (!inhibitWindStates) { Kfusion[14] = SK_MZ[0]*(P[14][21] + P[14][0]*SH_MAG[1] + P[14][3]*SH_MAG[0] - P[14][1]*SK_MZ[2] + P[14][2]*SK_MZ[3] + P[14][18]*SK_MZ[1] + P[14][16]*SK_MZ[5] - P[14][17]*SK_MZ[4]); Kfusion[15] = SK_MZ[0]*(P[15][21] + P[15][0]*SH_MAG[1] + P[15][3]*SH_MAG[0] - P[15][1]*SK_MZ[2] + P[15][2]*SK_MZ[3] + P[15][18]*SK_MZ[1] + P[15][16]*SK_MZ[5] - P[15][17]*SK_MZ[4]); } else { Kfusion[14] = 0.0f; Kfusion[15] = 0.0f; } // zero Kalman gains to inhibit magnetic field state estimation if (!inhibitMagStates) { Kfusion[16] = SK_MZ[0]*(P[16][21] + P[16][0]*SH_MAG[1] + P[16][3]*SH_MAG[0] - P[16][1]*SK_MZ[2] + P[16][2]*SK_MZ[3] + P[16][18]*SK_MZ[1] + P[16][16]*SK_MZ[5] - P[16][17]*SK_MZ[4]); Kfusion[17] = SK_MZ[0]*(P[17][21] + P[17][0]*SH_MAG[1] + P[17][3]*SH_MAG[0] - P[17][1]*SK_MZ[2] + P[17][2]*SK_MZ[3] + P[17][18]*SK_MZ[1] + P[17][16]*SK_MZ[5] - P[17][17]*SK_MZ[4]); Kfusion[18] = SK_MZ[0]*(P[18][21] + P[18][0]*SH_MAG[1] + P[18][3]*SH_MAG[0] - P[18][1]*SK_MZ[2] + P[18][2]*SK_MZ[3] + P[18][18]*SK_MZ[1] + P[18][16]*SK_MZ[5] - P[18][17]*SK_MZ[4]); Kfusion[19] = SK_MZ[0]*(P[19][21] + P[19][0]*SH_MAG[1] + P[19][3]*SH_MAG[0] - P[19][1]*SK_MZ[2] + P[19][2]*SK_MZ[3] + P[19][18]*SK_MZ[1] + P[19][16]*SK_MZ[5] - P[19][17]*SK_MZ[4]); Kfusion[20] = SK_MZ[0]*(P[20][21] + P[20][0]*SH_MAG[1] + P[20][3]*SH_MAG[0] - P[20][1]*SK_MZ[2] + P[20][2]*SK_MZ[3] + P[20][18]*SK_MZ[1] + P[20][16]*SK_MZ[5] - P[20][17]*SK_MZ[4]); Kfusion[21] = SK_MZ[0]*(P[21][21] + P[21][0]*SH_MAG[1] + P[21][3]*SH_MAG[0] - P[21][1]*SK_MZ[2] + P[21][2]*SK_MZ[3] + P[21][18]*SK_MZ[1] + P[21][16]*SK_MZ[5] - P[21][17]*SK_MZ[4]); } else { for (uint8_t i=16; i<=21; i++) { Kfusion[i] = 0.0f; } } // calculate the observation innovation variance varInnovMag[2] = 1.0f/SK_MZ[0]; // set flags to indicate to other processes that fusion has been performede and is required on the next frame // this can be used by other fusion processes to avoid fusing on the same frame as this expensive step magFusePerformed = true; magFuseRequired = false; } // calculate the measurement innovation innovMag[obsIndex] = MagPred[obsIndex] - magData[obsIndex]; // calculate the innovation test ratio magTestRatio[obsIndex] = sq(innovMag[obsIndex]) / (sq(_magInnovGate) * varInnovMag[obsIndex]); // check the last values from all components and set magnetometer health accordingly magHealth = (magTestRatio[0] < 1.0f && magTestRatio[1] < 1.0f && magTestRatio[2] < 1.0f); // Don't fuse unless all componenets pass. The exception is if the bad health has timed out and we are not a fly forward vehicle // In this case we might as well try using the magnetometer, but with a reduced weighting if (magHealth || ((magTestRatio[obsIndex] < 1.0f) && !assume_zero_sideslip() && magTimeout)) { // Attitude, velocity and position corrections are averaged across multiple prediction cycles between now and the anticipated time for the next measurement. // Don't do averaging of quaternion state corrections if total angle change across predicted interval is going to exceed 0.1 rad bool highRates = ((magUpdateCountMax * correctedDelAng.length()) > 0.1f); // Calculate the number of averaging frames left to go. This is required becasue magnetometer fusion is applied across three consecutive prediction cycles // There is no point averaging if the number of cycles left is less than 2 float minorFramesToGo = float(magUpdateCountMax) - float(magUpdateCount); // correct the state vector or store corrections to be applied incrementally for (uint8_t j= 0; j<=21; j++) { // If we are forced to use a bad compass in flight, we reduce the weighting by a factor of 4 if (!magHealth && !constPosMode) { Kfusion[j] *= 0.25f; } // If in the air and there is no other form of heading reference or we are yawing rapidly which creates larger inertial yaw errors, // we strengthen the magnetometer attitude correction if (vehicleArmed && (constPosMode || highYawRate) && j <= 3) { Kfusion[j] *= 4.0f; } // We don't need to spread corrections for non-dynamic states or if we are in a constant postion mode // We can't spread corrections if there is not enough time remaining // We don't spread corrections to attitude states if we are rotating rapidly if ((j <= 3 && highRates) || j >= 10 || constPosMode || minorFramesToGo < 1.5f ) { states[j] = states[j] - Kfusion[j] * innovMag[obsIndex]; } else { // scale the correction based on the number of averaging frames left to go magIncrStateDelta[j] -= Kfusion[j] * innovMag[obsIndex] * (magUpdateCountMaxInv * float(magUpdateCountMax) / minorFramesToGo); } } // normalise the quaternion states state.quat.normalize(); // correct the covariance P = (I - K*H)*P // take advantage of the empty columns in KH to reduce the // number of operations for (uint8_t i = 0; i<=21; i++) { for (uint8_t j = 0; j<=3; j++) { KH[i][j] = Kfusion[i] * H_MAG[j]; } for (uint8_t j = 4; j<=15; j++) { KH[i][j] = 0.0f; } if (!inhibitMagStates) { for (uint8_t j = 16; j<=21; j++) { KH[i][j] = Kfusion[i] * H_MAG[j]; } } else { for (uint8_t j = 16; j<=21; j++) { KH[i][j] = 0.0f; } } } for (uint8_t i = 0; i<=21; i++) { for (uint8_t j = 0; j<=21; j++) { KHP[i][j] = 0; for (uint8_t k = 0; k<=3; k++) { KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j]; } if (!inhibitMagStates) { for (uint8_t k = 16; k<=21; k++) { KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j]; } } } } for (uint8_t i = 0; i<=21; i++) { for (uint8_t j = 0; j<=21; j++) { P[i][j] = P[i][j] - KHP[i][j]; } } } // force the covariance matrix to be symmetrical and limit the variances to prevent // ill-condiioning. ForceSymmetry(); ConstrainVariances(); } /* Estimation of terrain offset using a single state EKF The filter can fuse motion compensated optiocal flow rates and range finder measurements */ void NavEKF::EstimateTerrainOffset() { // start performance timer perf_begin(_perf_OpticalFlowEKF); // constrain height above ground to be above range measured on ground float heightAboveGndEst = max((terrainState - state.position.z), rngOnGnd); // calculate a predicted LOS rate squared float velHorizSq = sq(state.velocity.x) + sq(state.velocity.y); float losRateSq = velHorizSq / sq(heightAboveGndEst); // don't update terrain offset state if there is no range finder and not generating enough LOS rate, or without GPS, as it is poorly observable if (!fuseRngData && (gpsNotAvailable || PV_AidingMode == AID_RELATIVE || velHorizSq < 25.0f || losRateSq < 0.01f || onGround)) { inhibitGndState = true; } else { inhibitGndState = false; // record the time we last updated the terrain offset state gndHgtValidTime_ms = imuSampleTime_ms; // propagate ground position state noise each time this is called using the difference in position since the last observations and an RMS gradient assumption // limit distance to prevent intialisation afer bad gps causing bad numerical conditioning float distanceTravelledSq = sq(statesAtRngTime.position[0] - prevPosN) + sq(statesAtRngTime.position[1] - prevPosE); distanceTravelledSq = min(distanceTravelledSq, 100.0f); prevPosN = statesAtRngTime.position[0]; prevPosE = statesAtRngTime.position[1]; // in addition to a terrain gradient error model, we also have a time based error growth that is scaled using the gradient parameter float timeLapsed = min(0.001f * (imuSampleTime_ms - timeAtLastAuxEKF_ms), 1.0f); float Pincrement = (distanceTravelledSq * sq(0.01f*float(_gndGradientSigma))) + sq(float(_gndGradientSigma) * timeLapsed); Popt += Pincrement; timeAtLastAuxEKF_ms = imuSampleTime_ms; // fuse range finder data if (fuseRngData) { // predict range float predRngMeas = max((terrainState - statesAtRngTime.position[2]),rngOnGnd) / Tnb_flow.c.z; // Copy required states to local variable names float q0 = statesAtRngTime.quat[0]; // quaternion at optical flow measurement time float q1 = statesAtRngTime.quat[1]; // quaternion at optical flow measurement time float q2 = statesAtRngTime.quat[2]; // quaternion at optical flow measurement time float q3 = statesAtRngTime.quat[3]; // quaternion at optical flow measurement time // Set range finder measurement noise variance. TODO make this a function of range and tilt to allow for sensor, alignment and AHRS errors float R_RNG = 0.5f; // calculate Kalman gain float SK_RNG = sq(q0) - sq(q1) - sq(q2) + sq(q3); float K_RNG = Popt/(SK_RNG*(R_RNG + Popt/sq(SK_RNG))); // Calculate the innovation variance for data logging varInnovRng = (R_RNG + Popt/sq(SK_RNG)); // constrain terrain height to be below the vehicle terrainState = max(terrainState, statesAtRngTime.position[2] + rngOnGnd); // Calculate the measurement innovation innovRng = predRngMeas - rngMea; // calculate the innovation consistency test ratio auxRngTestRatio = sq(innovRng) / (sq(_rngInnovGate) * varInnovRng); // Check the innovation for consistency and don't fuse if > 5Sigma if ((sq(innovRng)*SK_RNG) < 25.0f) { // correct the state terrainState -= K_RNG * innovRng; // constrain the state terrainState = max(terrainState, statesAtRngTime.position[2] + rngOnGnd); // correct the covariance Popt = Popt - sq(Popt)/(SK_RNG*(R_RNG + Popt/sq(SK_RNG))*(sq(q0) - sq(q1) - sq(q2) + sq(q3))); // prevent the state variance from becoming negative Popt = max(Popt,0.0f); } } if (fuseOptFlowData) { Vector3f vel; // velocity of sensor relative to ground in NED axes Vector3f relVelSensor; // velocity of sensor relative to ground in sensor axes float losPred; // predicted optical flow angular rate measurement float q0 = statesAtFlowTime.quat[0]; // quaternion at optical flow measurement time float q1 = statesAtFlowTime.quat[1]; // quaternion at optical flow measurement time float q2 = statesAtFlowTime.quat[2]; // quaternion at optical flow measurement time float q3 = statesAtFlowTime.quat[3]; // quaternion at optical flow measurement time float K_OPT; float H_OPT; // Correct velocities for GPS glitch recovery offset vel.x = statesAtFlowTime.velocity[0] - gpsVelGlitchOffset.x; vel.y = statesAtFlowTime.velocity[1] - gpsVelGlitchOffset.y; vel.z = statesAtFlowTime.velocity[2]; // predict range to centre of image float flowRngPred = max((terrainState - statesAtFlowTime.position[2]),rngOnGnd) / Tnb_flow.c.z; // constrain terrain height to be below the vehicle terrainState = max(terrainState, statesAtFlowTime.position[2] + rngOnGnd); // calculate relative velocity in sensor frame relVelSensor = Tnb_flow*vel; // divide velocity by range, subtract body rates and apply scale factor to // get predicted sensed angular optical rates relative to X and Y sensor axes losPred = relVelSensor.length()/flowRngPred; // calculate innovations auxFlowObsInnov = losPred - sqrtf(sq(flowRadXYcomp[0]) + sq(flowRadXYcomp[1])); // calculate observation jacobian float t3 = sq(q0); float t4 = sq(q1); float t5 = sq(q2); float t6 = sq(q3); float t10 = q0*q3*2.0f; float t11 = q1*q2*2.0f; float t14 = t3+t4-t5-t6; float t15 = t14*vel.x; float t16 = t10+t11; float t17 = t16*vel.y; float t18 = q0*q2*2.0f; float t19 = q1*q3*2.0f; float t20 = t18-t19; float t21 = t20*vel.z; float t2 = t15+t17-t21; float t7 = t3-t4-t5+t6; float t8 = statesAtFlowTime.position[2]-terrainState; float t9 = 1.0f/sq(t8); float t24 = t3-t4+t5-t6; float t25 = t24*vel.y; float t26 = t10-t11; float t27 = t26*vel.x; float t28 = q0*q1*2.0f; float t29 = q2*q3*2.0f; float t30 = t28+t29; float t31 = t30*vel.z; float t12 = t25-t27+t31; float t13 = sq(t7); float t22 = sq(t2); float t23 = 1.0f/(t8*t8*t8); float t32 = sq(t12); H_OPT = 0.5f*(t13*t22*t23*2.0f+t13*t23*t32*2.0f)/sqrtf(t9*t13*t22+t9*t13*t32); // calculate innovation variances auxFlowObsInnovVar = H_OPT*Popt*H_OPT + R_LOS; // calculate Kalman gain K_OPT = Popt*H_OPT/auxFlowObsInnovVar; // calculate the innovation consistency test ratio auxFlowTestRatio = sq(auxFlowObsInnov) / (sq(_flowInnovGate) * auxFlowObsInnovVar); // don't fuse if optical flow data is outside valid range if (max(flowRadXY[0],flowRadXY[1]) < _maxFlowRate) { // correct the state terrainState -= K_OPT * auxFlowObsInnov; // constrain the state terrainState = max(terrainState, statesAtFlowTime.position[2] + rngOnGnd); // correct the covariance Popt = Popt - K_OPT * H_OPT * Popt; // prevent the state variances from becoming negative Popt = max(Popt,0.0f); } } } // stop the performance timer perf_end(_perf_OpticalFlowEKF); } void NavEKF::FuseOptFlow() { Vector22 H_LOS; Vector8 tempVar; Vector3f velNED_local; Vector3f relVelSensor; uint8_t &obsIndex = flow_state.obsIndex; ftype &q0 = flow_state.q0; ftype &q1 = flow_state.q1; ftype &q2 = flow_state.q2; ftype &q3 = flow_state.q3; ftype *SH_LOS = &flow_state.SH_LOS[0]; ftype *SK_LOS = &flow_state.SK_LOS[0]; ftype &vn = flow_state.vn; ftype &ve = flow_state.ve; ftype &vd = flow_state.vd; ftype &pd = flow_state.pd; ftype *losPred = &flow_state.losPred[0]; // Copy required states to local variable names q0 = statesAtFlowTime.quat[0]; q1 = statesAtFlowTime.quat[1]; q2 = statesAtFlowTime.quat[2]; q3 = statesAtFlowTime.quat[3]; vn = statesAtFlowTime.velocity[0]; ve = statesAtFlowTime.velocity[1]; vd = statesAtFlowTime.velocity[2]; pd = statesAtFlowTime.position[2]; // Correct velocities for GPS glitch recovery offset velNED_local.x = vn - gpsVelGlitchOffset.x; velNED_local.y = ve - gpsVelGlitchOffset.y; velNED_local.z = vd; // constrain height above ground to be above range measured on ground float heightAboveGndEst = max((terrainState - pd), rngOnGnd); // Calculate observation jacobians and Kalman gains if (obsIndex == 0) { // calculate range from ground plain to centre of sensor fov assuming flat earth float range = constrain_float((heightAboveGndEst/Tnb_flow.c.z),rngOnGnd,1000.0f); // calculate relative velocity in sensor frame relVelSensor = Tnb_flow*velNED_local; // divide velocity by range to get predicted angular LOS rates relative to X and Y axes losPred[0] = relVelSensor.y/range; losPred[1] = -relVelSensor.x/range; // Calculate common expressions for observation jacobians SH_LOS[0] = sq(q0) - sq(q1) - sq(q2) + sq(q3); SH_LOS[1] = vn*(sq(q0) + sq(q1) - sq(q2) - sq(q3)) - vd*(2*q0*q2 - 2*q1*q3) + ve*(2*q0*q3 + 2*q1*q2); SH_LOS[2] = ve*(sq(q0) - sq(q1) + sq(q2) - sq(q3)) + vd*(2*q0*q1 + 2*q2*q3) - vn*(2*q0*q3 - 2*q1*q2); SH_LOS[3] = -1.0f/heightAboveGndEst; // Calculate common expressions for Kalman gains // calculate innovation variance for Y axis observation varInnovOptFlow[1] = (R_LOS + (SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) + 2*q0*SH_LOS[1]*SH_LOS[3])*(P[0][0]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) + 2*q0*SH_LOS[1]*SH_LOS[3]) + P[1][0]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q1*SH_LOS[1]*SH_LOS[3]) - P[2][0]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) + 2*q2*SH_LOS[1]*SH_LOS[3]) + P[3][0]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q3*SH_LOS[1]*SH_LOS[3]) + P[5][0]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 + 2*q1*q2) - P[6][0]*SH_LOS[0]*SH_LOS[3]*(2*q0*q2 - 2*q1*q3) - (P[9][0]*SH_LOS[0]*SH_LOS[1])/sq(pd - terrainState) + P[4][0]*SH_LOS[0]*SH_LOS[3]*(sq(q0) + sq(q1) - sq(q2) - sq(q3))) + (SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q1*SH_LOS[1]*SH_LOS[3])*(P[0][1]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) + 2*q0*SH_LOS[1]*SH_LOS[3]) + P[1][1]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q1*SH_LOS[1]*SH_LOS[3]) - P[2][1]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) + 2*q2*SH_LOS[1]*SH_LOS[3]) + P[3][1]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q3*SH_LOS[1]*SH_LOS[3]) + P[5][1]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 + 2*q1*q2) - P[6][1]*SH_LOS[0]*SH_LOS[3]*(2*q0*q2 - 2*q1*q3) - (P[9][1]*SH_LOS[0]*SH_LOS[1])/sq(pd - terrainState) + P[4][1]*SH_LOS[0]*SH_LOS[3]*(sq(q0) + sq(q1) - sq(q2) - sq(q3))) - (SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) + 2*q2*SH_LOS[1]*SH_LOS[3])*(P[0][2]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) + 2*q0*SH_LOS[1]*SH_LOS[3]) + P[1][2]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q1*SH_LOS[1]*SH_LOS[3]) - P[2][2]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) + 2*q2*SH_LOS[1]*SH_LOS[3]) + P[3][2]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q3*SH_LOS[1]*SH_LOS[3]) + P[5][2]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 + 2*q1*q2) - P[6][2]*SH_LOS[0]*SH_LOS[3]*(2*q0*q2 - 2*q1*q3) - (P[9][2]*SH_LOS[0]*SH_LOS[1])/sq(pd - terrainState) + P[4][2]*SH_LOS[0]*SH_LOS[3]*(sq(q0) + sq(q1) - sq(q2) - sq(q3))) + (SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q3*SH_LOS[1]*SH_LOS[3])*(P[0][3]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) + 2*q0*SH_LOS[1]*SH_LOS[3]) + P[1][3]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q1*SH_LOS[1]*SH_LOS[3]) - P[2][3]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) + 2*q2*SH_LOS[1]*SH_LOS[3]) + P[3][3]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q3*SH_LOS[1]*SH_LOS[3]) + P[5][3]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 + 2*q1*q2) - P[6][3]*SH_LOS[0]*SH_LOS[3]*(2*q0*q2 - 2*q1*q3) - (P[9][3]*SH_LOS[0]*SH_LOS[1])/sq(pd - terrainState) + P[4][3]*SH_LOS[0]*SH_LOS[3]*(sq(q0) + sq(q1) - sq(q2) - sq(q3))) + SH_LOS[0]*SH_LOS[3]*(sq(q0) + sq(q1) - sq(q2) - sq(q3))*(P[0][4]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) + 2*q0*SH_LOS[1]*SH_LOS[3]) + P[1][4]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q1*SH_LOS[1]*SH_LOS[3]) - P[2][4]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) + 2*q2*SH_LOS[1]*SH_LOS[3]) + P[3][4]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q3*SH_LOS[1]*SH_LOS[3]) + P[5][4]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 + 2*q1*q2) - P[6][4]*SH_LOS[0]*SH_LOS[3]*(2*q0*q2 - 2*q1*q3) - (P[9][4]*SH_LOS[0]*SH_LOS[1])/sq(pd - terrainState) + P[4][4]*SH_LOS[0]*SH_LOS[3]*(sq(q0) + sq(q1) - sq(q2) - sq(q3))) + SH_LOS[0]*SH_LOS[3]*(2*q0*q3 + 2*q1*q2)*(P[0][5]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) + 2*q0*SH_LOS[1]*SH_LOS[3]) + P[1][5]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q1*SH_LOS[1]*SH_LOS[3]) - P[2][5]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) + 2*q2*SH_LOS[1]*SH_LOS[3]) + P[3][5]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q3*SH_LOS[1]*SH_LOS[3]) + P[5][5]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 + 2*q1*q2) - P[6][5]*SH_LOS[0]*SH_LOS[3]*(2*q0*q2 - 2*q1*q3) - (P[9][5]*SH_LOS[0]*SH_LOS[1])/sq(pd - terrainState) + P[4][5]*SH_LOS[0]*SH_LOS[3]*(sq(q0) + sq(q1) - sq(q2) - sq(q3))) - SH_LOS[0]*SH_LOS[3]*(2*q0*q2 - 2*q1*q3)*(P[0][6]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) + 2*q0*SH_LOS[1]*SH_LOS[3]) + P[1][6]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q1*SH_LOS[1]*SH_LOS[3]) - P[2][6]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) + 2*q2*SH_LOS[1]*SH_LOS[3]) + P[3][6]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q3*SH_LOS[1]*SH_LOS[3]) + P[5][6]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 + 2*q1*q2) - P[6][6]*SH_LOS[0]*SH_LOS[3]*(2*q0*q2 - 2*q1*q3) - (P[9][6]*SH_LOS[0]*SH_LOS[1])/sq(pd - terrainState) + P[4][6]*SH_LOS[0]*SH_LOS[3]*(sq(q0) + sq(q1) - sq(q2) - sq(q3))) - (SH_LOS[0]*SH_LOS[1]*(P[0][9]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) + 2*q0*SH_LOS[1]*SH_LOS[3]) + P[1][9]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q1*SH_LOS[1]*SH_LOS[3]) - P[2][9]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) + 2*q2*SH_LOS[1]*SH_LOS[3]) + P[3][9]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q3*SH_LOS[1]*SH_LOS[3]) + P[5][9]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 + 2*q1*q2) - P[6][9]*SH_LOS[0]*SH_LOS[3]*(2*q0*q2 - 2*q1*q3) - (P[9][9]*SH_LOS[0]*SH_LOS[1])/sq(pd - terrainState) + P[4][9]*SH_LOS[0]*SH_LOS[3]*(sq(q0) + sq(q1) - sq(q2) - sq(q3))))/sq(pd - terrainState)); if (varInnovOptFlow[1] > R_LOS) { SK_LOS[0] = 1.0f/varInnovOptFlow[1]; } else { SK_LOS[0] = 1.0f/R_LOS; } // calculate innovation variance for X axis observation varInnovOptFlow[0] = (R_LOS + (SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q0*SH_LOS[2]*SH_LOS[3])*(P[0][0]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q0*SH_LOS[2]*SH_LOS[3]) + P[1][0]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) - 2*q1*SH_LOS[2]*SH_LOS[3]) + P[2][0]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q2*SH_LOS[2]*SH_LOS[3]) - P[3][0]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) - 2*q3*SH_LOS[2]*SH_LOS[3]) - P[4][0]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 - 2*q1*q2) + P[6][0]*SH_LOS[0]*SH_LOS[3]*(2*q0*q1 + 2*q2*q3) - (P[9][0]*SH_LOS[0]*SH_LOS[2])/sq(pd - terrainState) + P[5][0]*SH_LOS[0]*SH_LOS[3]*(sq(q0) - sq(q1) + sq(q2) - sq(q3))) + (SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) - 2*q1*SH_LOS[2]*SH_LOS[3])*(P[0][1]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q0*SH_LOS[2]*SH_LOS[3]) + P[1][1]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) - 2*q1*SH_LOS[2]*SH_LOS[3]) + P[2][1]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q2*SH_LOS[2]*SH_LOS[3]) - P[3][1]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) - 2*q3*SH_LOS[2]*SH_LOS[3]) - P[4][1]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 - 2*q1*q2) + P[6][1]*SH_LOS[0]*SH_LOS[3]*(2*q0*q1 + 2*q2*q3) - (P[9][1]*SH_LOS[0]*SH_LOS[2])/sq(pd - terrainState) + P[5][1]*SH_LOS[0]*SH_LOS[3]*(sq(q0) - sq(q1) + sq(q2) - sq(q3))) + (SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q2*SH_LOS[2]*SH_LOS[3])*(P[0][2]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q0*SH_LOS[2]*SH_LOS[3]) + P[1][2]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) - 2*q1*SH_LOS[2]*SH_LOS[3]) + P[2][2]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q2*SH_LOS[2]*SH_LOS[3]) - P[3][2]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) - 2*q3*SH_LOS[2]*SH_LOS[3]) - P[4][2]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 - 2*q1*q2) + P[6][2]*SH_LOS[0]*SH_LOS[3]*(2*q0*q1 + 2*q2*q3) - (P[9][2]*SH_LOS[0]*SH_LOS[2])/sq(pd - terrainState) + P[5][2]*SH_LOS[0]*SH_LOS[3]*(sq(q0) - sq(q1) + sq(q2) - sq(q3))) - (SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) - 2*q3*SH_LOS[2]*SH_LOS[3])*(P[0][3]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q0*SH_LOS[2]*SH_LOS[3]) + P[1][3]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) - 2*q1*SH_LOS[2]*SH_LOS[3]) + P[2][3]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q2*SH_LOS[2]*SH_LOS[3]) - P[3][3]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) - 2*q3*SH_LOS[2]*SH_LOS[3]) - P[4][3]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 - 2*q1*q2) + P[6][3]*SH_LOS[0]*SH_LOS[3]*(2*q0*q1 + 2*q2*q3) - (P[9][3]*SH_LOS[0]*SH_LOS[2])/sq(pd - terrainState) + P[5][3]*SH_LOS[0]*SH_LOS[3]*(sq(q0) - sq(q1) + sq(q2) - sq(q3))) + SH_LOS[0]*SH_LOS[3]*(sq(q0) - sq(q1) + sq(q2) - sq(q3))*(P[0][5]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q0*SH_LOS[2]*SH_LOS[3]) + P[1][5]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) - 2*q1*SH_LOS[2]*SH_LOS[3]) + P[2][5]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q2*SH_LOS[2]*SH_LOS[3]) - P[3][5]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) - 2*q3*SH_LOS[2]*SH_LOS[3]) - P[4][5]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 - 2*q1*q2) + P[6][5]*SH_LOS[0]*SH_LOS[3]*(2*q0*q1 + 2*q2*q3) - (P[9][5]*SH_LOS[0]*SH_LOS[2])/sq(pd - terrainState) + P[5][5]*SH_LOS[0]*SH_LOS[3]*(sq(q0) - sq(q1) + sq(q2) - sq(q3))) - SH_LOS[0]*SH_LOS[3]*(2*q0*q3 - 2*q1*q2)*(P[0][4]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q0*SH_LOS[2]*SH_LOS[3]) + P[1][4]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) - 2*q1*SH_LOS[2]*SH_LOS[3]) + P[2][4]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q2*SH_LOS[2]*SH_LOS[3]) - P[3][4]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) - 2*q3*SH_LOS[2]*SH_LOS[3]) - P[4][4]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 - 2*q1*q2) + P[6][4]*SH_LOS[0]*SH_LOS[3]*(2*q0*q1 + 2*q2*q3) - (P[9][4]*SH_LOS[0]*SH_LOS[2])/sq(pd - terrainState) + P[5][4]*SH_LOS[0]*SH_LOS[3]*(sq(q0) - sq(q1) + sq(q2) - sq(q3))) + SH_LOS[0]*SH_LOS[3]*(2*q0*q1 + 2*q2*q3)*(P[0][6]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q0*SH_LOS[2]*SH_LOS[3]) + P[1][6]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) - 2*q1*SH_LOS[2]*SH_LOS[3]) + P[2][6]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q2*SH_LOS[2]*SH_LOS[3]) - P[3][6]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) - 2*q3*SH_LOS[2]*SH_LOS[3]) - P[4][6]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 - 2*q1*q2) + P[6][6]*SH_LOS[0]*SH_LOS[3]*(2*q0*q1 + 2*q2*q3) - (P[9][6]*SH_LOS[0]*SH_LOS[2])/sq(pd - terrainState) + P[5][6]*SH_LOS[0]*SH_LOS[3]*(sq(q0) - sq(q1) + sq(q2) - sq(q3))) - (SH_LOS[0]*SH_LOS[2]*(P[0][9]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q0*SH_LOS[2]*SH_LOS[3]) + P[1][9]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) - 2*q1*SH_LOS[2]*SH_LOS[3]) + P[2][9]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q2*SH_LOS[2]*SH_LOS[3]) - P[3][9]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) - 2*q3*SH_LOS[2]*SH_LOS[3]) - P[4][9]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 - 2*q1*q2) + P[6][9]*SH_LOS[0]*SH_LOS[3]*(2*q0*q1 + 2*q2*q3) - (P[9][9]*SH_LOS[0]*SH_LOS[2])/sq(pd - terrainState) + P[5][9]*SH_LOS[0]*SH_LOS[3]*(sq(q0) - sq(q1) + sq(q2) - sq(q3))))/sq(pd - terrainState)); if (varInnovOptFlow[0] > R_LOS) { SK_LOS[1] = 1.0f/varInnovOptFlow[0]; } else { SK_LOS[1] = 1.0f/R_LOS; } SK_LOS[2] = SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn); SK_LOS[3] = SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn); SK_LOS[4] = SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn); SK_LOS[5] = SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn); SK_LOS[6] = sq(q0) - sq(q1) + sq(q2) - sq(q3); SK_LOS[7] = 1.0f/sq(heightAboveGndEst); SK_LOS[8] = sq(q0) + sq(q1) - sq(q2) - sq(q3); SK_LOS[9] = SH_LOS[3]; // Calculate common intermediate terms tempVar[0] = SK_LOS[4] + 2*q0*SH_LOS[2]*SK_LOS[9]; tempVar[1] = SK_LOS[3] - 2*q1*SH_LOS[2]*SK_LOS[9]; tempVar[2] = SK_LOS[2] - 2*q3*SH_LOS[2]*SK_LOS[9]; tempVar[3] = SH_LOS[0]*SK_LOS[9]*(2*q0*q3 - 2*q1*q2); tempVar[4] = SH_LOS[0]*SK_LOS[9]*(2*q0*q1 + 2*q2*q3); tempVar[5] = SH_LOS[0]*SH_LOS[2]*SK_LOS[7]; tempVar[6] = SH_LOS[0]*SK_LOS[6]*SK_LOS[9]; tempVar[7] = SK_LOS[5] - 2*q2*SH_LOS[2]*SK_LOS[9]; // calculate observation jacobians for X LOS rate memset(&H_LOS[0], 0, sizeof(H_LOS)); H_LOS[0] = - SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) - 2*q0*SH_LOS[2]*SH_LOS[3]; H_LOS[1] = 2*q1*SH_LOS[2]*SH_LOS[3] - SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn); H_LOS[2] = 2*q2*SH_LOS[2]*SH_LOS[3] - SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn); H_LOS[3] = SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) - 2*q3*SH_LOS[2]*SH_LOS[3]; H_LOS[4] = SH_LOS[0]*SH_LOS[3]*(2*q0*q3 - 2*q1*q2); H_LOS[5] = -SH_LOS[0]*SH_LOS[3]*(sq(q0) - sq(q1) + sq(q2) - sq(q3)); H_LOS[6] = -SH_LOS[0]*SH_LOS[3]*(2*q0*q1 + 2*q2*q3); H_LOS[9] = (SH_LOS[0]*SH_LOS[2])/sq(heightAboveGndEst); // calculate Kalman gains for X LOS rate Kfusion[0] = -SK_LOS[1]*(P[0][0]*tempVar[0] + P[0][1]*tempVar[1] - P[0][3]*tempVar[2] + P[0][2]*tempVar[7] - P[0][4]*tempVar[3] + P[0][6]*tempVar[4] - P[0][9]*tempVar[5] + P[0][5]*tempVar[6]); Kfusion[1] = -SK_LOS[1]*(P[1][0]*tempVar[0] + P[1][1]*tempVar[1] - P[1][3]*tempVar[2] + P[1][2]*tempVar[7] - P[1][4]*tempVar[3] + P[1][6]*tempVar[4] - P[1][9]*tempVar[5] + P[1][5]*tempVar[6]); Kfusion[2] = -SK_LOS[1]*(P[2][0]*tempVar[0] + P[2][1]*tempVar[1] - P[2][3]*tempVar[2] + P[2][2]*tempVar[7] - P[2][4]*tempVar[3] + P[2][6]*tempVar[4] - P[2][9]*tempVar[5] + P[2][5]*tempVar[6]); Kfusion[3] = -SK_LOS[1]*(P[3][0]*tempVar[0] + P[3][1]*tempVar[1] - P[3][3]*tempVar[2] + P[3][2]*tempVar[7] - P[3][4]*tempVar[3] + P[3][6]*tempVar[4] - P[3][9]*tempVar[5] + P[3][5]*tempVar[6]); Kfusion[4] = -SK_LOS[1]*(P[4][0]*tempVar[0] + P[4][1]*tempVar[1] - P[4][3]*tempVar[2] + P[4][2]*tempVar[7] - P[4][4]*tempVar[3] + P[4][6]*tempVar[4] - P[4][9]*tempVar[5] + P[4][5]*tempVar[6]); Kfusion[5] = -SK_LOS[1]*(P[5][0]*tempVar[0] + P[5][1]*tempVar[1] - P[5][3]*tempVar[2] + P[5][2]*tempVar[7] - P[5][4]*tempVar[3] + P[5][6]*tempVar[4] - P[5][9]*tempVar[5] + P[5][5]*tempVar[6]); // Don't allow optical flow measurements to modify vertical velocity as it can produce height offsets Kfusion[6] = 0.0f;//-SK_LOS[1]*(P[6][0]*tempVar[0] + P[6][1]*tempVar[1] - P[6][3]*tempVar[2] + P[6][2]*tempVar[7] - P[6][4]*tempVar[3] + P[6][6]*tempVar[4] - P[6][9]*tempVar[5] + P[6][5]*tempVar[6]); Kfusion[7] = -SK_LOS[1]*(P[7][0]*tempVar[0] + P[7][1]*tempVar[1] - P[7][3]*tempVar[2] + P[7][2]*tempVar[7] - P[7][4]*tempVar[3] + P[7][6]*tempVar[4] - P[7][9]*tempVar[5] + P[7][5]*tempVar[6]); Kfusion[8] = -SK_LOS[1]*(P[8][0]*tempVar[0] + P[8][1]*tempVar[1] - P[8][3]*tempVar[2] + P[8][2]*tempVar[7] - P[8][4]*tempVar[3] + P[8][6]*tempVar[4] - P[8][9]*tempVar[5] + P[8][5]*tempVar[6]); // Don't allow optical flow measurements to modify vertical position as it can produce height offsets Kfusion[9] = 0.0f;//-SK_LOS[1]*(P[9][0]*tempVar[0] + P[9][1]*tempVar[1] - P[9][3]*tempVar[2] + P[9][2]*tempVar[7] - P[9][4]*tempVar[3] + P[9][6]*tempVar[4] - P[9][9]*tempVar[5] + P[9][5]*tempVar[6]); Kfusion[10] = -SK_LOS[1]*(P[10][0]*tempVar[0] + P[10][1]*tempVar[1] - P[10][3]*tempVar[2] + P[10][2]*tempVar[7] - P[10][4]*tempVar[3] + P[10][6]*tempVar[4] - P[10][9]*tempVar[5] + P[10][5]*tempVar[6]); Kfusion[11] = -SK_LOS[1]*(P[11][0]*tempVar[0] + P[11][1]*tempVar[1] - P[11][3]*tempVar[2] + P[11][2]*tempVar[7] - P[11][4]*tempVar[3] + P[11][6]*tempVar[4] - P[11][9]*tempVar[5] + P[11][5]*tempVar[6]); Kfusion[12] = -SK_LOS[1]*(P[12][0]*tempVar[0] + P[12][1]*tempVar[1] - P[12][3]*tempVar[2] + P[12][2]*tempVar[7] - P[12][4]*tempVar[3] + P[12][6]*tempVar[4] - P[12][9]*tempVar[5] + P[12][5]*tempVar[6]); // only height measurements are allowed to modify the Z bias state to improve the stability of the estimate Kfusion[13] = 0.0f;//Kfusion[13] = -SK_LOS[1]*(P[13][0]*tempVar[0] + P[13][1]*tempVar[1] - P[13][3]*tempVar[2] + P[13][2]*tempVar[7] - P[13][4]*tempVar[3] + P[13][6]*tempVar[4] - P[13][9]*tempVar[5] + P[13][5]*tempVar[6]); if (inhibitWindStates) { Kfusion[14] = -SK_LOS[1]*(P[14][0]*tempVar[0] + P[14][1]*tempVar[1] - P[14][3]*tempVar[2] + P[14][2]*tempVar[7] - P[14][4]*tempVar[3] + P[14][6]*tempVar[4] - P[14][9]*tempVar[5] + P[14][5]*tempVar[6]); Kfusion[15] = -SK_LOS[1]*(P[15][0]*tempVar[0] + P[15][1]*tempVar[1] - P[15][3]*tempVar[2] + P[15][2]*tempVar[7] - P[15][4]*tempVar[3] + P[15][6]*tempVar[4] - P[15][9]*tempVar[5] + P[15][5]*tempVar[6]); } else { Kfusion[14] = 0.0f; Kfusion[15] = 0.0f; } if (inhibitMagStates) { Kfusion[16] = -SK_LOS[1]*(P[16][0]*tempVar[0] + P[16][1]*tempVar[1] - P[16][3]*tempVar[2] + P[16][2]*tempVar[7] - P[16][4]*tempVar[3] + P[16][6]*tempVar[4] - P[16][9]*tempVar[5] + P[16][5]*tempVar[6]); Kfusion[17] = -SK_LOS[1]*(P[17][0]*tempVar[0] + P[17][1]*tempVar[1] - P[17][3]*tempVar[2] + P[17][2]*tempVar[7] - P[17][4]*tempVar[3] + P[17][6]*tempVar[4] - P[17][9]*tempVar[5] + P[17][5]*tempVar[6]); Kfusion[18] = -SK_LOS[1]*(P[18][0]*tempVar[0] + P[18][1]*tempVar[1] - P[18][3]*tempVar[2] + P[18][2]*tempVar[7] - P[18][4]*tempVar[3] + P[18][6]*tempVar[4] - P[18][9]*tempVar[5] + P[18][5]*tempVar[6]); Kfusion[19] = -SK_LOS[1]*(P[19][0]*tempVar[0] + P[19][1]*tempVar[1] - P[19][3]*tempVar[2] + P[19][2]*tempVar[7] - P[19][4]*tempVar[3] + P[19][6]*tempVar[4] - P[19][9]*tempVar[5] + P[19][5]*tempVar[6]); Kfusion[20] = -SK_LOS[1]*(P[20][0]*tempVar[0] + P[20][1]*tempVar[1] - P[20][3]*tempVar[2] + P[20][2]*tempVar[7] - P[20][4]*tempVar[3] + P[20][6]*tempVar[4] - P[20][9]*tempVar[5] + P[20][5]*tempVar[6]); Kfusion[21] = -SK_LOS[1]*(P[21][0]*tempVar[0] + P[21][1]*tempVar[1] - P[21][3]*tempVar[2] + P[21][2]*tempVar[7] - P[21][4]*tempVar[3] + P[21][6]*tempVar[4] - P[21][9]*tempVar[5] + P[21][5]*tempVar[6]); } else { for (uint8_t i = 16; i <= 21; i++) { Kfusion[i] = 0.0f; } } // calculate innovation for X axis observation innovOptFlow[0] = losPred[0] - flowRadXYcomp[0]; } else if (obsIndex == 1) { // calculate intermediate common variables tempVar[0] = SK_LOS[2] + 2*q0*SH_LOS[1]*SK_LOS[9]; tempVar[1] = SK_LOS[5] - 2*q1*SH_LOS[1]*SK_LOS[9]; tempVar[2] = SK_LOS[3] + 2*q2*SH_LOS[1]*SK_LOS[9]; tempVar[3] = SK_LOS[4] + 2*q3*SH_LOS[1]*SK_LOS[9]; tempVar[4] = SH_LOS[0]*SK_LOS[9]*(2*q0*q3 + 2*q1*q2); tempVar[5] = SH_LOS[0]*SK_LOS[9]*(2*q0*q2 - 2*q1*q3); tempVar[6] = SH_LOS[0]*SH_LOS[1]*SK_LOS[7]; tempVar[7] = SH_LOS[0]*SK_LOS[8]*SK_LOS[9]; // Calculate observation jacobians for Y LOS rate memset(&H_LOS[0], 0, sizeof(H_LOS)); H_LOS[0] = SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) + 2*q0*SH_LOS[1]*SH_LOS[3]; H_LOS[1] = SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q1*SH_LOS[1]*SH_LOS[3]; H_LOS[2] = - SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) - 2*q2*SH_LOS[1]*SH_LOS[3]; H_LOS[3] = SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q3*SH_LOS[1]*SH_LOS[3]; H_LOS[4] = SH_LOS[0]*SH_LOS[3]*(sq(q0) + sq(q1) - sq(q2) - sq(q3)); H_LOS[5] = SH_LOS[0]*SH_LOS[3]*(2*q0*q3 + 2*q1*q2); H_LOS[6] = -SH_LOS[0]*SH_LOS[3]*(2*q0*q2 - 2*q1*q3); H_LOS[9] = -(SH_LOS[0]*SH_LOS[1])/sq(heightAboveGndEst); // Calculate Kalman gains for Y LOS rate Kfusion[0] = SK_LOS[0]*(P[0][0]*tempVar[0] + P[0][1]*tempVar[1] - P[0][2]*tempVar[2] + P[0][3]*tempVar[3] + P[0][5]*tempVar[4] - P[0][6]*tempVar[5] - P[0][9]*tempVar[6] + P[0][4]*tempVar[7]); Kfusion[1] = SK_LOS[0]*(P[1][0]*tempVar[0] + P[1][1]*tempVar[1] - P[1][2]*tempVar[2] + P[1][3]*tempVar[3] + P[1][5]*tempVar[4] - P[1][6]*tempVar[5] - P[1][9]*tempVar[6] + P[1][4]*tempVar[7]); Kfusion[2] = SK_LOS[0]*(P[2][0]*tempVar[0] + P[2][1]*tempVar[1] - P[2][2]*tempVar[2] + P[2][3]*tempVar[3] + P[2][5]*tempVar[4] - P[2][6]*tempVar[5] - P[2][9]*tempVar[6] + P[2][4]*tempVar[7]); Kfusion[3] = SK_LOS[0]*(P[3][0]*tempVar[0] + P[3][1]*tempVar[1] - P[3][2]*tempVar[2] + P[3][3]*tempVar[3] + P[3][5]*tempVar[4] - P[3][6]*tempVar[5] - P[3][9]*tempVar[6] + P[3][4]*tempVar[7]); Kfusion[4] = SK_LOS[0]*(P[4][0]*tempVar[0] + P[4][1]*tempVar[1] - P[4][2]*tempVar[2] + P[4][3]*tempVar[3] + P[4][5]*tempVar[4] - P[4][6]*tempVar[5] - P[4][9]*tempVar[6] + P[4][4]*tempVar[7]); Kfusion[5] = SK_LOS[0]*(P[5][0]*tempVar[0] + P[5][1]*tempVar[1] - P[5][2]*tempVar[2] + P[5][3]*tempVar[3] + P[5][5]*tempVar[4] - P[5][6]*tempVar[5] - P[5][9]*tempVar[6] + P[5][4]*tempVar[7]); // Don't allow optical flow measurements to modify vertical velocity as it can produce height offsets Kfusion[6] = 0.0f;//SK_LOS[0]*(P[6][0]*tempVar[0] + P[6][1]*tempVar[1] - P[6][2]*tempVar[2] + P[6][3]*tempVar[3] + P[6][5]*tempVar[4] - P[6][6]*tempVar[5] - P[6][9]*tempVar[6] + P[6][4]*tempVar[7]); Kfusion[7] = SK_LOS[0]*(P[7][0]*tempVar[0] + P[7][1]*tempVar[1] - P[7][2]*tempVar[2] + P[7][3]*tempVar[3] + P[7][5]*tempVar[4] - P[7][6]*tempVar[5] - P[7][9]*tempVar[6] + P[7][4]*tempVar[7]); Kfusion[8] = SK_LOS[0]*(P[8][0]*tempVar[0] + P[8][1]*tempVar[1] - P[8][2]*tempVar[2] + P[8][3]*tempVar[3] + P[8][5]*tempVar[4] - P[8][6]*tempVar[5] - P[8][9]*tempVar[6] + P[8][4]*tempVar[7]); // Don't allow optical flow measurements to modify vertical position as it can produce height offsets Kfusion[9] = 0.0f;//SK_LOS[0]*(P[9][0]*tempVar[0] + P[9][1]*tempVar[1] - P[9][2]*tempVar[2] + P[9][3]*tempVar[3] + P[9][5]*tempVar[4] - P[9][6]*tempVar[5] - P[9][9]*tempVar[6] + P[9][4]*tempVar[7]); Kfusion[10] = SK_LOS[0]*(P[10][0]*tempVar[0] + P[10][1]*tempVar[1] - P[10][2]*tempVar[2] + P[10][3]*tempVar[3] + P[10][5]*tempVar[4] - P[10][6]*tempVar[5] - P[10][9]*tempVar[6] + P[10][4]*tempVar[7]); Kfusion[11] = SK_LOS[0]*(P[11][0]*tempVar[0] + P[11][1]*tempVar[1] - P[11][2]*tempVar[2] + P[11][3]*tempVar[3] + P[11][5]*tempVar[4] - P[11][6]*tempVar[5] - P[11][9]*tempVar[6] + P[11][4]*tempVar[7]); Kfusion[12] = SK_LOS[0]*(P[12][0]*tempVar[0] + P[12][1]*tempVar[1] - P[12][2]*tempVar[2] + P[12][3]*tempVar[3] + P[12][5]*tempVar[4] - P[12][6]*tempVar[5] - P[12][9]*tempVar[6] + P[12][4]*tempVar[7]); // only height measurements are allowed to modify the Z bias state to improve the stability of the estimate Kfusion[13] = 0.0f;//SK_LOS[0]*(P[13][0]*tempVar[0] + P[13][1]*tempVar[1] - P[13][2]*tempVar[2] + P[13][3]*tempVar[3] + P[13][5]*tempVar[4] - P[13][6]*tempVar[5] - P[13][9]*tempVar[6] + P[13][4]*tempVar[7]); if (inhibitWindStates) { Kfusion[14] = SK_LOS[0]*(P[14][0]*tempVar[0] + P[14][1]*tempVar[1] - P[14][2]*tempVar[2] + P[14][3]*tempVar[3] + P[14][5]*tempVar[4] - P[14][6]*tempVar[5] - P[14][9]*tempVar[6] + P[14][4]*tempVar[7]); Kfusion[15] = SK_LOS[0]*(P[15][0]*tempVar[0] + P[15][1]*tempVar[1] - P[15][2]*tempVar[2] + P[15][3]*tempVar[3] + P[15][5]*tempVar[4] - P[15][6]*tempVar[5] - P[15][9]*tempVar[6] + P[15][4]*tempVar[7]); } else { Kfusion[14] = 0.0f; Kfusion[15] = 0.0f; } if (inhibitMagStates) { Kfusion[16] = SK_LOS[0]*(P[16][0]*tempVar[0] + P[16][1]*tempVar[1] - P[16][2]*tempVar[2] + P[16][3]*tempVar[3] + P[16][5]*tempVar[4] - P[16][6]*tempVar[5] - P[16][9]*tempVar[6] + P[16][4]*tempVar[7]); Kfusion[17] = SK_LOS[0]*(P[17][0]*tempVar[0] + P[17][1]*tempVar[1] - P[17][2]*tempVar[2] + P[17][3]*tempVar[3] + P[17][5]*tempVar[4] - P[17][6]*tempVar[5] - P[17][9]*tempVar[6] + P[17][4]*tempVar[7]); Kfusion[18] = SK_LOS[0]*(P[18][0]*tempVar[0] + P[18][1]*tempVar[1] - P[18][2]*tempVar[2] + P[18][3]*tempVar[3] + P[18][5]*tempVar[4] - P[18][6]*tempVar[5] - P[18][9]*tempVar[6] + P[18][4]*tempVar[7]); Kfusion[19] = SK_LOS[0]*(P[19][0]*tempVar[0] + P[19][1]*tempVar[1] - P[19][2]*tempVar[2] + P[19][3]*tempVar[3] + P[19][5]*tempVar[4] - P[19][6]*tempVar[5] - P[19][9]*tempVar[6] + P[19][4]*tempVar[7]); Kfusion[20] = SK_LOS[0]*(P[20][0]*tempVar[0] + P[20][1]*tempVar[1] - P[20][2]*tempVar[2] + P[20][3]*tempVar[3] + P[20][5]*tempVar[4] - P[20][6]*tempVar[5] - P[20][9]*tempVar[6] + P[20][4]*tempVar[7]); Kfusion[21] = SK_LOS[0]*(P[21][0]*tempVar[0] + P[21][1]*tempVar[1] - P[21][2]*tempVar[2] + P[21][3]*tempVar[3] + P[21][5]*tempVar[4] - P[21][6]*tempVar[5] - P[21][9]*tempVar[6] + P[21][4]*tempVar[7]); } else { for (uint8_t i = 16; i <= 21; i++) { Kfusion[i] = 0.0f; } } // calculate innovation for Y observation innovOptFlow[1] = losPred[1] - flowRadXYcomp[1]; } // calculate the innovation consistency test ratio flowTestRatio[obsIndex] = sq(innovOptFlow[obsIndex]) / (sq(_flowInnovGate) * varInnovOptFlow[obsIndex]); // Check the innovation for consistency and don't fuse if out of bounds or flow is too fast to be reliable if ((flowTestRatio[obsIndex]) < 1.0f && (flowRadXY[obsIndex] < _maxFlowRate)) { // record the last time both X and Y observations were accepted for fusion if (obsIndex == 0) { flowXfailed = false; } else if (!flowXfailed) { prevFlowFuseTime_ms = imuSampleTime_ms; } // Attitude, velocity and position corrections are averaged across multiple prediction cycles between now and the anticipated time for the next measurement. // Don't do averaging of quaternion state corrections if total angle change across predicted interval is going to exceed 0.1 rad bool highRates = ((flowUpdateCountMax * correctedDelAng.length()) > 0.1f); // Calculate the number of averaging frames left to go. // There is no point averaging if the number of cycles left is less than 2 float minorFramesToGo = float(flowUpdateCountMax) - float(flowUpdateCount); for (uint8_t i = 0; i<=21; i++) { if ((i <= 3 && highRates) || i >= 10 || minorFramesToGo < 1.5f) { states[i] = states[i] - Kfusion[i] * innovOptFlow[obsIndex]; } else { flowIncrStateDelta[i] -= Kfusion[i] * innovOptFlow[obsIndex] * (flowUpdateCountMaxInv * float(flowUpdateCountMax) / minorFramesToGo); } } // normalise the quaternion states state.quat.normalize(); // correct the covariance P = (I - K*H)*P // take advantage of the empty columns in KH to reduce the // number of operations for (uint8_t i = 0; i <= 21; i++) { for (uint8_t j = 0; j <= 6; j++) { KH[i][j] = Kfusion[i] * H_LOS[j]; } for (uint8_t j = 7; j <= 8; j++) { KH[i][j] = 0.0f; } KH[i][9] = Kfusion[i] * H_LOS[9]; for (uint8_t j = 10; j <= 21; j++) { KH[i][j] = 0.0f; } } for (uint8_t i = 0; i <= 21; i++) { for (uint8_t j = 0; j <= 21; j++) { KHP[i][j] = 0.0f; for (uint8_t k = 0; k <= 6; k++) { KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j]; } KHP[i][j] = KHP[i][j] + KH[i][9] * P[9][j]; } } for (uint8_t i = 0; i <= 21; i++) { for (uint8_t j = 0; j <= 21; j++) { P[i][j] = P[i][j] - KHP[i][j]; } } } else if (obsIndex == 0) { // store the fact we have failed the X conponent so that a combined X and Y axis pass/fail can be calculated next time round flowXfailed = true; } ForceSymmetry(); ConstrainVariances(); } // fuse true airspeed measurements void NavEKF::FuseAirspeed() { // start performance timer perf_begin(_perf_FuseAirspeed); // declarations float vn; float ve; float vd; float vwn; float vwe; float EAS2TAS = _ahrs->get_EAS2TAS(); const float R_TAS = sq(constrain_float(_easNoise, 0.5f, 5.0f) * constrain_float(EAS2TAS, 0.9f, 10.0f)); Vector3f SH_TAS; float SK_TAS; Vector22 H_TAS; float VtasPred; // health is set bad until test passed tasHealth = false; // copy required states to local variable names vn = statesAtVtasMeasTime.velocity.x; ve = statesAtVtasMeasTime.velocity.y; vd = statesAtVtasMeasTime.velocity.z; vwn = statesAtVtasMeasTime.wind_vel.x; vwe = statesAtVtasMeasTime.wind_vel.y; // calculate the predicted airspeed, compensating for bias in GPS velocity when we are pulling a glitch offset back in VtasPred = pythagorous3((ve - gpsVelGlitchOffset.y - vwe) , (vn - gpsVelGlitchOffset.x - vwn) , vd); // perform fusion of True Airspeed measurement if (VtasPred > 1.0f) { // calculate observation jacobians SH_TAS[0] = 1.0f/VtasPred; SH_TAS[1] = (SH_TAS[0]*(2*ve - 2*vwe))/2; SH_TAS[2] = (SH_TAS[0]*(2*vn - 2*vwn))/2; for (uint8_t i=0; i<=21; i++) H_TAS[i] = 0.0f; H_TAS[4] = SH_TAS[2]; H_TAS[5] = SH_TAS[1]; H_TAS[6] = vd*SH_TAS[0]; H_TAS[14] = -SH_TAS[2]; H_TAS[15] = -SH_TAS[1]; // calculate Kalman gains float temp = (R_TAS + SH_TAS[2]*(P[4][4]*SH_TAS[2] + P[5][4]*SH_TAS[1] - P[14][4]*SH_TAS[2] - P[15][4]*SH_TAS[1] + P[6][4]*vd*SH_TAS[0]) + SH_TAS[1]*(P[4][5]*SH_TAS[2] + P[5][5]*SH_TAS[1] - P[14][5]*SH_TAS[2] - P[15][5]*SH_TAS[1] + P[6][5]*vd*SH_TAS[0]) - SH_TAS[2]*(P[4][14]*SH_TAS[2] + P[5][14]*SH_TAS[1] - P[14][14]*SH_TAS[2] - P[15][14]*SH_TAS[1] + P[6][14]*vd*SH_TAS[0]) - SH_TAS[1]*(P[4][15]*SH_TAS[2] + P[5][15]*SH_TAS[1] - P[14][15]*SH_TAS[2] - P[15][15]*SH_TAS[1] + P[6][15]*vd*SH_TAS[0]) + vd*SH_TAS[0]*(P[4][6]*SH_TAS[2] + P[5][6]*SH_TAS[1] - P[14][6]*SH_TAS[2] - P[15][6]*SH_TAS[1] + P[6][6]*vd*SH_TAS[0])); if (temp >= R_TAS) { SK_TAS = 1.0f / temp; faultStatus.bad_airspeed = false; } else { // the calculation is badly conditioned, so we cannot perform fusion on this step // we increase the wind state variances and try again next time P[14][14] += 0.05f*R_TAS; P[15][15] += 0.05f*R_TAS; faultStatus.bad_airspeed = true; return; } Kfusion[0] = SK_TAS*(P[0][4]*SH_TAS[2] - P[0][14]*SH_TAS[2] + P[0][5]*SH_TAS[1] - P[0][15]*SH_TAS[1] + P[0][6]*vd*SH_TAS[0]); Kfusion[1] = SK_TAS*(P[1][4]*SH_TAS[2] - P[1][14]*SH_TAS[2] + P[1][5]*SH_TAS[1] - P[1][15]*SH_TAS[1] + P[1][6]*vd*SH_TAS[0]); Kfusion[2] = SK_TAS*(P[2][4]*SH_TAS[2] - P[2][14]*SH_TAS[2] + P[2][5]*SH_TAS[1] - P[2][15]*SH_TAS[1] + P[2][6]*vd*SH_TAS[0]); Kfusion[3] = SK_TAS*(P[3][4]*SH_TAS[2] - P[3][14]*SH_TAS[2] + P[3][5]*SH_TAS[1] - P[3][15]*SH_TAS[1] + P[3][6]*vd*SH_TAS[0]); Kfusion[4] = SK_TAS*(P[4][4]*SH_TAS[2] - P[4][14]*SH_TAS[2] + P[4][5]*SH_TAS[1] - P[4][15]*SH_TAS[1] + P[4][6]*vd*SH_TAS[0]); Kfusion[5] = SK_TAS*(P[5][4]*SH_TAS[2] - P[5][14]*SH_TAS[2] + P[5][5]*SH_TAS[1] - P[5][15]*SH_TAS[1] + P[5][6]*vd*SH_TAS[0]); Kfusion[6] = SK_TAS*(P[6][4]*SH_TAS[2] - P[6][14]*SH_TAS[2] + P[6][5]*SH_TAS[1] - P[6][15]*SH_TAS[1] + P[6][6]*vd*SH_TAS[0]); Kfusion[7] = SK_TAS*(P[7][4]*SH_TAS[2] - P[7][14]*SH_TAS[2] + P[7][5]*SH_TAS[1] - P[7][15]*SH_TAS[1] + P[7][6]*vd*SH_TAS[0]); Kfusion[8] = SK_TAS*(P[8][4]*SH_TAS[2] - P[8][14]*SH_TAS[2] + P[8][5]*SH_TAS[1] - P[8][15]*SH_TAS[1] + P[8][6]*vd*SH_TAS[0]); Kfusion[9] = SK_TAS*(P[9][4]*SH_TAS[2] - P[9][14]*SH_TAS[2] + P[9][5]*SH_TAS[1] - P[9][15]*SH_TAS[1] + P[9][6]*vd*SH_TAS[0]); Kfusion[10] = SK_TAS*(P[10][4]*SH_TAS[2] - P[10][14]*SH_TAS[2] + P[10][5]*SH_TAS[1] - P[10][15]*SH_TAS[1] + P[10][6]*vd*SH_TAS[0]); Kfusion[11] = SK_TAS*(P[11][4]*SH_TAS[2] - P[11][14]*SH_TAS[2] + P[11][5]*SH_TAS[1] - P[11][15]*SH_TAS[1] + P[11][6]*vd*SH_TAS[0]); Kfusion[12] = SK_TAS*(P[12][4]*SH_TAS[2] - P[12][14]*SH_TAS[2] + P[12][5]*SH_TAS[1] - P[12][15]*SH_TAS[1] + P[12][6]*vd*SH_TAS[0]); // this term has been zeroed to improve stability of the Z accel bias Kfusion[13] = 0.0f;//SK_TAS*(P[13][4]*SH_TAS[2] - P[13][14]*SH_TAS[2] + P[13][5]*SH_TAS[1] - P[13][15]*SH_TAS[1] + P[13][6]*vd*SH_TAS[0]); Kfusion[14] = SK_TAS*(P[14][4]*SH_TAS[2] - P[14][14]*SH_TAS[2] + P[14][5]*SH_TAS[1] - P[14][15]*SH_TAS[1] + P[14][6]*vd*SH_TAS[0]); Kfusion[15] = SK_TAS*(P[15][4]*SH_TAS[2] - P[15][14]*SH_TAS[2] + P[15][5]*SH_TAS[1] - P[15][15]*SH_TAS[1] + P[15][6]*vd*SH_TAS[0]); // zero Kalman gains to inhibit magnetic field state estimation if (!inhibitMagStates) { Kfusion[16] = SK_TAS*(P[16][4]*SH_TAS[2] - P[16][14]*SH_TAS[2] + P[16][5]*SH_TAS[1] - P[16][15]*SH_TAS[1] + P[16][6]*vd*SH_TAS[0]); Kfusion[17] = SK_TAS*(P[17][4]*SH_TAS[2] - P[17][14]*SH_TAS[2] + P[17][5]*SH_TAS[1] - P[17][15]*SH_TAS[1] + P[17][6]*vd*SH_TAS[0]); Kfusion[18] = SK_TAS*(P[18][4]*SH_TAS[2] - P[18][14]*SH_TAS[2] + P[18][5]*SH_TAS[1] - P[18][15]*SH_TAS[1] + P[18][6]*vd*SH_TAS[0]); Kfusion[19] = SK_TAS*(P[19][4]*SH_TAS[2] - P[19][14]*SH_TAS[2] + P[19][5]*SH_TAS[1] - P[19][15]*SH_TAS[1] + P[19][6]*vd*SH_TAS[0]); Kfusion[20] = SK_TAS*(P[20][4]*SH_TAS[2] - P[20][14]*SH_TAS[2] + P[20][5]*SH_TAS[1] - P[20][15]*SH_TAS[1] + P[20][6]*vd*SH_TAS[0]); Kfusion[21] = SK_TAS*(P[21][4]*SH_TAS[2] - P[21][14]*SH_TAS[2] + P[21][5]*SH_TAS[1] - P[21][15]*SH_TAS[1] + P[21][6]*vd*SH_TAS[0]); } else { for (uint8_t i=16; i<=21; i++) { Kfusion[i] = 0.0f; } } // calculate measurement innovation variance varInnovVtas = 1.0f/SK_TAS; // calculate measurement innovation innovVtas = VtasPred - VtasMeas; // calculate the innovation consistency test ratio tasTestRatio = sq(innovVtas) / (sq(_tasInnovGate) * varInnovVtas); // fail if the ratio is > 1, but don't fail if bad IMU data tasHealth = ((tasTestRatio < 1.0f) || badIMUdata); tasTimeout = (imuSampleTime_ms - lastTasPassTime) > tasRetryTime; // test the ratio before fusing data, forcing fusion if airspeed and position are timed out as we have no choice but to try and use airspeed to constrain error growth if (tasHealth || (tasTimeout && posTimeout)) { // restart the counter lastTasPassTime = imuSampleTime_ms; // correct the state vector for (uint8_t j=0; j<=21; j++) { states[j] = states[j] - Kfusion[j] * innovVtas; } state.quat.normalize(); // correct the covariance P = (I - K*H)*P // take advantage of the empty columns in H to reduce the number of operations for (uint8_t i = 0; i<=21; i++) { for (uint8_t j = 0; j<=3; j++) KH[i][j] = 0.0f; for (uint8_t j = 4; j<=6; j++) { KH[i][j] = Kfusion[i] * H_TAS[j]; } for (uint8_t j = 7; j<=13; j++) KH[i][j] = 0.0f; for (uint8_t j = 14; j<=15; j++) { KH[i][j] = Kfusion[i] * H_TAS[j]; } for (uint8_t j = 16; j<=21; j++) KH[i][j] = 0.0f; } for (uint8_t i = 0; i<=21; i++) { for (uint8_t j = 0; j<=21; j++) { KHP[i][j] = 0; for (uint8_t k = 4; k<=6; k++) { KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j]; } for (uint8_t k = 14; k<=15; k++) { KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j]; } } } for (uint8_t i = 0; i<=21; i++) { for (uint8_t j = 0; j<=21; j++) { P[i][j] = P[i][j] - KHP[i][j]; } } } } // force the covariance matrix to me symmetrical and limit the variances to prevent ill-condiioning. ForceSymmetry(); ConstrainVariances(); // stop performance timer perf_end(_perf_FuseAirspeed); } // fuse sythetic sideslip measurement of zero void NavEKF::FuseSideslip() { // start performance timer perf_begin(_perf_FuseSideslip); // declarations float q0; float q1; float q2; float q3; float vn; float ve; float vd; float vwn; float vwe; const float R_BETA = 0.03f; // assume a sideslip angle RMS of ~10 deg Vector13 SH_BETA; Vector8 SK_BETA; Vector3f vel_rel_wind; Vector22 H_BETA; float innovBeta; // copy required states to local variable names q0 = state.quat[0]; q1 = state.quat[1]; q2 = state.quat[2]; q3 = state.quat[3]; vn = state.velocity.x; ve = state.velocity.y; vd = state.velocity.z; vwn = state.wind_vel.x; vwe = state.wind_vel.y; // calculate predicted wind relative velocity in NED, compensating for offset in velcity when we are pulling a GPS glitch offset back in vel_rel_wind.x = vn - vwn - gpsVelGlitchOffset.x; vel_rel_wind.y = ve - vwe - gpsVelGlitchOffset.y; vel_rel_wind.z = vd; // rotate into body axes vel_rel_wind = prevTnb * vel_rel_wind; // perform fusion of assumed sideslip = 0 if (vel_rel_wind.x > 5.0f) { // Calculate observation jacobians SH_BETA[0] = (vn - vwn)*(sq(q0) + sq(q1) - sq(q2) - sq(q3)) - vd*(2*q0*q2 - 2*q1*q3) + (ve - vwe)*(2*q0*q3 + 2*q1*q2); if (fabsf(SH_BETA[0]) <= 1e-9f) { faultStatus.bad_sideslip = true; return; } else { faultStatus.bad_sideslip = false; } SH_BETA[1] = (ve - vwe)*(sq(q0) - sq(q1) + sq(q2) - sq(q3)) + vd*(2*q0*q1 + 2*q2*q3) - (vn - vwn)*(2*q0*q3 - 2*q1*q2); SH_BETA[2] = vn - vwn; SH_BETA[3] = ve - vwe; SH_BETA[4] = 1/sq(SH_BETA[0]); SH_BETA[5] = 1/SH_BETA[0]; SH_BETA[6] = SH_BETA[5]*(sq(q0) - sq(q1) + sq(q2) - sq(q3)); SH_BETA[7] = sq(q0) + sq(q1) - sq(q2) - sq(q3); SH_BETA[8] = 2*q0*SH_BETA[3] - 2*q3*SH_BETA[2] + 2*q1*vd; SH_BETA[9] = 2*q0*SH_BETA[2] + 2*q3*SH_BETA[3] - 2*q2*vd; SH_BETA[10] = 2*q2*SH_BETA[2] - 2*q1*SH_BETA[3] + 2*q0*vd; SH_BETA[11] = 2*q1*SH_BETA[2] + 2*q2*SH_BETA[3] + 2*q3*vd; SH_BETA[12] = 2*q0*q3; for (uint8_t i=0; i<=21; i++) { H_BETA[i] = 0.0f; } H_BETA[0] = SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]; H_BETA[1] = SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]; H_BETA[2] = SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]; H_BETA[3] = - SH_BETA[5]*SH_BETA[9] - SH_BETA[1]*SH_BETA[4]*SH_BETA[8]; H_BETA[4] = - SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) - SH_BETA[1]*SH_BETA[4]*SH_BETA[7]; H_BETA[5] = SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2); H_BETA[6] = SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3); H_BETA[14] = SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]; H_BETA[15] = SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2) - SH_BETA[6]; // Calculate Kalman gains float temp = (R_BETA - (SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7])*(P[14][4]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][4]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][4]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][4]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][4]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][4]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][4]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][4]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][4]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) + (SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7])*(P[14][14]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][14]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][14]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][14]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][14]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][14]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][14]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][14]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][14]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) + (SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2))*(P[14][5]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][5]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][5]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][5]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][5]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][5]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][5]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][5]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][5]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) - (SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2))*(P[14][15]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][15]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][15]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][15]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][15]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][15]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][15]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][15]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][15]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) + (SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9])*(P[14][0]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][0]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][0]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][0]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][0]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][0]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][0]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][0]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][0]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) + (SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11])*(P[14][1]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][1]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][1]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][1]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][1]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][1]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][1]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][1]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][1]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) + (SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10])*(P[14][2]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][2]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][2]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][2]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][2]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][2]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][2]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][2]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][2]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) - (SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8])*(P[14][3]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][3]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][3]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][3]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][3]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][3]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][3]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][3]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][3]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) + (SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))*(P[14][6]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][6]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][6]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][6]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][6]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][6]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][6]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][6]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][6]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3)))); if (temp >= R_BETA) { SK_BETA[0] = 1.0f / temp; faultStatus.bad_sideslip = false; } else { // the calculation is badly conditioned, so we cannot perform fusion on this step faultStatus.bad_sideslip = true; return; } SK_BETA[1] = SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]; SK_BETA[2] = SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2); SK_BETA[3] = SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3); SK_BETA[4] = SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]; SK_BETA[5] = SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]; SK_BETA[6] = SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]; SK_BETA[7] = SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]; Kfusion[0] = SK_BETA[0]*(P[0][0]*SK_BETA[5] + P[0][1]*SK_BETA[4] - P[0][4]*SK_BETA[1] + P[0][5]*SK_BETA[2] + P[0][2]*SK_BETA[6] + P[0][6]*SK_BETA[3] - P[0][3]*SK_BETA[7] + P[0][14]*SK_BETA[1] - P[0][15]*SK_BETA[2]); Kfusion[1] = SK_BETA[0]*(P[1][0]*SK_BETA[5] + P[1][1]*SK_BETA[4] - P[1][4]*SK_BETA[1] + P[1][5]*SK_BETA[2] + P[1][2]*SK_BETA[6] + P[1][6]*SK_BETA[3] - P[1][3]*SK_BETA[7] + P[1][14]*SK_BETA[1] - P[1][15]*SK_BETA[2]); Kfusion[2] = SK_BETA[0]*(P[2][0]*SK_BETA[5] + P[2][1]*SK_BETA[4] - P[2][4]*SK_BETA[1] + P[2][5]*SK_BETA[2] + P[2][2]*SK_BETA[6] + P[2][6]*SK_BETA[3] - P[2][3]*SK_BETA[7] + P[2][14]*SK_BETA[1] - P[2][15]*SK_BETA[2]); Kfusion[3] = SK_BETA[0]*(P[3][0]*SK_BETA[5] + P[3][1]*SK_BETA[4] - P[3][4]*SK_BETA[1] + P[3][5]*SK_BETA[2] + P[3][2]*SK_BETA[6] + P[3][6]*SK_BETA[3] - P[3][3]*SK_BETA[7] + P[3][14]*SK_BETA[1] - P[3][15]*SK_BETA[2]); Kfusion[4] = SK_BETA[0]*(P[4][0]*SK_BETA[5] + P[4][1]*SK_BETA[4] - P[4][4]*SK_BETA[1] + P[4][5]*SK_BETA[2] + P[4][2]*SK_BETA[6] + P[4][6]*SK_BETA[3] - P[4][3]*SK_BETA[7] + P[4][14]*SK_BETA[1] - P[4][15]*SK_BETA[2]); Kfusion[5] = SK_BETA[0]*(P[5][0]*SK_BETA[5] + P[5][1]*SK_BETA[4] - P[5][4]*SK_BETA[1] + P[5][5]*SK_BETA[2] + P[5][2]*SK_BETA[6] + P[5][6]*SK_BETA[3] - P[5][3]*SK_BETA[7] + P[5][14]*SK_BETA[1] - P[5][15]*SK_BETA[2]); Kfusion[6] = SK_BETA[0]*(P[6][0]*SK_BETA[5] + P[6][1]*SK_BETA[4] - P[6][4]*SK_BETA[1] + P[6][5]*SK_BETA[2] + P[6][2]*SK_BETA[6] + P[6][6]*SK_BETA[3] - P[6][3]*SK_BETA[7] + P[6][14]*SK_BETA[1] - P[6][15]*SK_BETA[2]); Kfusion[7] = SK_BETA[0]*(P[7][0]*SK_BETA[5] + P[7][1]*SK_BETA[4] - P[7][4]*SK_BETA[1] + P[7][5]*SK_BETA[2] + P[7][2]*SK_BETA[6] + P[7][6]*SK_BETA[3] - P[7][3]*SK_BETA[7] + P[7][14]*SK_BETA[1] - P[7][15]*SK_BETA[2]); Kfusion[8] = SK_BETA[0]*(P[8][0]*SK_BETA[5] + P[8][1]*SK_BETA[4] - P[8][4]*SK_BETA[1] + P[8][5]*SK_BETA[2] + P[8][2]*SK_BETA[6] + P[8][6]*SK_BETA[3] - P[8][3]*SK_BETA[7] + P[8][14]*SK_BETA[1] - P[8][15]*SK_BETA[2]); Kfusion[9] = SK_BETA[0]*(P[9][0]*SK_BETA[5] + P[9][1]*SK_BETA[4] - P[9][4]*SK_BETA[1] + P[9][5]*SK_BETA[2] + P[9][2]*SK_BETA[6] + P[9][6]*SK_BETA[3] - P[9][3]*SK_BETA[7] + P[9][14]*SK_BETA[1] - P[9][15]*SK_BETA[2]); Kfusion[10] = SK_BETA[0]*(P[10][0]*SK_BETA[5] + P[10][1]*SK_BETA[4] - P[10][4]*SK_BETA[1] + P[10][5]*SK_BETA[2] + P[10][2]*SK_BETA[6] + P[10][6]*SK_BETA[3] - P[10][3]*SK_BETA[7] + P[10][14]*SK_BETA[1] - P[10][15]*SK_BETA[2]); Kfusion[11] = SK_BETA[0]*(P[11][0]*SK_BETA[5] + P[11][1]*SK_BETA[4] - P[11][4]*SK_BETA[1] + P[11][5]*SK_BETA[2] + P[11][2]*SK_BETA[6] + P[11][6]*SK_BETA[3] - P[11][3]*SK_BETA[7] + P[11][14]*SK_BETA[1] - P[11][15]*SK_BETA[2]); Kfusion[12] = SK_BETA[0]*(P[12][0]*SK_BETA[5] + P[12][1]*SK_BETA[4] - P[12][4]*SK_BETA[1] + P[12][5]*SK_BETA[2] + P[12][2]*SK_BETA[6] + P[12][6]*SK_BETA[3] - P[12][3]*SK_BETA[7] + P[12][14]*SK_BETA[1] - P[12][15]*SK_BETA[2]); // this term has been zeroed to improve stability of the Z accel bias Kfusion[13] = 0.0f;//SK_BETA[0]*(P[13][0]*SK_BETA[5] + P[13][1]*SK_BETA[4] - P[13][4]*SK_BETA[1] + P[13][5]*SK_BETA[2] + P[13][2]*SK_BETA[6] + P[13][6]*SK_BETA[3] - P[13][3]*SK_BETA[7] + P[13][14]*SK_BETA[1] - P[13][15]*SK_BETA[2]); Kfusion[14] = SK_BETA[0]*(P[14][0]*SK_BETA[5] + P[14][1]*SK_BETA[4] - P[14][4]*SK_BETA[1] + P[14][5]*SK_BETA[2] + P[14][2]*SK_BETA[6] + P[14][6]*SK_BETA[3] - P[14][3]*SK_BETA[7] + P[14][14]*SK_BETA[1] - P[14][15]*SK_BETA[2]); Kfusion[15] = SK_BETA[0]*(P[15][0]*SK_BETA[5] + P[15][1]*SK_BETA[4] - P[15][4]*SK_BETA[1] + P[15][5]*SK_BETA[2] + P[15][2]*SK_BETA[6] + P[15][6]*SK_BETA[3] - P[15][3]*SK_BETA[7] + P[15][14]*SK_BETA[1] - P[15][15]*SK_BETA[2]); // zero Kalman gains to inhibit magnetic field state estimation if (!inhibitMagStates) { Kfusion[16] = SK_BETA[0]*(P[16][0]*SK_BETA[5] + P[16][1]*SK_BETA[4] - P[16][4]*SK_BETA[1] + P[16][5]*SK_BETA[2] + P[16][2]*SK_BETA[6] + P[16][6]*SK_BETA[3] - P[16][3]*SK_BETA[7] + P[16][14]*SK_BETA[1] - P[16][15]*SK_BETA[2]); Kfusion[17] = SK_BETA[0]*(P[17][0]*SK_BETA[5] + P[17][1]*SK_BETA[4] - P[17][4]*SK_BETA[1] + P[17][5]*SK_BETA[2] + P[17][2]*SK_BETA[6] + P[17][6]*SK_BETA[3] - P[17][3]*SK_BETA[7] + P[17][14]*SK_BETA[1] - P[17][15]*SK_BETA[2]); Kfusion[18] = SK_BETA[0]*(P[18][0]*SK_BETA[5] + P[18][1]*SK_BETA[4] - P[18][4]*SK_BETA[1] + P[18][5]*SK_BETA[2] + P[18][2]*SK_BETA[6] + P[18][6]*SK_BETA[3] - P[18][3]*SK_BETA[7] + P[18][14]*SK_BETA[1] - P[18][15]*SK_BETA[2]); Kfusion[19] = SK_BETA[0]*(P[19][0]*SK_BETA[5] + P[19][1]*SK_BETA[4] - P[19][4]*SK_BETA[1] + P[19][5]*SK_BETA[2] + P[19][2]*SK_BETA[6] + P[19][6]*SK_BETA[3] - P[19][3]*SK_BETA[7] + P[19][14]*SK_BETA[1] - P[19][15]*SK_BETA[2]); Kfusion[20] = SK_BETA[0]*(P[20][0]*SK_BETA[5] + P[20][1]*SK_BETA[4] - P[20][4]*SK_BETA[1] + P[20][5]*SK_BETA[2] + P[20][2]*SK_BETA[6] + P[20][6]*SK_BETA[3] - P[20][3]*SK_BETA[7] + P[20][14]*SK_BETA[1] - P[20][15]*SK_BETA[2]); Kfusion[21] = SK_BETA[0]*(P[21][0]*SK_BETA[5] + P[21][1]*SK_BETA[4] - P[21][4]*SK_BETA[1] + P[21][5]*SK_BETA[2] + P[21][2]*SK_BETA[6] + P[21][6]*SK_BETA[3] - P[21][3]*SK_BETA[7] + P[21][14]*SK_BETA[1] - P[21][15]*SK_BETA[2]); } else { for (uint8_t i=16; i<=21; i++) { Kfusion[i] = 0.0f; } } // calculate predicted sideslip angle and innovation using small angle approximation innovBeta = vel_rel_wind.y / vel_rel_wind.x; // reject measurement if greater than 3-sigma inconsistency if (innovBeta > 0.5f) { return; } // correct the state vector for (uint8_t j=0; j<=21; j++) { states[j] = states[j] - Kfusion[j] * innovBeta; } state.quat.normalize(); // correct the covariance P = (I - K*H)*P // take advantage of the empty columns in H to reduce the // number of operations for (uint8_t i = 0; i<=21; i++) { for (uint8_t j = 0; j<=6; j++) { KH[i][j] = Kfusion[i] * H_BETA[j]; } for (uint8_t j = 7; j<=13; j++) KH[i][j] = 0.0f; for (uint8_t j = 14; j<=15; j++) { KH[i][j] = Kfusion[i] * H_BETA[j]; } for (uint8_t j = 16; j<=21; j++) KH[i][j] = 0.0f; } for (uint8_t i = 0; i<=21; i++) { for (uint8_t j = 0; j<=21; j++) { KHP[i][j] = 0; for (uint8_t k = 0; k<=6; k++) { KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j]; } for (uint8_t k = 14; k<=15; k++) { KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j]; } } } for (uint8_t i = 0; i<=21; i++) { for (uint8_t j = 0; j<=21; j++) { P[i][j] = P[i][j] - KHP[i][j]; } } } // force the covariance matrix to me symmetrical and limit the variances to prevent ill-condiioning. ForceSymmetry(); ConstrainVariances(); // stop the performance timer perf_end(_perf_FuseSideslip); } // zero specified range of rows in the state covariance matrix void NavEKF::zeroRows(Matrix22 &covMat, uint8_t first, uint8_t last) { uint8_t row; for (row=first; row<=last; row++) { memset(&covMat[row][0], 0, sizeof(covMat[0][0])*22); } } // zero specified range of columns in the state covariance matrix void NavEKF::zeroCols(Matrix22 &covMat, uint8_t first, uint8_t last) { uint8_t row; for (row=0; row<=21; row++) { memset(&covMat[row][first], 0, sizeof(covMat[0][0])*(1+last-first)); } } // store states in a history array along with time stamp void NavEKF::StoreStates() { // Don't need to store states more often than every 10 msec if (imuSampleTime_ms - lastStateStoreTime_ms >= 10) { lastStateStoreTime_ms = imuSampleTime_ms; if (storeIndex > 49) { storeIndex = 0; } storedStates[storeIndex] = state; statetimeStamp[storeIndex] = lastStateStoreTime_ms; storeIndex = storeIndex + 1; } } // reset the stored state history and store the current state void NavEKF::StoreStatesReset() { // clear stored state history memset(&storedStates[0], 0, sizeof(storedStates)); memset(&statetimeStamp[0], 0, sizeof(statetimeStamp)); // store current state vector in first column storeIndex = 0; storedStates[storeIndex] = state; statetimeStamp[storeIndex] = imuSampleTime_ms; storeIndex = storeIndex + 1; } // recall state vector stored at closest time to the one specified by msec void NavEKF::RecallStates(state_elements &statesForFusion, uint32_t msec) { uint32_t timeDelta; uint32_t bestTimeDelta = 200; uint8_t bestStoreIndex = 0; for (uint8_t i=0; i<=49; i++) { timeDelta = msec - statetimeStamp[i]; if (timeDelta < bestTimeDelta) { bestStoreIndex = i; bestTimeDelta = timeDelta; } } if (bestTimeDelta < 200) // only output stored state if < 200 msec retrieval error { statesForFusion = storedStates[bestStoreIndex]; } else // otherwise output current state { statesForFusion = state; } } // recall omega (angular rate vector) average across the time interval from msecStart to msecEnd void NavEKF::RecallOmega(Vector3f &omegaAvg, uint32_t msecStart, uint32_t msecEnd) { // calculate average angular rate vector over the time interval from msecStart to msecEnd // if no values are inside the time window, return the current angular rate omegaAvg.zero(); uint8_t numAvg = 0; for (uint8_t i=0; i<=49; i++) { if (msecStart <= statetimeStamp[i] && msecEnd >= statetimeStamp[i]) { omegaAvg += storedStates[i].omega; numAvg += 1; } } if (numAvg >= 1) { omegaAvg = omegaAvg / float(numAvg); } else if (dtIMUactual > 0) { omegaAvg = correctedDelAng / dtIMUactual; } else { omegaAvg.zero(); } } // calculate nav to body quaternions from body to nav rotation matrix void NavEKF::quat2Tbn(Matrix3f &Tbn, const Quaternion &quat) const { // Calculate the body to nav cosine matrix quat.rotation_matrix(Tbn); } // return the Euler roll, pitch and yaw angle in radians void NavEKF::getEulerAngles(Vector3f &euler) const { state.quat.to_euler(euler.x, euler.y, euler.z); euler = euler - _ahrs->get_trim(); } // This returns the specific forces in the NED frame void NavEKF::getAccelNED(Vector3f &accelNED) const { accelNED = velDotNED; accelNED.z -= GRAVITY_MSS; } // return NED velocity in m/s // void NavEKF::getVelNED(Vector3f &vel) const { vel = state.velocity; } // Return the last calculated NED position relative to the reference point (m). // if a calculated solution is not available, use the best available data and return false bool NavEKF::getPosNED(Vector3f &pos) const { // The EKF always has a height estimate regardless of mode of operation pos.z = state.position.z; // There are three modes of operation, absolute position (GPS fusion), relative position (optical flow fusion) and constant position (no position estimate available) nav_filter_status status; getFilterStatus(status); if (status.flags.horiz_pos_abs || status.flags.horiz_pos_rel) { // This is the normal mode of operation where we can use the EKF position states pos.x = state.position.x; pos.y = state.position.y; return true; } else { // In constant position mode the EKF position states are at the origin, so we cannot use them as a position estimate if(validOrigin) { if ((_ahrs->get_gps().status() >= AP_GPS::GPS_OK_FIX_2D)) { // If the origin has been set and we have GPS, then return the GPS position relative to the origin const struct Location &gpsloc = _ahrs->get_gps().location(); Vector2f tempPosNE = location_diff(EKF_origin, gpsloc); pos.x = tempPosNE.x; pos.y = tempPosNE.y; return false; } else { // If no GPS fix is available, all we can do is provide the last known position pos.x = state.position.x + lastKnownPositionNE.x; pos.y = state.position.y + lastKnownPositionNE.y; return false; } } else { // If the origin has not been set, then we have no means of providing a relative position pos.x = 0.0f; pos.y = 0.0f; return false; } } return false; } // return body axis gyro bias estimates in rad/sec void NavEKF::getGyroBias(Vector3f &gyroBias) const { if (dtIMUavg < 1e-6f) { gyroBias.zero(); return; } gyroBias = state.gyro_bias / dtIMUavg; } // reset the body axis gyro bias states to zero and re-initialise the corresponding covariances void NavEKF::resetGyroBias(void) { state.gyro_bias.zero(); zeroRows(P,10,12); zeroCols(P,10,12); P[10][10] = sq(radians(InitialGyroBiasUncertainty() * dtIMUavg)); P[11][11] = P[10][10]; P[12][12] = P[10][10]; } // Reset the baro so that it reads zero at the current height // Reset the EKF height to zero // Adjust the EKf origin height so that the EKF height + origin height is the same as before // Return true if the height datum reset has been performed // If using a range finder for height do not reset and return false bool NavEKF::resetHeightDatum(void) { // if we are using a range finder for height, return false if (_altSource == 1) { return false; } // record the old height estimate float oldHgt = -state.position.z; // reset the barometer so that it reads zero at the current height _baro.update_calibration(); // reset the height state state.position.z = 0.0f; // reset the stored height states from previous time steps for (uint8_t i=0; i<=49; i++){ storedStates[i].position.z = state.position.z; } // adjust the height of the EKF origin so that the origin plus baro height before and afer the reset is the same if (validOrigin) { EKF_origin.alt += oldHgt*100; } return true; } // Commands the EKF to not use GPS. // This command must be sent prior to arming // This command is forgotten by the EKF each time the vehicle disarms // Returns 0 if command rejected // Returns 1 if attitude, vertical velocity and vertical position will be provided // Returns 2 if attitude, 3D-velocity, vertical position and relative horizontal position will be provided uint8_t NavEKF::setInhibitGPS(void) { if(!vehicleArmed) { return 0; } if (optFlowDataPresent()) { _fusionModeGPS = 3; return 2; } else { return 1; } } // return the horizontal speed limit in m/s set by optical flow sensor limits // return the scale factor to be applied to navigation velocity gains to compensate for increase in velocity noise with height when using optical flow void NavEKF::getEkfControlLimits(float &ekfGndSpdLimit, float &ekfNavVelGainScaler) const { if (PV_AidingMode == AID_RELATIVE) { // allow 1.0 rad/sec margin for angular motion ekfGndSpdLimit = max((_maxFlowRate - 1.0f), 0.0f) * max((terrainState - state.position[2]), rngOnGnd); // use standard gains up to 5.0 metres height and reduce above that ekfNavVelGainScaler = 4.0f / max((terrainState - state.position[2]),4.0f); } else { ekfGndSpdLimit = 400.0f; //return 80% of max filter speed ekfNavVelGainScaler = 1.0f; } } // return weighting of first IMU in blending function void NavEKF::getIMU1Weighting(float &ret) const { ret = IMU1_weighting; } // return the individual Z-accel bias estimates in m/s^2 void NavEKF::getAccelZBias(float &zbias1, float &zbias2) const { if (dtIMUavg > 0) { zbias1 = state.accel_zbias1 / dtIMUavg; zbias2 = state.accel_zbias2 / dtIMUavg; } else { zbias1 = 0; zbias2 = 0; } } // return the NED wind speed estimates in m/s (positive is air moving in the direction of the axis) void NavEKF::getWind(Vector3f &wind) const { wind.x = state.wind_vel.x; wind.y = state.wind_vel.y; wind.z = 0.0f; // currently don't estimate this } // return earth magnetic field estimates in measurement units / 1000 void NavEKF::getMagNED(Vector3f &magNED) const { magNED = state.earth_magfield * 1000.0f; } // return body magnetic field estimates in measurement units / 1000 void NavEKF::getMagXYZ(Vector3f &magXYZ) const { magXYZ = state.body_magfield*1000.0f; } // return magnetometer offsets // return true if offsets are valid bool NavEKF::getMagOffsets(Vector3f &magOffsets) const { // compass offsets are valid if we have finalised magnetic field initialisation and magnetic field learning is not prohibited and primary compass is valid if (secondMagYawInit && (_magCal != 2) && _ahrs->get_compass()->healthy()) { magOffsets = _ahrs->get_compass()->get_offsets() - state.body_magfield*1000.0f; return true; } else { magOffsets = _ahrs->get_compass()->get_offsets(); return false; } } // Return the last calculated latitude, longitude and height in WGS-84 // If a calculated location isn't available, return a raw GPS measurement // The status will return true if a calculation or raw measurement is available // The getFilterStatus() function provides a more detailed description of data health and must be checked if data is to be used for flight control bool NavEKF::getLLH(struct Location &loc) const { if(validOrigin) { // Altitude returned is an absolute altitude relative to the WGS-84 spherioid loc.alt = EKF_origin.alt - state.position.z*100; loc.flags.relative_alt = 0; loc.flags.terrain_alt = 0; // there are three modes of operation, absolute position (GPS fusion), relative position (optical flow fusion) and constant position (no aiding) nav_filter_status status; getFilterStatus(status); if (status.flags.horiz_pos_abs || status.flags.horiz_pos_rel) { loc.lat = EKF_origin.lat; loc.lng = EKF_origin.lng; location_offset(loc, state.position.x, state.position.y); return true; } else { // we could be in constant position mode becasue the vehicle has taken off without GPS, or has lost GPS // in this mode we cannot use the EKF states to estimate position so will return the best available data if ((_ahrs->get_gps().status() >= AP_GPS::GPS_OK_FIX_2D)) { // we have a GPS position fix to return const struct Location &gpsloc = _ahrs->get_gps().location(); loc.lat = gpsloc.lat; loc.lng = gpsloc.lng; return true; } else { // if no GPS fix, provide last known position before entering the mode location_offset(loc, lastKnownPositionNE.x, lastKnownPositionNE.y); return false; } } } else { // If no origin has been defined for the EKF, then we cannot use its position states so return a raw // GPS reading if available and return false if ((_ahrs->get_gps().status() >= AP_GPS::GPS_OK_FIX_3D)) { const struct Location &gpsloc = _ahrs->get_gps().location(); loc = gpsloc; loc.flags.relative_alt = 0; loc.flags.terrain_alt = 0; } return false; } } // return the estimated height above ground level bool NavEKF::getHAGL(float &HAGL) const { HAGL = terrainState - state.position.z; // If we know the terrain offset and altitude, then we have a valid height above ground estimate return !hgtTimeout && gndOffsetValid && healthy(); } // return data for debugging optical flow fusion void NavEKF::getFlowDebug(float &varFlow, float &gndOffset, float &flowInnovX, float &flowInnovY, float &auxInnov, float &HAGL, float &rngInnov, float &range, float &gndOffsetErr) const { varFlow = max(flowTestRatio[0],flowTestRatio[1]); gndOffset = terrainState; flowInnovX = innovOptFlow[0]; flowInnovY = innovOptFlow[1]; auxInnov = auxFlowObsInnov; HAGL = terrainState - state.position.z; rngInnov = innovRng; range = rngMea; gndOffsetErr = sqrtf(Popt); // note Popt is constrained to be non-negative in EstimateTerrainOffset() } // calculate whether the flight vehicle is on the ground or flying from height, airspeed and GPS speed void NavEKF::SetFlightAndFusionModes() { // determine if the vehicle is manoevring if (accNavMagHoriz > 0.5f){ manoeuvring = true; } else { manoeuvring = false; } // if we are a fly forward type vehicle, then in-air mode can be determined through a combination of speed and height criteria if (assume_zero_sideslip()) { // Evaluate a numerical score that defines the likelihood we are in the air float gndSpdSq = sq(velNED[0]) + sq(velNED[1]); bool highGndSpd = false; bool highAirSpd = false; bool largeHgtChange = false; // trigger at 8 m/s airspeed if (_ahrs->airspeed_sensor_enabled()) { const AP_Airspeed *airspeed = _ahrs->get_airspeed(); if (airspeed->get_airspeed() * airspeed->get_EAS2TAS() > 10.0f) { highAirSpd = true; } } // trigger at 10 m/s GPS velocity, but not if GPS is reporting bad velocity errors if (gndSpdSq > 100.0f && gpsSpdAccuracy < 1.0f) { highGndSpd = true; } // trigger if more than 10m away from initial height if (fabsf(hgtMea) > 10.0f) { largeHgtChange = true; } // to go to in-air mode we also need enough GPS velocity to be able to calculate a reliable ground track heading and either a lerge height or airspeed change if (onGround && highGndSpd && (highAirSpd || largeHgtChange)) { onGround = false; } // if is possible we are in flight, set the time this condition was last detected if (highGndSpd || highAirSpd || largeHgtChange) { airborneDetectTime_ms = imuSampleTime_ms; } // after 5 seconds of not detecting a possible flight condition, we transition to on-ground mode if(!onGround && ((imuSampleTime_ms - airborneDetectTime_ms) > 5000)) { onGround = true; } // perform a yaw alignment check against GPS if exiting on-ground mode, bu tonly if we have enough ground speed // this is done to protect against unrecoverable heading alignment errors due to compass faults if (!onGround && prevOnGround) { alignYawGPS(); } // If we aren't using an airspeed sensor we set the wind velocity to the reciprocal // of the velocity vector and scale states so that the wind speed is equal to 3m/s. This helps prevent gains // being too high at the start of flight if launching into a headwind until the first turn when the EKF can form // a wind speed estimate and also corrects bad initial wind estimates due to heading errors if (!onGround && prevOnGround && !useAirspeed()) { setWindVelStates(); } } // store current on-ground status for next time prevOnGround = onGround; // If we are on ground, or in constant position mode, or don't have the right vehicle and sensing to estimate wind, inhibit wind states inhibitWindStates = ((!useAirspeed() && !assume_zero_sideslip()) || onGround || constPosMode); // request mag calibration for both in-air and manoeuvre threshold options bool magCalRequested = ((_magCal == 0) && !onGround) || ((_magCal == 1) && manoeuvring) || (_magCal == 3); // deny mag calibration request if we aren't using the compass, are in the pre-arm constant position mode or it has been inhibited by the user bool magCalDenied = !use_compass() || constPosMode || (_magCal == 2); // inhibit the magnetic field calibration if not requested or denied inhibitMagStates = (!magCalRequested || magCalDenied); } // initialise the covariance matrix void NavEKF::CovarianceInit() { // zero the matrix for (uint8_t i=1; i<=21; i++) { for (uint8_t j=0; j<=21; j++) { P[i][j] = 0.0f; } } // quaternions - TODO better maths for initial quaternion covariances that uses roll, pitch and yaw P[0][0] = 1.0e-9f; P[1][1] = 0.25f*sq(radians(1.0f)); P[2][2] = 0.25f*sq(radians(1.0f)); P[3][3] = 0.25f*sq(radians(1.0f)); // velocities P[4][4] = sq(0.7f); P[5][5] = P[4][4]; P[6][6] = sq(0.7f); // positions P[7][7] = sq(15.0f); P[8][8] = P[7][7]; P[9][9] = sq(_baroAltNoise); // delta angle biases P[10][10] = sq(radians(InitialGyroBiasUncertainty() * dtIMUavg)); P[11][11] = P[10][10]; P[12][12] = P[10][10]; // Z delta velocity bias P[13][13] = sq(INIT_ACCEL_BIAS_UNCERTAINTY * dtIMUavg); // wind velocities P[14][14] = 0.0f; P[15][15] = P[14][14]; // earth magnetic field P[16][16] = 0.0f; P[17][17] = P[16][16]; P[18][18] = P[16][16]; // body magnetic field P[19][19] = 0.0f; P[20][20] = P[19][19]; P[21][21] = P[19][19]; // optical flow ground height covariance Popt = 0.25f; } // force symmetry on the covariance matrix to prevent ill-conditioning void NavEKF::ForceSymmetry() { for (uint8_t i=1; i<=21; i++) { for (uint8_t j=0; j<=i-1; j++) { float temp = 0.5f*(P[i][j] + P[j][i]); P[i][j] = temp; P[j][i] = temp; } } } // copy covariances across from covariance prediction calculation and fix numerical errors void NavEKF::CopyAndFixCovariances() { // copy predicted variances for (uint8_t i=0; i<=21; i++) { P[i][i] = nextP[i][i]; } // copy predicted covariances and force symmetry for (uint8_t i=1; i<=21; i++) { for (uint8_t j=0; j<=i-1; j++) { P[i][j] = 0.5f*(nextP[i][j] + nextP[j][i]); P[j][i] = P[i][j]; } } } // constrain variances (diagonal terms) in the state covariance matrix to prevent ill-conditioning void NavEKF::ConstrainVariances() { for (uint8_t i=0; i<=3; i++) P[i][i] = constrain_float(P[i][i],0.0f,1.0f); // quaternions for (uint8_t i=4; i<=6; i++) P[i][i] = constrain_float(P[i][i],0.0f,1.0e3f); // velocities for (uint8_t i=7; i<=9; i++) P[i][i] = constrain_float(P[i][i],0.0f,1.0e6f); // positions for (uint8_t i=10; i<=12; i++) P[i][i] = constrain_float(P[i][i],0.0f,sq(0.175f * dtIMUavg)); // delta angle biases P[13][13] = constrain_float(P[13][13],0.0f,sq(10.0f * dtIMUavg)); // delta velocity bias for (uint8_t i=14; i<=15; i++) P[i][i] = constrain_float(P[i][i],0.0f,1.0e3f); // earth magnetic field for (uint8_t i=16; i<=21; i++) P[i][i] = constrain_float(P[i][i],0.0f,1.0f); // body magnetic field } // constrain states to prevent ill-conditioning void NavEKF::ConstrainStates() { // quaternions are limited between +-1 for (uint8_t i=0; i<=3; i++) states[i] = constrain_float(states[i],-1.0f,1.0f); // velocity limit 500 m/sec (could set this based on some multiple of max airspeed * EAS2TAS) for (uint8_t i=4; i<=6; i++) states[i] = constrain_float(states[i],-5.0e2f,5.0e2f); // position limit 1000 km - TODO apply circular limit for (uint8_t i=7; i<=8; i++) states[i] = constrain_float(states[i],-1.0e6f,1.0e6f); // height limit covers home alt on everest through to home alt at SL and ballon drop state.position.z = constrain_float(state.position.z,-4.0e4f,1.0e4f); // gyro bias limit ~6 deg/sec (this needs to be set based on manufacturers specs) for (uint8_t i=10; i<=12; i++) states[i] = constrain_float(states[i],-0.1f*dtIMUavg,0.1f*dtIMUavg); // Z accel bias limit 1.0 m/s^2 (this needs to be finalised from test data) states[13] = constrain_float(states[13],-1.0f*dtIMUavg,1.0f*dtIMUavg); states[22] = constrain_float(states[22],-1.0f*dtIMUavg,1.0f*dtIMUavg); // wind velocity limit 100 m/s (could be based on some multiple of max airspeed * EAS2TAS) - TODO apply circular limit for (uint8_t i=14; i<=15; i++) states[i] = constrain_float(states[i],-100.0f,100.0f); // earth magnetic field limit for (uint8_t i=16; i<=18; i++) states[i] = constrain_float(states[i],-1.0f,1.0f); // body magnetic field limit for (uint8_t i=19; i<=21; i++) states[i] = constrain_float(states[i],-0.5f,0.5f); // constrain the terrain offset state terrainState = max(terrainState, state.position.z + rngOnGnd); } bool NavEKF::readDeltaVelocity(uint8_t ins_index, Vector3f &dVel, float &dVel_dt) { const AP_InertialSensor &ins = _ahrs->get_ins(); if (ins_index < ins.get_accel_count()) { ins.get_delta_velocity(ins_index,dVel); dVel_dt = ins.get_delta_velocity_dt(ins_index); return true; } return false; } bool NavEKF::readDeltaAngle(uint8_t ins_index, Vector3f &dAng) { const AP_InertialSensor &ins = _ahrs->get_ins(); if (ins_index < ins.get_gyro_count()) { ins.get_delta_angle(ins_index,dAng); return true; } return false; } // update IMU delta angle and delta velocity measurements void NavEKF::readIMUData() { const AP_InertialSensor &ins = _ahrs->get_ins(); dtIMUavg = 1.0f/ins.get_sample_rate(); dtIMUactual = max(ins.get_delta_time(),1.0e-4f); // the imu sample time is used as a common time reference throughout the filter imuSampleTime_ms = hal.scheduler->millis(); if (ins.get_accel_health(0) && ins.get_accel_health(1)) { // dual accel mode // read IMU1 delta velocity data readDeltaVelocity(0, dVelIMU1, dtDelVel1); // apply a peak hold decaying envelope filter to the rate of increase if clip events on IMU1 float alpha = 1.0f - 5.0f*dtDelVel1; clipRateFilt1 = max(float(ins.get_accel_clip_count(0) - lastClipCount1), alpha*clipRateFilt1); lastClipCount1 = ins.get_accel_clip_count(0); // read IMU2 delta velocity data readDeltaVelocity(1, dVelIMU2, dtDelVel2); // apply a peak hold decaying envelope filter to the rate of increase if clip events on IMU2 alpha = 1.0f - 5.0f*dtDelVel2; clipRateFilt2 = max(float(ins.get_accel_clip_count(1) - lastClipCount2), alpha*clipRateFilt2); lastClipCount2 = ins.get_accel_clip_count(1); } else { // single accel mode - one of the first two accelerometers are unhealthy // read primary accelerometer into dVelIMU1 and copy to dVelIMU2 readDeltaVelocity(ins.get_primary_accel(), dVelIMU1, dtDelVel1); // apply a peak hold decaying envelope filter to the rate of increase if clip events on IMU1 float alpha = 1.0f - 5.0f*dtDelVel1; clipRateFilt1 = max(float(ins.get_accel_clip_count(0) - lastClipCount1), alpha*clipRateFilt1); lastClipCount1 = ins.get_accel_clip_count(0); clipRateFilt2 = clipRateFilt1; dtDelVel2 = dtDelVel1; dVelIMU2 = dVelIMU1; } if (ins.get_gyro_health(0) && ins.get_gyro_health(1)) { // dual gyro mode - average first two gyros Vector3f dAng; dAngIMU.zero(); readDeltaAngle(0, dAng); dAngIMU += dAng; readDeltaAngle(1, dAng); dAngIMU += dAng; dAngIMU *= 0.5f; } else { // single gyro mode - one of the first two gyros are unhealthy or don't exist // just read primary gyro readDeltaAngle(ins.get_primary_gyro(), dAngIMU); } } // check for new valid GPS data and update stored measurement if available void NavEKF::readGpsData() { bool goodToAlign = false; // check for new GPS data if ((_ahrs->get_gps().last_message_time_ms() != lastFixTime_ms) && (_ahrs->get_gps().status() >= AP_GPS::GPS_OK_FIX_3D)) { // store fix time from previous read secondLastFixTime_ms = lastFixTime_ms; // get current fix time lastFixTime_ms = _ahrs->get_gps().last_message_time_ms(); // set flag that lets other functions know that new GPS data has arrived newDataGps = true; // get state vectors that were stored at the time that is closest to when the the GPS measurement // time after accounting for measurement delays RecallStates(statesAtVelTime, (imuSampleTime_ms - constrain_int16(_msecVelDelay, 0, 500))); RecallStates(statesAtPosTime, (imuSampleTime_ms - constrain_int16(_msecPosDelay, 0, 500))); // read the NED velocity from the GPS velNED = _ahrs->get_gps().velocity(); // Use the speed accuracy from the GPS if available, otherwise set it to zero. // Apply a decaying envelope filter with a 5 second time constant to the raw speed accuracy data float alpha = constrain_float(0.0002f * (lastFixTime_ms - secondLastFixTime_ms),0.0f,1.0f); gpsSpdAccuracy *= (1.0f - alpha); float gpsSpdAccRaw; if (!_ahrs->get_gps().speed_accuracy(gpsSpdAccRaw)) { gpsSpdAccuracy = 0.0f; } else { gpsSpdAccuracy = max(gpsSpdAccuracy,gpsSpdAccRaw); } // check if we have enough GPS satellites and increase the gps noise scaler if we don't if (_ahrs->get_gps().num_sats() >= 6 && !constPosMode) { gpsNoiseScaler = 1.0f; } else if (_ahrs->get_gps().num_sats() == 5 && !constPosMode) { gpsNoiseScaler = 1.4f; } else { // <= 4 satellites or in constant position mode gpsNoiseScaler = 2.0f; } // Check if GPS can output vertical velocity and set GPS fusion mode accordingly if (_ahrs->get_gps().have_vertical_velocity() && _fusionModeGPS == 0) { useGpsVertVel = true; } else { useGpsVertVel = false; } // Monitor quality of the GPS velocity data for alignment goodToAlign = calcGpsGoodToAlign(); // read latitutde and longitude from GPS and convert to local NE position relative to the stored origin // If we don't have an origin, then set it to the current GPS coordinates const struct Location &gpsloc = _ahrs->get_gps().location(); if (validOrigin) { gpsPosNE = location_diff(EKF_origin, gpsloc); } else if (goodToAlign){ // Set the NE origin to the current GPS position setOrigin(); // Now we know the location we have an estimate for the magnetic field declination and adjust the earth field accordingly alignMagStateDeclination(); // Set the height of the NED origin to ‘height of baro height datum relative to GPS height datum' EKF_origin.alt = gpsloc.alt - hgtMea; // We are by definition at the origin at the instant of alignment so set NE position to zero gpsPosNE.zero(); // If the vehicle is in flight (use arm status to determine) and GPS useage isn't explicitly prohibited, we switch to absolute position mode if (vehicleArmed && _fusionModeGPS != 3) { constPosMode = false; PV_AidingMode = AID_ABSOLUTE; gpsNotAvailable = false; // Initialise EKF position and velocity states ResetPosition(); ResetVelocity(); } } // calculate a position offset which is applied to NE position and velocity wherever it is used throughout code to allow GPS position jumps to be accommodated gradually decayGpsOffset(); } // If no previous GPS lock or told not to use it, or EKF origin not set, we declare the GPS unavailable for use if ((_ahrs->get_gps().status() < AP_GPS::GPS_OK_FIX_3D) || _fusionModeGPS == 3 || !validOrigin) { gpsNotAvailable = true; } else { gpsNotAvailable = false; } } // check for new altitude measurement data and update stored measurement if available void NavEKF::readHgtData() { // check to see if baro measurement has changed so we know if a new measurement has arrived if (_baro.get_last_update() != lastHgtMeasTime) { // Don't use Baro height if operating in optical flow mode as we use range finder instead if (_fusionModeGPS == 3 && _altSource == 1) { if ((imuSampleTime_ms - rngValidMeaTime_ms) < 2000) { // adjust range finder measurement to allow for effect of vehicle tilt and height of sensor hgtMea = max(rngMea * Tnb_flow.c.z, rngOnGnd); // get states that were stored at the time closest to the measurement time, taking measurement delay into account statesAtHgtTime = statesAtFlowTime; // calculate offset to baro data that enables baro to be used as a backup // filter offset to reduce effect of baro noise and other transient errors on estimate baroHgtOffset = 0.1f * (_baro.get_altitude() + state.position.z) + 0.9f * baroHgtOffset; } else if (vehicleArmed && takeOffDetected) { // use baro measurement and correct for baro offset - failsafe use only as baro will drift hgtMea = max(_baro.get_altitude() - baroHgtOffset, rngOnGnd); // get states that were stored at the time closest to the measurement time, taking measurement delay into account RecallStates(statesAtHgtTime, (imuSampleTime_ms - msecHgtDelay)); } else { // If we are on ground and have no range finder reading, assume the nominal on-ground height hgtMea = rngOnGnd; // get states that were stored at the time closest to the measurement time, taking measurement delay into account statesAtHgtTime = state; // calculate offset to baro data that enables baro to be used as a backup // filter offset to reduce effect of baro noise and other transient errors on estimate baroHgtOffset = 0.1f * (_baro.get_altitude() + state.position.z) + 0.9f * baroHgtOffset; } } else { // use baro measurement and correct for baro offset hgtMea = _baro.get_altitude(); // get states that were stored at the time closest to the measurement time, taking measurement delay into account RecallStates(statesAtHgtTime, (imuSampleTime_ms - msecHgtDelay)); } // filtered baro data used to provide a reference for takeoff // it is is reset to last height measurement on disarming in performArmingChecks() if (!getTakeoffExpected()) { static const float gndHgtFiltTC = 0.5f; static const float dtBaro = msecHgtAvg*1.0e-3f; float alpha = constrain_float(dtBaro / (dtBaro+gndHgtFiltTC),0.0f,1.0f); meaHgtAtTakeOff += (hgtMea-meaHgtAtTakeOff)*alpha; } else if (vehicleArmed && getTakeoffExpected()) { // If we are in takeoff mode, the height measurement is limited to be no less than the measurement at start of takeoff // This prevents negative baro disturbances due to copter downwash corrupting the EKF altitude during initial ascent hgtMea = max(hgtMea, meaHgtAtTakeOff); } // set flag to let other functions know new data has arrived newDataHgt = true; // time stamp used to check for new measurement lastHgtMeasTime = _baro.get_last_update(); } else { newDataHgt = false; } } // check for new magnetometer data and update store measurements if available void NavEKF::readMagData() { if (use_compass() && _ahrs->get_compass()->last_update_usec() != lastMagUpdate) { // store time of last measurement update lastMagUpdate = _ahrs->get_compass()->last_update_usec(); // read compass data and scale to improve numerical conditioning magData = _ahrs->get_compass()->get_field() * 0.001f; // get states stored at time closest to measurement time after allowance for measurement delay RecallStates(statesAtMagMeasTime, (imuSampleTime_ms - msecMagDelay)); // let other processes know that new compass data has arrived newDataMag = true; // check if compass offsets have ben changed and adjust EKF bias states to maintain consistent innovations if (_ahrs->get_compass()->healthy()) { Vector3f nowMagOffsets = _ahrs->get_compass()->get_offsets(); bool changeDetected = (!is_equal(nowMagOffsets.x,lastMagOffsets.x) || !is_equal(nowMagOffsets.y,lastMagOffsets.y) || !is_equal(nowMagOffsets.z,lastMagOffsets.z)); // Ignore bias changes before final mag field and yaw initialisation, as there may have been a compass calibration if (changeDetected && secondMagYawInit) { state.body_magfield.x += (nowMagOffsets.x - lastMagOffsets.x) * 0.001f; state.body_magfield.y += (nowMagOffsets.y - lastMagOffsets.y) * 0.001f; state.body_magfield.z += (nowMagOffsets.z - lastMagOffsets.z) * 0.001f; } lastMagOffsets = nowMagOffsets; } } else { newDataMag = false; } } // check for new airspeed data and update stored measurements if available void NavEKF::readAirSpdData() { // if airspeed reading is valid and is set by the user to be used and has been updated then // we take a new reading, convert from EAS to TAS and set the flag letting other functions // know a new measurement is available const AP_Airspeed *aspeed = _ahrs->get_airspeed(); if (aspeed && aspeed->use() && aspeed->last_update_ms() != lastAirspeedUpdate) { VtasMeas = aspeed->get_airspeed() * aspeed->get_EAS2TAS(); lastAirspeedUpdate = aspeed->last_update_ms(); newDataTas = true; RecallStates(statesAtVtasMeasTime, (imuSampleTime_ms - msecTasDelay)); } else { newDataTas = false; } } // write the raw optical flow measurements // this needs to be called externally. void NavEKF::writeOptFlowMeas(uint8_t &rawFlowQuality, Vector2f &rawFlowRates, Vector2f &rawGyroRates, uint32_t &msecFlowMeas) { // The raw measurements need to be optical flow rates in radians/second averaged across the time since the last update // The PX4Flow sensor outputs flow rates with the following axis and sign conventions: // A positive X rate is produced by a positive sensor rotation about the X axis // A positive Y rate is produced by a positive sensor rotation about the Y axis // This filter uses a different definition of optical flow rates to the sensor with a positive optical flow rate produced by a // negative rotation about that axis. For example a positive rotation of the flight vehicle about its X (roll) axis would produce a negative X flow rate flowMeaTime_ms = imuSampleTime_ms; flowQuality = rawFlowQuality; // recall angular rates averaged across flow observation period allowing for processing, transmission and intersample delays RecallOmega(omegaAcrossFlowTime, imuSampleTime_ms - flowTimeDeltaAvg_ms - _msecFLowDelay, imuSampleTime_ms - _msecFLowDelay); // calculate bias errors on flow sensor gyro rates, but protect against spikes in data flowGyroBias.x = 0.99f * flowGyroBias.x + 0.01f * constrain_float((rawGyroRates.x - omegaAcrossFlowTime.x),-0.1f,0.1f); flowGyroBias.y = 0.99f * flowGyroBias.y + 0.01f * constrain_float((rawGyroRates.y - omegaAcrossFlowTime.y),-0.1f,0.1f); // check for takeoff if relying on optical flow and zero measurements until takeoff detected // if we haven't taken off - constrain position and velocity states if (_fusionModeGPS == 3) { detectOptFlowTakeoff(); } // recall vehicle states at mid sample time for flow observations allowing for delays RecallStates(statesAtFlowTime, imuSampleTime_ms - _msecFLowDelay - flowTimeDeltaAvg_ms/2); // calculate rotation matrices at mid sample time for flow observations statesAtFlowTime.quat.rotation_matrix(Tbn_flow); Tnb_flow = Tbn_flow.transposed(); // don't use data with a low quality indicator or extreme rates (helps catch corrupt sensor data) if ((rawFlowQuality > 0) && rawFlowRates.length() < 4.2f && rawGyroRates.length() < 4.2f) { // correct flow sensor rates for bias omegaAcrossFlowTime.x = rawGyroRates.x - flowGyroBias.x; omegaAcrossFlowTime.y = rawGyroRates.y - flowGyroBias.y; // write uncorrected flow rate measurements that will be used by the focal length scale factor estimator // note correction for different axis and sign conventions used by the px4flow sensor flowRadXY[0] = - rawFlowRates.x; // raw (non motion compensated) optical flow angular rate about the X axis (rad/sec) flowRadXY[1] = - rawFlowRates.y; // raw (non motion compensated) optical flow angular rate about the Y axis (rad/sec) // write flow rate measurements corrected for body rates flowRadXYcomp[0] = flowRadXY[0] + omegaAcrossFlowTime.x; flowRadXYcomp[1] = flowRadXY[1] + omegaAcrossFlowTime.y; // set flag that will trigger observations newDataFlow = true; flowValidMeaTime_ms = imuSampleTime_ms; } else { newDataFlow = false; } } // calculate the NED earth spin vector in rad/sec void NavEKF::calcEarthRateNED(Vector3f &omega, int32_t latitude) const { float lat_rad = radians(latitude*1.0e-7f); omega.x = earthRate*cosf(lat_rad); omega.y = 0; omega.z = -earthRate*sinf(lat_rad); } // initialise the earth magnetic field states using declination, suppled roll/pitch // and magnetometer measurements and return initial attitude quaternion // if no magnetometer data, do not update magnetic field states and assume zero yaw angle Quaternion NavEKF::calcQuatAndFieldStates(float roll, float pitch) { // declare local variables required to calculate initial orientation and magnetic field float yaw; Matrix3f Tbn; Vector3f initMagNED; Quaternion initQuat; if (use_compass()) { // calculate rotation matrix from body to NED frame Tbn.from_euler(roll, pitch, 0.0f); // read the magnetometer data readMagData(); // rotate the magnetic field into NED axes initMagNED = Tbn * magData; // calculate heading of mag field rel to body heading float magHeading = atan2f(initMagNED.y, initMagNED.x); // get the magnetic declination float magDecAng = use_compass() ? _ahrs->get_compass()->get_declination() : 0; // calculate yaw angle rel to true north yaw = magDecAng - magHeading; yawAligned = true; // calculate initial filter quaternion states using yaw from magnetometer if mag heading healthy // otherwise use existing heading if (!badMag) { // store the yaw change so that it can be retrieved externally for use by the control loops to prevent yaw disturbances following a reset Vector3f tempEuler; state.quat.to_euler(tempEuler.x, tempEuler.y, tempEuler.z); yawResetAngle = wrap_PI(yaw - tempEuler.z); // set the flag to indicate that an in-flight yaw reset has been performed // this will be cleared when the reset value is retrieved yawResetAngleWaiting = true; // calculate an initial quaternion using the new yaw value initQuat.from_euler(roll, pitch, yaw); } else { initQuat = state.quat; } // calculate initial Tbn matrix and rotate Mag measurements into NED // to set initial NED magnetic field states initQuat.rotation_matrix(Tbn); state.earth_magfield = Tbn * magData; // align the NE earth magnetic field states with the published declination alignMagStateDeclination(); // clear bad magnetometer status badMag = false; } else { initQuat.from_euler(roll, pitch, 0.0f); yawAligned = false; } // return attitude quaternion return initQuat; } // this function is used to do a forced alignment of the yaw angle to align with the horizontal velocity // vector from GPS. It is used to align the yaw angle after launch or takeoff. void NavEKF::alignYawGPS() { if ((sq(velNED[0]) + sq(velNED[1])) > 25.0f) { float roll; float pitch; float oldYaw; float newYaw; float yawErr; // get quaternion from existing filter states and calculate roll, pitch and yaw angles state.quat.to_euler(roll, pitch, oldYaw); // calculate course yaw angle oldYaw = atan2f(state.velocity.y,state.velocity.x); // calculate yaw angle from GPS velocity newYaw = atan2f(velNED[1],velNED[0]); // estimate the yaw error yawErr = wrap_PI(newYaw - oldYaw); // If the inertial course angle disagrees with the GPS by more than 45 degrees, we declare the compass as bad badMag = (fabsf(yawErr) > 0.7854f); // correct yaw angle using GPS ground course compass failed or if not previously aligned if (badMag || !yawAligned) { // correct the yaw angle newYaw = oldYaw + yawErr; // calculate new filter quaternion states from Euler angles state.quat.from_euler(roll, pitch, newYaw); // the yaw angle is now aligned so update its status yawAligned = true; // reset the position and velocity states ResetPosition(); ResetVelocity(); // reset the covariance for the quaternion, velocity and position states // zero the matrix entries zeroRows(P,0,9); zeroCols(P,0,9); // quaternions - TODO maths that sets them based on different roll, yaw and pitch uncertainties P[0][0] = 1.0e-9f; P[1][1] = 0.25f*sq(radians(1.0f)); P[2][2] = 0.25f*sq(radians(1.0f)); P[3][3] = 0.25f*sq(radians(1.0f)); // velocities - we could have a big error coming out of constant position mode due to GPS lag P[4][4] = 400.0f; P[5][5] = P[4][4]; P[6][6] = sq(0.7f); // positions - we could have a big error coming out of constant position mode due to GPS lag P[7][7] = 400.0f; P[8][8] = P[7][7]; P[9][9] = sq(5.0f); } // Update magnetic field states if the magnetometer is bad if (badMag) { Vector3f eulerAngles; getEulerAngles(eulerAngles); calcQuatAndFieldStates(eulerAngles.x, eulerAngles.y); } } } // This function is used to do a forced alignment of the wind velocity // states so that they are set to the reciprocal of the ground speed // and scaled to STARTUP_WIND_SPEED m/s. This is used when launching a // fly-forward vehicle without an airspeed sensor on the assumption // that launch will be into wind and STARTUP_WIND_SPEED is // representative of typical launch wind void NavEKF::setWindVelStates() { float gndSpd = pythagorous2(state.velocity.x, state.velocity.y); if (gndSpd > 4.0f) { // set the wind states to be the reciprocal of the velocity and scale float scaleFactor = STARTUP_WIND_SPEED / gndSpd; state.wind_vel.x = - state.velocity.x * scaleFactor; state.wind_vel.y = - state.velocity.y * scaleFactor; // reinitialise the wind state covariances zeroRows(P,14,15); zeroCols(P,14,15); P[14][14] = 64.0f; P[15][15] = P[14][14]; } } // return the transformation matrix from XYZ (body) to NED axes void NavEKF::getRotationBodyToNED(Matrix3f &mat) const { Vector3f trim = _ahrs->get_trim(); state.quat.rotation_matrix(mat); mat.rotateXYinv(trim); } // return the innovations for the NED Pos, NED Vel, XYZ Mag and Vtas measurements void NavEKF::getInnovations(Vector3f &velInnov, Vector3f &posInnov, Vector3f &magInnov, float &tasInnov) const { velInnov.x = innovVelPos[0]; velInnov.y = innovVelPos[1]; velInnov.z = innovVelPos[2]; posInnov.x = innovVelPos[3]; posInnov.y = innovVelPos[4]; posInnov.z = innovVelPos[5]; magInnov.x = 1e3f*innovMag[0]; // Convert back to sensor units magInnov.y = 1e3f*innovMag[1]; // Convert back to sensor units magInnov.z = 1e3f*innovMag[2]; // Convert back to sensor units tasInnov = innovVtas; } // return the innovation consistency test ratios for the velocity, position, magnetometer and true airspeed measurements // this indicates the amount of margin available when tuning the various error traps // also return the current offsets applied to the GPS position measurements void NavEKF::getVariances(float &velVar, float &posVar, float &hgtVar, Vector3f &magVar, float &tasVar, Vector2f &offset) const { velVar = sqrtf(velTestRatio); posVar = sqrtf(posTestRatio); hgtVar = sqrtf(hgtTestRatio); magVar.x = sqrtf(magTestRatio.x); magVar.y = sqrtf(magTestRatio.y); magVar.z = sqrtf(magTestRatio.z); tasVar = sqrtf(tasTestRatio); offset = gpsPosGlitchOffsetNE; } // Use a function call rather than a constructor to initialise variables because it enables the filter to be re-started in flight if necessary. void NavEKF::InitialiseVariables() { // initialise time stamps imuSampleTime_ms = hal.scheduler->millis(); lastHealthyMagTime_ms = imuSampleTime_ms; TASmsecPrev = imuSampleTime_ms; BETAmsecPrev = imuSampleTime_ms; lastMagUpdate = 0; lastHgtMeasTime = imuSampleTime_ms; lastAirspeedUpdate = 0; lastVelPassTime = imuSampleTime_ms; lastPosPassTime = imuSampleTime_ms; lastPosFailTime = 0; lastHgtPassTime = imuSampleTime_ms; lastTasPassTime = imuSampleTime_ms; lastStateStoreTime_ms = imuSampleTime_ms; lastFixTime_ms = 0; secondLastFixTime_ms = 0; lastDecayTime_ms = imuSampleTime_ms; timeAtLastAuxEKF_ms = imuSampleTime_ms; flowValidMeaTime_ms = imuSampleTime_ms; rngValidMeaTime_ms = imuSampleTime_ms; flowMeaTime_ms = 0; prevFlowFuseTime_ms = imuSampleTime_ms; gndHgtValidTime_ms = 0; ekfStartTime_ms = imuSampleTime_ms; lastGpsVelFail_ms = 0; lastGpsAidBadTime_ms = 0; // initialise other variables gpsNoiseScaler = 1.0f; hgtTimeout = true; magTimeout = true; tasTimeout = true; badMag = false; badIMUdata = false; firstArmComplete = false; firstMagYawInit = false; secondMagYawInit = false; storeIndex = 0; dtIMUavg = 0.0025f; dtIMUactual = 0.0025f; dt = 0; hgtMea = 0; storeIndex = 0; lastGyroBias.zero(); lastAngRate.zero(); lastAccel1.zero(); lastAccel2.zero(); velDotNEDfilt.zero(); summedDelAng.zero(); summedDelVel.zero(); velNED.zero(); gpsPosGlitchOffsetNE.zero(); lastKnownPositionNE.zero(); gpsPosNE.zero(); prevTnb.zero(); memset(&P[0][0], 0, sizeof(P)); memset(&nextP[0][0], 0, sizeof(nextP)); memset(&processNoise[0], 0, sizeof(processNoise)); memset(&storedStates[0], 0, sizeof(storedStates)); memset(&statetimeStamp[0], 0, sizeof(statetimeStamp)); memset(&gpsIncrStateDelta[0], 0, sizeof(gpsIncrStateDelta)); memset(&hgtIncrStateDelta[0], 0, sizeof(hgtIncrStateDelta)); memset(&magIncrStateDelta[0], 0, sizeof(magIncrStateDelta)); memset(&flowIncrStateDelta[0], 0, sizeof(flowIncrStateDelta)); newDataFlow = false; flowDataValid = false; newDataRng = false; flowFusePerformed = false; fuseOptFlowData = false; Popt = 0.0f; terrainState = 0.0f; prevPosN = gpsPosNE.x; prevPosE = gpsPosNE.y; fuseRngData = false; inhibitGndState = true; flowGyroBias.x = 0; flowGyroBias.y = 0; constVelMode = false; lastConstVelMode = false; heldVelNE.zero(); PV_AidingMode = AID_NONE; posTimeout = true; velTimeout = true; gpsVelGlitchOffset.zero(); vehicleArmed = false; prevVehicleArmed = false; constPosMode = true; memset(&faultStatus, 0, sizeof(faultStatus)); hgtRate = 0.0f; mag_state.q0 = 1; mag_state.DCM.identity(); IMU1_weighting = 0.5f; onGround = true; manoeuvring = false; yawAligned = false; inhibitWindStates = true; inhibitMagStates = true; gndOffsetValid = false; flowXfailed = false; validOrigin = false; takeoffExpectedSet_ms = 0; expectGndEffectTakeoff = false; touchdownExpectedSet_ms = 0; expectGndEffectTouchdown = false; gpsSpdAccuracy = 0.0f; baroHgtOffset = 0.0f; gpsAidingBad = false; highYawRate = false; yawRateFilt = 0.0f; yawResetAngle = 0.0f; yawResetAngleWaiting = false; const AP_InertialSensor &ins = _ahrs->get_ins(); lastClipCount1 = ins.get_accel_clip_count(0); lastClipCount2 = ins.get_accel_clip_count(1); } // return true if we should use the airspeed sensor bool NavEKF::useAirspeed(void) const { return _ahrs->airspeed_sensor_enabled(); } // return true if we should use the range finder sensor bool NavEKF::useRngFinder(void) const { // TO-DO add code to set this based in setting of optical flow use parameter and presence of sensor return true; } // return true if optical flow data is available bool NavEKF::optFlowDataPresent(void) const { if (imuSampleTime_ms - flowMeaTime_ms < 5000) { return true; } else { return false; } } // return true if the vehicle is requesting the filter to be ready for flight bool NavEKF::getVehicleArmStatus(void) const { return hal.util->get_soft_armed() || _ahrs->get_correct_centrifugal(); } // return true if we should use the compass bool NavEKF::use_compass(void) const { return _ahrs->get_compass() && _ahrs->get_compass()->use_for_yaw(); } // decay GPS horizontal position offset to close to zero at a rate of 1 m/s for copters and 5 m/s for planes // limit radius to a maximum of 50m void NavEKF::decayGpsOffset() { float offsetDecaySpd; if (assume_zero_sideslip()) { offsetDecaySpd = 5.0f; } else { offsetDecaySpd = 1.0f; } float lapsedTime = 0.001f*float(imuSampleTime_ms - lastDecayTime_ms); lastDecayTime_ms = imuSampleTime_ms; float offsetRadius = pythagorous2(gpsPosGlitchOffsetNE.x, gpsPosGlitchOffsetNE.y); // decay radius if larger than offset decay speed multiplied by lapsed time (plus a margin to prevent divide by zero) if (offsetRadius > (offsetDecaySpd * lapsedTime + 0.1f)) { // Calculate the GPS velocity offset required. This is necessary to prevent the position measurement being rejected for inconsistency when the radius is being pulled back in. gpsVelGlitchOffset = -gpsPosGlitchOffsetNE*offsetDecaySpd/offsetRadius; // calculate scale factor to be applied to both offset components float scaleFactor = constrain_float((offsetRadius - offsetDecaySpd * lapsedTime), 0.0f, 50.0f) / offsetRadius; gpsPosGlitchOffsetNE.x *= scaleFactor; gpsPosGlitchOffsetNE.y *= scaleFactor; } else { gpsVelGlitchOffset.zero(); gpsPosGlitchOffsetNE.zero(); } } /* should we assume zero sideslip? */ bool NavEKF::assume_zero_sideslip(void) const { // we don't assume zero sideslip for ground vehicles as EKF could // be quite sensitive to a rapid spin of the ground vehicle if // traction is lost return _ahrs->get_fly_forward() && _ahrs->get_vehicle_class() != AHRS_VEHICLE_GROUND; } /* vehicle specific initial gyro bias uncertainty */ float NavEKF::InitialGyroBiasUncertainty(void) const { switch (_ahrs->get_ins().get_sample_rate()) { case AP_InertialSensor::RATE_50HZ: return 1.0f; default: return 0.1f; } } /* return the filter fault status as a bitmasked integer 0 = quaternions are NaN 1 = velocities are NaN 2 = badly conditioned X magnetometer fusion 3 = badly conditioned Y magnetometer fusion 5 = badly conditioned Z magnetometer fusion 6 = badly conditioned airspeed fusion 7 = badly conditioned synthetic sideslip fusion 7 = filter is not initialised */ void NavEKF::getFilterFaults(uint8_t &faults) const { faults = (state.quat.is_nan()<<0 | state.velocity.is_nan()<<1 | faultStatus.bad_xmag<<2 | faultStatus.bad_ymag<<3 | faultStatus.bad_zmag<<4 | faultStatus.bad_airspeed<<5 | faultStatus.bad_sideslip<<6 | !statesInitialised<<7); } /* return filter timeout status as a bitmasked integer 0 = position measurement timeout 1 = velocity measurement timeout 2 = height measurement timeout 3 = magnetometer measurement timeout 4 = true airspeed measurement timeout 5 = unassigned 6 = unassigned 7 = unassigned */ void NavEKF::getFilterTimeouts(uint8_t &timeouts) const { timeouts = (posTimeout<<0 | velTimeout<<1 | hgtTimeout<<2 | magTimeout<<3 | tasTimeout<<4); } /* return filter function status as a bitmasked integer 0 = attitude estimate valid 1 = horizontal velocity estimate valid 2 = vertical velocity estimate valid 3 = relative horizontal position estimate valid 4 = absolute horizontal position estimate valid 5 = vertical position estimate valid 6 = terrain height estimate valid 7 = constant position mode */ void NavEKF::getFilterStatus(nav_filter_status &status) const { // init return value status.value = 0; bool doingFlowNav = (PV_AidingMode == AID_RELATIVE) && flowDataValid; bool doingWindRelNav = !tasTimeout && assume_zero_sideslip(); bool doingNormalGpsNav = !posTimeout && (PV_AidingMode == AID_ABSOLUTE); bool notDeadReckoning = !constVelMode && !constPosMode; bool someVertRefData = (!velTimeout && useGpsVertVel) || !hgtTimeout; bool someHorizRefData = !(velTimeout && posTimeout && tasTimeout) || doingFlowNav; bool optFlowNavPossible = flowDataValid && (_fusionModeGPS == 3); bool gpsNavPossible = !gpsNotAvailable && (_fusionModeGPS <= 2); bool filterHealthy = healthy(); // set individual flags status.flags.attitude = !state.quat.is_nan() && filterHealthy; // attitude valid (we need a better check) status.flags.horiz_vel = someHorizRefData && notDeadReckoning && filterHealthy; // horizontal velocity estimate valid status.flags.vert_vel = someVertRefData && filterHealthy; // vertical velocity estimate valid status.flags.horiz_pos_rel = ((doingFlowNav && gndOffsetValid) || doingWindRelNav || doingNormalGpsNav) && notDeadReckoning && filterHealthy; // relative horizontal position estimate valid status.flags.horiz_pos_abs = !gpsAidingBad && doingNormalGpsNav && notDeadReckoning && filterHealthy; // absolute horizontal position estimate valid status.flags.vert_pos = !hgtTimeout && filterHealthy; // vertical position estimate valid status.flags.terrain_alt = gndOffsetValid && filterHealthy; // terrain height estimate valid status.flags.const_pos_mode = constPosMode && filterHealthy; // constant position mode status.flags.pred_horiz_pos_rel = (optFlowNavPossible || gpsNavPossible) && filterHealthy; // we should be able to estimate a relative position when we enter flight mode status.flags.pred_horiz_pos_abs = gpsNavPossible && filterHealthy; // we should be able to estimate an absolute position when we enter flight mode status.flags.takeoff_detected = takeOffDetected; // takeoff for optical flow navigation has been detected status.flags.takeoff = expectGndEffectTakeoff; // The EKF has been told to expect takeoff and is in a ground effect mitigation mode status.flags.touchdown = expectGndEffectTouchdown; // The EKF has been told to detect touchdown and is in a ground effect mitigation mode status.flags.using_gps = (imuSampleTime_ms - lastPosPassTime) < 4000; } // send an EKF_STATUS message to GCS void NavEKF::send_status_report(mavlink_channel_t chan) { // get filter status nav_filter_status filt_state; getFilterStatus(filt_state); // prepare flags uint16_t flags = 0; if (filt_state.flags.attitude) { flags |= EKF_ATTITUDE; } if (filt_state.flags.horiz_vel) { flags |= EKF_VELOCITY_HORIZ; } if (filt_state.flags.vert_vel) { flags |= EKF_VELOCITY_VERT; } if (filt_state.flags.horiz_pos_rel) { flags |= EKF_POS_HORIZ_REL; } if (filt_state.flags.horiz_pos_abs) { flags |= EKF_POS_HORIZ_ABS; } if (filt_state.flags.vert_pos) { flags |= EKF_POS_VERT_ABS; } if (filt_state.flags.terrain_alt) { flags |= EKF_POS_VERT_AGL; } if (filt_state.flags.const_pos_mode) { flags |= EKF_CONST_POS_MODE; } if (filt_state.flags.pred_horiz_pos_rel) { flags |= EKF_PRED_POS_HORIZ_REL; } if (filt_state.flags.pred_horiz_pos_abs) { flags |= EKF_PRED_POS_HORIZ_ABS; } // get variances float velVar, posVar, hgtVar, tasVar; Vector3f magVar; Vector2f offset; getVariances(velVar, posVar, hgtVar, magVar, tasVar, offset); // send message mavlink_msg_ekf_status_report_send(chan, flags, velVar, posVar, hgtVar, magVar.length(), tasVar); } // Check arm status and perform required checks and mode changes void NavEKF::performArmingChecks() { // determine vehicle arm status and don't allow filter to arm until it has been running for long enough to stabilise prevVehicleArmed = vehicleArmed; vehicleArmed = (getVehicleArmStatus() && (imuSampleTime_ms - ekfStartTime_ms) > 1000); // check to see if arm status has changed and reset states if it has if (vehicleArmed != prevVehicleArmed) { // only reset the magnetic field and heading on the first arm. This prevents in-flight learning being forgotten for vehicles that do multiple short flights and disarm in-between. if (vehicleArmed && !firstArmComplete) { firstArmComplete = true; Vector3f eulerAngles; getEulerAngles(eulerAngles); state.quat = calcQuatAndFieldStates(eulerAngles.x, eulerAngles.y); } // store vertical position at arming to use as a reference for ground relative cehcks if (vehicleArmed) { posDownAtArming = state.position.z; } // zero stored velocities used to do dead-reckoning heldVelNE.zero(); // reset the flag that indicates takeoff for use by optical flow navigation takeOffDetected = false; // set various useage modes based on the condition at arming. These are then held until the vehicle is disarmed. if (!vehicleArmed) { PV_AidingMode = AID_NONE; // When dis-armed, we only estimate orientation & height using the constant position mode posTimeout = true; velTimeout = true; constPosMode = true; constVelMode = false; // always clear constant velocity mode if constant position mode is active lastConstVelMode = false; // store the current position to be used to keep reporting the last known position when disarmed lastKnownPositionNE.x = state.position.x; lastKnownPositionNE.y = state.position.y; // initialise filtered altitude used to provide a takeoff reference to current baro on disarm // this reduces the time required for the filter to settle before the estimate can be used meaHgtAtTakeOff = hgtMea; // reset the vertical position state to faster recover from baro errors experienced during touchdown state.position.z = -hgtMea; } else if (_fusionModeGPS == 3) { // arming when GPS useage has been prohibited if (optFlowDataPresent()) { PV_AidingMode = AID_RELATIVE; // we have optical flow data and can estimate all vehicle states posTimeout = true; velTimeout = true; constPosMode = false; constVelMode = false; } else { PV_AidingMode = AID_NONE; // we don't have optical flow data and will only be able to estimate orientation and height posTimeout = true; velTimeout = true; constPosMode = true; constVelMode = false; // always clear constant velocity mode if constant position mode is active } // Reset the last valid flow measurement time flowValidMeaTime_ms = imuSampleTime_ms; // Reset the last valid flow fusion time prevFlowFuseTime_ms = imuSampleTime_ms; // this avoids issues casued by the time delay associated with arming that can trigger short timeouts rngValidMeaTime_ms = imuSampleTime_ms; // store the range finder measurement which will be used as a reference to detect when we have taken off rangeAtArming = rngMea; // set the time at which we arm to assist with takeoff detection timeAtArming_ms = imuSampleTime_ms; } else { // arming when GPS useage is allowed if (gpsNotAvailable) { PV_AidingMode = AID_NONE; // we don't have have GPS data and will only be able to estimate orientation and height posTimeout = true; velTimeout = true; constPosMode = true; constVelMode = false; // always clear constant velocity mode if constant position mode is active } else { PV_AidingMode = AID_ABSOLUTE; // we have GPS data and can estimate all vehicle states posTimeout = false; velTimeout = false; constPosMode = false; constVelMode = false; // we need to reset the GPS timers to prevent GPS timeout logic being invoked on entry into GPS aiding // this is becasue the EKF can be interrupted for an arbitrary amount of time during vehicle arming checks lastFixTime_ms = imuSampleTime_ms; secondLastFixTime_ms = imuSampleTime_ms; // reset the last valid position fix time to prevent unwanted activation of GPS glitch logic lastPosPassTime = imuSampleTime_ms; // reset the fail time to prevent premature reporting of loss of position accruacy lastPosFailTime = 0; } } if (vehicleArmed) { // Reset filter position to GPS when transitioning into flight mode // We need to do this becasue the vehicle may have moved since the EKF origin was set ResetPosition(); StoreStatesReset(); } else { // Reset all position and velocity states when transitioning out of flight mode // We need to do this becasue we are going into a mode that assumes zero position and velocity ResetVelocity(); ResetPosition(); StoreStatesReset(); } } else if (vehicleArmed && !firstMagYawInit && (state.position.z - posDownAtArming) < -1.5f && !assume_zero_sideslip()) { // Do the first in-air yaw and earth mag field initialisation when the vehicle has gained 1.5m of altitude after arming if it is a non-fly forward vehicle (vertical takeoff) // This is done to prevent magnetic field distoration from steel roofs and adjacent structures causing bad earth field and initial yaw values Vector3f eulerAngles; getEulerAngles(eulerAngles); state.quat = calcQuatAndFieldStates(eulerAngles.x, eulerAngles.y); firstMagYawInit = true; } else if (vehicleArmed && !secondMagYawInit && (state.position.z - posDownAtArming) < -5.0f && !assume_zero_sideslip()) { // Do the second and final yaw and earth mag field initialisation when the vehicle has gained 5.0m of altitude after arming if it is a non-fly forward vehicle (vertical takeoff) // This second and final correction is needed for flight from large metal structures where the magnetic field distortion can extend up to 5m Vector3f eulerAngles; getEulerAngles(eulerAngles); state.quat = calcQuatAndFieldStates(eulerAngles.x, eulerAngles.y); secondMagYawInit = true; } // Always turn aiding off when the vehicle is disarmed if (!vehicleArmed) { PV_AidingMode = AID_NONE; posTimeout = true; velTimeout = true; // set constant position mode if aiding is inhibited constPosMode = true; constVelMode = false; // always clear constant velocity mode if constant position mode is active lastConstVelMode = false; } } // Set the NED origin to be used until the next filter reset void NavEKF::setOrigin() { EKF_origin = _ahrs->get_gps().location(); validOrigin = true; } // return the LLH location of the filters NED origin bool NavEKF::getOriginLLH(struct Location &loc) const { if (validOrigin) { loc = EKF_origin; } return validOrigin; } // set the LLH location of the filters NED origin bool NavEKF::setOriginLLH(struct Location &loc) { if (vehicleArmed) { return false; } EKF_origin = loc; validOrigin = true; return true; } // determine if a takeoff is expected so that we can compensate for expected barometer errors due to ground effect bool NavEKF::getTakeoffExpected() { if (expectGndEffectTakeoff && imuSampleTime_ms - takeoffExpectedSet_ms > gndEffectTimeout_ms) { expectGndEffectTakeoff = false; } return expectGndEffectTakeoff; } // called by vehicle code to specify that a takeoff is happening // causes the EKF to compensate for expected barometer errors due to ground effect void NavEKF::setTakeoffExpected(bool val) { takeoffExpectedSet_ms = imuSampleTime_ms; expectGndEffectTakeoff = val; } // determine if a touchdown is expected so that we can compensate for expected barometer errors due to ground effect bool NavEKF::getTouchdownExpected() { if (expectGndEffectTouchdown && imuSampleTime_ms - touchdownExpectedSet_ms > gndEffectTimeout_ms) { expectGndEffectTouchdown = false; } return expectGndEffectTouchdown; } // called by vehicle code to specify that a touchdown is expected to happen // causes the EKF to compensate for expected barometer errors due to ground effect void NavEKF::setTouchdownExpected(bool val) { touchdownExpectedSet_ms = imuSampleTime_ms; expectGndEffectTouchdown = val; } // Monitor GPS data to see if quality is good enough to initialise the EKF // Monitor magnetometer innovations to to see if the heading is good enough to use GPS // Return true if all criteria pass for 10 seconds bool NavEKF::calcGpsGoodToAlign(void) { // calculate absolute difference between GPS vert vel and inertial vert vel float velDiffAbs; if (_ahrs->get_gps().have_vertical_velocity()) { velDiffAbs = fabsf(velNED.z - state.velocity.z); } else { velDiffAbs = 0.0f; } // fail if velocity difference or reported speed accuracy greater than threshold bool gpsVelFail = (velDiffAbs > 1.0f) || (gpsSpdAccuracy > 1.0f); // fail if not enough sats bool numSatsFail = _ahrs->get_gps().num_sats() < 6; // fail if horiziontal position accuracy not sufficient float hAcc = 0.0f; bool hAccFail; if (_ahrs->get_gps().horizontal_accuracy(hAcc)) { hAccFail = hAcc > 5.0f; } else { hAccFail = false; } // fail if magnetometer innovations are outside limits indicating bad yaw // with bad yaw we are unable to use GPS bool yawFail; if (magTestRatio.x > 1.0f || magTestRatio.y > 1.0f) { yawFail = true; } else { yawFail = false; } // record time of fail // assume fail first time called if (gpsVelFail || numSatsFail || hAccFail || yawFail || lastGpsVelFail_ms == 0) { lastGpsVelFail_ms = imuSampleTime_ms; } // DEBUG PRINT //hal.console->printf("velDiff = %5.2f, nSats = %i, hAcc = %5.2f, sAcc = %5.2f, delTime = %i\n", velDiffAbs, _ahrs->get_gps().num_sats(), hAcc, gpsSpdAccuracy, imuSampleTime_ms - lastGpsVelFail_ms); // continuous period without fail required to return healthy if (imuSampleTime_ms - lastGpsVelFail_ms > 10000) { return true; } else { return false; } } // Read the range finder and take new measurements if available // Read at 20Hz and apply a median filter void NavEKF::readRangeFinder(void) { static float storedRngMeas[3]; static uint32_t storedRngMeasTime_ms[3]; static uint32_t lastRngMeasTime_ms = 0; static uint8_t rngMeasIndex = 0; uint8_t midIndex; uint8_t maxIndex; uint8_t minIndex; // get theoretical correct range when the vehicle is on the ground rngOnGnd = _rng.ground_clearance_cm() * 0.01f; if (_rng.status() == RangeFinder::RangeFinder_Good && (imuSampleTime_ms - lastRngMeasTime_ms) > 50) { // store samples and sample time into a ring buffer rngMeasIndex ++; if (rngMeasIndex > 2) { rngMeasIndex = 0; } storedRngMeasTime_ms[rngMeasIndex] = imuSampleTime_ms; storedRngMeas[rngMeasIndex] = _rng.distance_cm() * 0.01f; // check for three fresh samples and take median bool sampleFresh[3]; for (uint8_t index = 0; index <= 2; index++) { sampleFresh[index] = (imuSampleTime_ms - storedRngMeasTime_ms[index]) < 500; } if (sampleFresh[0] && sampleFresh[1] && sampleFresh[2]) { if (storedRngMeas[0] > storedRngMeas[1]) { minIndex = 1; maxIndex = 0; } else { maxIndex = 0; minIndex = 1; } if (storedRngMeas[2] > storedRngMeas[maxIndex]) { midIndex = maxIndex; } else if (storedRngMeas[2] < storedRngMeas[minIndex]) { midIndex = minIndex; } else { midIndex = 2; } rngMea = max(storedRngMeas[midIndex],rngOnGnd); newDataRng = true; rngValidMeaTime_ms = imuSampleTime_ms; // recall vehicle states at mid sample time for range finder RecallStates(statesAtRngTime, storedRngMeasTime_ms[midIndex] - 25); } else if (!vehicleArmed) { // if not armed and no return, we assume on ground range rngMea = rngOnGnd; newDataRng = true; rngValidMeaTime_ms = imuSampleTime_ms; // assume synthetic measurement is at current time (no delay) statesAtRngTime = state; } else { newDataRng = false; } lastRngMeasTime_ms = imuSampleTime_ms; } } // Detect takeoff for optical flow navigation void NavEKF::detectOptFlowTakeoff(void) { if (vehicleArmed && !takeOffDetected && (imuSampleTime_ms - timeAtArming_ms) > 1000) { const AP_InertialSensor &ins = _ahrs->get_ins(); Vector3f angRateVec; Vector3f gyroBias; getGyroBias(gyroBias); bool dual_ins = ins.get_gyro_health(0) && ins.get_gyro_health(1); if (dual_ins) { angRateVec = (ins.get_gyro(0) + ins.get_gyro(1)) * 0.5f - gyroBias; } else { angRateVec = ins.get_gyro() - gyroBias; } takeOffDetected = (takeOffDetected || (angRateVec.length() > 0.1f) || (rngMea > (rangeAtArming + 0.1f))); } } // provides the height limit to be observed by the control loops // returns false if no height limiting is required // this is needed to ensure the vehicle does not fly too high when using optical flow navigation bool NavEKF::getHeightControlLimit(float &height) const { // only ask for limiting if we are doing optical flow navigation if (_fusionModeGPS == 3) { // If are doing optical flow nav, ensure the height above ground is within range finder limits after accounting for vehicle tilt and control errors height = max(float(_rng.max_distance_cm()) * 0.007f - 1.0f, 1.0f); return true; } else { return false; } } // provides the delta quaternion that was used by the INS calculation to rotate from the previous orientation to the orientation at the current time // the delta quaternion returned will be a zero rotation if the INS calculation was not performed on that time step Quaternion NavEKF::getDeltaQuaternion(void) const { // Note: correctedDelAngQuat is reset to a zero rotation at the start of every update cycle in UpdateFilter() return correctedDelAngQuat; } // return the quaternions defining the rotation from NED to XYZ (body) axes void NavEKF::getQuaternion(Quaternion& ret) const { ret = state.quat; } // align the NE earth magnetic field states with the published declination void NavEKF::alignMagStateDeclination() { // get the magnetic declination float magDecAng = use_compass() ? _ahrs->get_compass()->get_declination() : 0; // rotate the NE values so that the declination matches the published value Vector3f initMagNED = state.earth_magfield; float magLengthNE = pythagorous2(initMagNED.x,initMagNED.y); state.earth_magfield.x = magLengthNE * cosf(magDecAng); state.earth_magfield.y = magLengthNE * sinf(magDecAng); } // return the amount of yaw angle change due to the last yaw angle reset in radians // returns true if a reset yaw angle has been updated and not queried // this function should not have more than one client bool NavEKF::getLastYawResetAngle(float &yawAng) { if (yawResetAngleWaiting) { yawAng = yawResetAngle; yawResetAngleWaiting = false; return true; } else { yawAng = yawResetAngle; return false; } } #endif // HAL_CPU_CLASS