/// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: nil -*- #include #if HAL_CPU_CLASS >= HAL_CPU_CLASS_150 // uncomment this to force the optimisation of this code, note that // this makes debugging harder #if CONFIG_HAL_BOARD == HAL_BOARD_AVR_SITL || CONFIG_HAL_BOARD == HAL_BOARD_LINUX #pragma GCC optimize("O0") #else #pragma GCC optimize("O3") #endif #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 0.0001f #define MAGE_PNOISE_DEFAULT 0.0003f #define MAGB_PNOISE_DEFAULT 0.0003f #define VEL_GATE_DEFAULT 6 #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 10 #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 1E-06f #define ABIAS_PNOISE_DEFAULT 0.0002f #define MAGE_PNOISE_DEFAULT 0.0003f #define MAGB_PNOISE_DEFAULT 0.0003f #define VEL_GATE_DEFAULT 6 #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 #else // generic defaults (and for plane) #define VELNE_NOISE_DEFAULT 0.3f #define VELD_NOISE_DEFAULT 0.5f #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 0.25f #define GBIAS_PNOISE_DEFAULT 1E-06f #define ABIAS_PNOISE_DEFAULT 0.0002f #define MAGE_PNOISE_DEFAULT 0.0003f #define MAGB_PNOISE_DEFAULT 0.0003f #define VEL_GATE_DEFAULT 6 #define POS_GATE_DEFAULT 10 #define HGT_GATE_DEFAULT 20 #define MAG_GATE_DEFAULT 3 #define MAG_CAL_DEFAULT 0 #define GLITCH_ACCEL_DEFAULT 150 #define GLITCH_RADIUS_DEFAULT 15 #define FLOW_MEAS_DELAY 25 #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 gyro bias uncertainty (deg/sec) #define INIT_GYRO_BIAS_UNCERTAINTY 0.1f // Define tuning parameters const AP_Param::GroupInfo NavEKF::var_info[] PROGMEM = { // @Param: VELNE_NOISE // @DisplayName: GPS horizontal velocity measurement noise (m/s) // @Description: This is the RMS value of noise in the North and East GPS velocity measurements. 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 (m/s) // @Description: This is the RMS value of noise in the vertical GPS velocity measurement. 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 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 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 magnetometer measurements. Increasing it reduces the weighting on these measurements. // @Range: 0.5 5.0 // @Increment: 0.1 // @User: Advanced 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 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 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 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 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 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 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 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 AP_GROUPINFO("POS_DELAY", 15, NavEKF, _msecPosDelay, 220), // @Param: GPS_TYPE // @DisplayName: GPS velocity mode control // @Description: This parameter controls use of GPS velocity measurements : 0 = use 3D velocity, 1 = use 2D velocity, 2 = use no velocity, 3 = use no GPS // @Range: 0 3 // @Increment: 1 // @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 // @Increment: 1 // @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 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 AP_GROUPINFO("FLOW_NOISE", 26, NavEKF, _flowNoise, 0.3f), // @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, 3), // @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 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), AP_GROUPEND }; // constructor NavEKF::NavEKF(const AP_AHRS *ahrs, AP_Baro &baro) : _ahrs(ahrs), _baro(baro), state(*reinterpret_cast(&states)), 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 staticMode(true), // staticMode forces position and velocity fusion with zero values prevStaticMode(true), // staticMode from previous filter update yawAligned(false), // set true when heading or yaw angle has been aligned inhibitWindStates(true), // inhibit wind state updates on startup inhibitMagStates(true), // inhibit magnetometer state updates on startup onGround(true), // initialise assuming we are on ground manoeuvring(false) // initialise assuming we are not maneouvring #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); // Tuning parameters _gpsNEVelVarAccScale = 0.05f; // Scale factor applied to NE velocity measurement variance due to manoeuvre acceleration _gpsDVelVarAccScale = 0.07f; // Scale factor applied to vertical velocity measurement variance due to manoeuvre acceleration _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 = 20000; // GPS retry time with airspeed measurements (msec) _gpsRetryTimeNoTAS = 10000; // GPS retry time without airspeed measurements (msec) _hgtRetryTimeMode0 = 10000; // Height retry time with vertical velocity measurement (msec) _hgtRetryTimeMode12 = 5000; // Height retry time without vertical velocity measurement (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 gyro bias state process noise when on ground _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 = 0.02; // number of seconds between position and velocity corrections. This should be a multiple of the imu update interval. // Misc initial conditions hgtRate = 0.0f; mag_state.q0 = 1; mag_state.DCM.identity(); IMU1_weighting = 0.5f; memset(&faultStatus, 0, sizeof(faultStatus)); // variables added for optical flow fusion 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 = 200; // maximum allowable time between flow fusion events } // Check basic filter health metrics and return a consolidated health status bool NavEKF::healthy(void) const { if (!statesInitialised) { return false; } if (state.quat.is_nan()) { return false; } if (state.velocity.is_nan()) { return false; } if (_fallback && velTestRatio > 1 && posTestRatio > 1 && hgtTestRatio > 1) { // all three metrics being above 1 means the filter is // extremely unhealthy. return false; } // If measurements have failed innovation consistency checks for long enough to time-out // and force fusion then the nav solution can be conidered to be unhealthy // This will only be set as a transient if (_fallback && (posTimeout || velTimeout || hgtTimeout)) { return false; } // all OK return true; } // return true if filter is dead-reckoning height bool NavEKF::HeightDrifting(void) const { // Set to true if height measurements are failing the innovation consistency check return !hgtHealth; } // return true if filter is dead-reckoning position bool NavEKF::PositionDrifting(void) const { // Set to true if position measurements are failing the innovation consistency check return !posHealth; } // resets position states to last GPS measurement or to zero if in static mode void NavEKF::ResetPosition(void) { if (staticMode) { state.position.x = 0; state.position.y = 0; } else if (_ahrs->get_gps().status() >= AP_GPS::GPS_OK_FIX_3D) { // read the GPS readGpsData(); // 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); } // stored horizontal position states to prevent subsequent GPS measurements from being rejected for (uint8_t i=0; i<=49; i++){ storedStates[i].position[0] = state.position[0]; storedStates[i].position[1] = state.position[1]; } // reset the glitch ofset correction states gpsPosGlitchOffsetNE.zero(); } // resets velocity states to last GPS measurement or to zero if in static mode void NavEKF::ResetVelocity(void) { if (staticMode) { state.velocity.zero(); state.vel1.zero(); state.vel2.zero(); } else if (_ahrs->get_gps().status() >= AP_GPS::GPS_OK_FIX_3D) { // read the GPS readGpsData(); // reset horizontal velocity states if (_fusionModeGPS <= 1) { states[4] = velNED[0]; // north velocity from blended accel data states[5] = velNED[1]; // east velocity from blended accel data states[23] = velNED[0]; // north velocity from IMU1 accel data states[24] = velNED[1]; // east velocity from IMU1 accel data states[27] = velNED[0]; // north velocity from IMU2 accel data states[28] = velNED[1]; // 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[0] = velNED[0]; storedStates[i].velocity[1] = velNED[1]; } } // reset filter velocity states state.velocity = velNED; state.vel1 = velNED; state.vel2 = velNED; // reset stored velocity states to prevent subsequent GPS measurements from being rejected for (uint8_t i=0; i<=49; i++){ storedStates[i].velocity = velNED; } } } // 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; } flowStates[1] = states[9] + 0.1f; } // 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 void 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; // Set re-used variables to zero ZeroVariables(); // get initial time deltat between IMU measurements (sec) dtIMU = constrain_float(_ahrs->get_ins().get_delta_time(),0.001f,1.0f); dtIMUinv = 1.0f / dtIMU; // If we have a high rate update step of >100 Hz, then there may not be enough time to do all the fusion steps at once, so load levelling is used if (dtIMU < 0.009f) { inhibitLoadLeveling = false; } else { inhibitLoadLeveling = true; } // set number of updates over which gps and baro measurements are applied to the velocity and position states gpsUpdateCountMaxInv = (dtIMU * 1000.0f)/float(_msecGpsAvg); gpsUpdateCountMax = uint8_t(1.0f/gpsUpdateCountMaxInv); hgtUpdateCountMaxInv = (dtIMU * 1000.0f)/float(_msecHgtAvg); hgtUpdateCountMax = uint8_t(1.0f/hgtUpdateCountMaxInv); magUpdateCountMaxInv = (dtIMU * 1000.0f)/float(_msecMagAvg); magUpdateCountMax = uint8_t(1.0f/magUpdateCountMaxInv); flowUpdateCountMaxInv = (dtIMU * 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(); ResetVelocity(); ResetPosition(); ResetHeight(); state.body_magfield.zero(); // set stored states to current state StoreStatesReset(); // set to true now that states have be initialised statesInitialised = true; // initialise the covariance matrix CovarianceInit(); // define Earth rotation vector in the NED navigation frame calcEarthRateNED(earthRateNED, _ahrs->get_home().lat); // initialise IMU pre-processing states readIMUData(); } // Initialise the states from accelerometer and magnetometer data (if present) // This method can only be used when the vehicle is static void NavEKF::InitialiseFilterBootstrap(void) { // set re-used variables to zero ZeroVariables(); // get initial time deltat between IMU measurements (sec) dtIMU = constrain_float(_ahrs->get_ins().get_delta_time(),0.001f,1.0f); dtIMUinv = 1.0f / dtIMU; // If we have a high rate update step of >100 Hz, then there may not enough time to all the fusion steps at once, so load levelling is used if (dtIMU < 0.009f) { inhibitLoadLeveling = false; } else { inhibitLoadLeveling = true; } // set number of updates over which gps and baro measurements are applied to the velocity and position states gpsUpdateCountMaxInv = (dtIMU * 1000.0f)/float(_msecGpsAvg); gpsUpdateCountMax = uint8_t(1.0f/gpsUpdateCountMaxInv); hgtUpdateCountMaxInv = (dtIMU * 1000.0f)/float(_msecHgtAvg); hgtUpdateCountMax = uint8_t(1.0f/hgtUpdateCountMaxInv); magUpdateCountMaxInv = (dtIMU * 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); // read the GPS readGpsData(); // read the barometer readHgtData(); // 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(); // set stored states to current state StoreStatesReset(); // set to true now we have intialised the states statesInitialised = true; // initialise the covariance matrix CovarianceInit(); // define Earth rotation vector in the NED navigation frame calcEarthRateNED(earthRateNED, _ahrs->get_home().lat); // initialise IMU pre-processing states readIMUData(); } // Update Filter States - this should be called whenever new IMU data is available void NavEKF::UpdateFilter() { // 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(); // detect if the filter update has been delayed for too long if (dtIMU > 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(); // define rules used to set staticMode // staticMode enables ground operation without GPS by fusing zeros for position and height measurements if (static_mode_demanded()) { staticMode = true; } else { staticMode = false; } // check to see if static mode has changed and reset states if it has if (prevStaticMode != staticMode) { ResetVelocity(); ResetPosition(); ResetHeight(); StoreStatesReset(); // 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 (!staticMode && !firstArmComplete) { firstArmComplete = true; state.quat = calcQuatAndFieldStates(_ahrs->roll, _ahrs->pitch); firstArmPosD = state.position.z; } calcQuatAndFieldStates(_ahrs->roll, _ahrs->pitch); heldVelNE.zero(); prevStaticMode = staticMode; } else if (!staticMode && !finalMagYawInit && firstArmPosD - state.position.z > 1.5f && !assume_zero_sideslip()) { // Do a final 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) state.quat = calcQuatAndFieldStates(_ahrs->roll, _ahrs->pitch); finalMagYawInit = true; } // 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 + correctedDelVel1; dt += dtIMU; // 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 - dtIMU)) || (summedDelAng.length() > covDelAngMax))) { CovariancePrediction(); covPredStep = true; summedDelAng.zero(); summedDelVel.zero(); dt = 0.0; } else { covPredStep = false; } // 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 new data, specify which measurements should be used and check data for freshness if (!staticMode && !velHoldMode) { // check for and read new GPS data readGpsData(); // command fusion of GPS data and reset states as required if (newDataGps) { // 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; // select which of velocity and position measurements will be fused if (_fusionModeGPS < 3) { // 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 uint32_t gpsRetryTimeout = useAirspeed() ? _gpsRetryTimeUseTAS : _gpsRetryTimeNoTAS; if (imuSampleTime_ms - secondLastFixTime_ms > gpsRetryTimeout) { ResetPosition(); ResetVelocity(); StoreStatesReset(); } } else { fuseVelData = false; fusePosData = false; } } else { fuseVelData = false; fusePosData = false; } } else if (staticMode ) { // in static 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 (velHoldMode) { // In velocity hold mode we fuse the last valid velocity vector // 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(); // 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) { 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]; } } } // select fusion of magnetometer data void NavEKF::SelectMagFusion() { // 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) { fuseMagData = true; // 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; } else { fuseMagData = false; } // delay if covariance prediction is being performed on this prediction cycle unless load levelling is inhibited if (!covPredStep || inhibitLoadLeveling) { 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]; } } } // select fusion of optical flow measurements void NavEKF::SelectFlowFusion() { // if we don't have flow measurements and are not using GPS, dead reckon using current velocity vector unless we are in static mode if (imuSampleTime_ms - flowMeaTime_ms > 200 && !staticMode && _fusionModeGPS > 2) { velHoldMode = true; } else { velHoldMode = false; } if (velHoldMode && !lastHoldVelocity) { heldVelNE.x = state.velocity.x; heldVelNE.y = state.velocity.y; } lastHoldVelocity = velHoldMode; // Apply tilt check bool tiltOK = (Tnb_flow.c.z > DCM33FlowMin); // if we have waited too long, set a timeout flag which will force fusion to occur regardless of load spreading bool timeout = ((imuSampleTime_ms - prevFlowFusionTime_ms) >= flowIntervalMax_ms); // check if fusion should be delayed to spread load. Setting fuseMeNow to true disables this load spreading feature. bool delayFusion = ((covPredStep || magFusePerformed) && !(timeout || inhibitLoadLeveling)); // if the filter is initialised, we have data to fuse and the vehicle is not excessively tilted, then perform optical flow fusion if (useOptFlow() && newDataFlow && tiltOK && !delayFusion && !staticMode) { // 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)); // Fuse the optical flow X axis data into the main filter flow_state.obsIndex = 0; FuseOptFlow(); // increment the index to fuse the Y axis data on the next prediction cycle flow_state.obsIndex = 1; // 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; // update the time stamp prevFlowFusionTime_ms = imuSampleTime_ms; } else if (flow_state.obsIndex == 1 && !delayFusion){ // Fuse the optical flow Y axis data into the main filter FuseOptFlow(); // increment the index to fuse the X and Y data using the 2-state EKF on the next prediction cycle flow_state.obsIndex = 2; // indicate that flow fusion has been performed. This is used for load spreading. flowFusePerformed = true; } else if (flow_state.obsIndex == 2 || newDataRng) { // enable fusion of range data if available and permitted if(newDataRng && useRngFinder()) { fuseRngData = true; } else { fuseRngData = false; } // the fact that we have got this far means we do have optical flow data fuseOptFlowData = true; // Estimate the focal length scale factor and terrain offset (runs a two state EKF) RunAuxiliaryEKF(); // turn of fusion permissions // increment the index so that no further flow fusion is performed using this measurement flow_state.obsIndex = 3; // clear the flag indicating that flow fusion has been performed. The 2-state fusion is relatively computationally // cheap and can be perfomred on the same prediction cycle with subsequent fusion steps flowFusePerformed = false; // reset the flag to indicate that no new range finder data is available for fusion newDataRng = false; } // 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]; } } } // select fusion of true airspeed measurements void NavEKF::SelectTasFusion() { // get true airspeed measurement readAirSpdData(); // if the filter is initialised, wind states are not inhibited and we have data to fuse, then queue TAS fusion tasDataWaiting = (statesInitialised && !inhibitWindStates && (tasDataWaiting || newDataTas)); // if we have waited too long, set a timeout flag which will force fusion to occur bool timeout = ((imuSampleTime_ms - TASmsecPrev) >= TASmsecMax); // we don't fuse airspeed measurements if magnetometer fusion has been performed in the same frame, unless timed out or the fuseMeNow option is selected // this helps to spreasthe load associated with fusion of different measurements across multiple frames // setting fuseMeNow to true disables this load spreading feature if (tasDataWaiting && (!(covPredStep || magFusePerformed || flowFusePerformed) || timeout || inhibitLoadLeveling)) { FuseAirspeed(); TASmsecPrev = imuSampleTime_ms; tasDataWaiting = 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 to true if fusion is locked out due to magnetometer fusion on the same time step (done for load levelling) bool f_lockedOut = (magFusePerformed && !inhibitLoadLeveling); // 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, enough time has lapsed since the last fusion and it is not locked out if (f_feasible && f_required && f_timeTrigger && !f_lockedOut) { 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 float rotationMag; // magnitude of rotation vector from previous to current time step float rotScaler; // scaling variable used to calculate delta quaternion from last to current time step Quaternion qUpdated; // quaternion at current time step after application of delta quaternion Quaternion deltaQuat; // quaternion from last to current time step const Vector3f gravityNED(0, 0, GRAVITY_MSS); // NED gravity vector m/s^2 // 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 corrections for earths rotation rate and coning errors // % * - and + operators have been overloaded correctedDelAng = correctedDelAng - prevTnb * earthRateNED*dtIMU + (prevDelAng % correctedDelAng) * 8.333333e-2f; // save current measurements prevDelAng = correctedDelAng; // convert the rotation vector to its equivalent quaternion rotationMag = correctedDelAng.length(); if (rotationMag < 1e-12f) { deltaQuat[0] = 1; deltaQuat[1] = 0; deltaQuat[2] = 0; deltaQuat[3] = 0; } else { deltaQuat[0] = cosf(0.5f * rotationMag); rotScaler = (sinf(0.5f * rotationMag)) / rotationMag; deltaQuat[1] = correctedDelAng.x * rotScaler; deltaQuat[2] = correctedDelAng.y * rotScaler; deltaQuat[3] = correctedDelAng.z * rotScaler; } // update the quaternions by rotating from the previous attitude through // the delta angle rotation quaternion qUpdated[0] = states[0]*deltaQuat[0] - states[1]*deltaQuat[1] - states[2]*deltaQuat[2] - states[3]*deltaQuat[3]; qUpdated[1] = states[0]*deltaQuat[1] + states[1]*deltaQuat[0] + states[2]*deltaQuat[3] - states[3]*deltaQuat[2]; qUpdated[2] = states[0]*deltaQuat[2] + states[2]*deltaQuat[0] + states[3]*deltaQuat[1] - states[1]*deltaQuat[3]; qUpdated[3] = states[0]*deltaQuat[3] + states[3]*deltaQuat[0] + states[1]*deltaQuat[2] - states[2]*deltaQuat[1]; // normalise the quaternions and update the quaternion states qUpdated.normalize(); state.quat = qUpdated; // calculate the body to nav cosine matrix Matrix3f Tbn_temp; state.quat.rotation_matrix(Tbn_temp); prevTnb = Tbn_temp.transposed(); // transform body delta velocities to delta velocities in the nav frame // * and + operators have been overloaded // blended IMU calc delVelNav = Tbn_temp*correctedDelVel12 + gravityNED*dtIMU; // single IMU calcs delVelNav1 = Tbn_temp*correctedDelVel1 + gravityNED*dtIMU; delVelNav2 = Tbn_temp*correctedDelVel2 + gravityNED*dtIMU; // calculate the rate of change of velocity (used for launch detect and other functions) velDotNED = delVelNav / dtIMU ; // 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) * (dtIMU*0.5f); state.posD1 += (state.vel1.z + lastVel1.z) * (dtIMU*0.5f); state.posD2 += (state.vel2.z + lastVel2.z) * (dtIMU*0.5f); // capture current angular rate to augmented state vector for use by optical flow fusion state.omega = correctedDelAng * dtIMUinv; // 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 in static mode to allow for faster bias estimation for (uint8_t i=10; i<=12; i++) { processNoise[i] = dAngBiasSigma; if (staticMode) { processNoise[i] *= _gyroBiasNoiseScaler; } } 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); dazCov = sq(dt*_gyrNoise); _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 1E6 (1000m), 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]) > 1e6f) { 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(); perf_end(_perf_CovariancePrediction); } // fuse selected position, velocity and height measurements, checking dat for consistency // provide a static mode that allows maintenance of the attitude reference without GPS provided the vehicle is not accelerating // check innovation consistency of velocity states calculated using IMU1 and IMU2 and calculate the optimal weighting of accel data 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; Vector2 posInnov; float hgtInnov = 0; // 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 NEvelErr; float DvelErr; float posErr; Vector6 R_OBS; 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 static mode or velocity hold is active 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. // in static mode, only position and height fusion is used if (staticMode) { statesAtPosTime = state; statesAtHgtTime = state; } else if (velHoldMode) { 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 static mode // If in velocity hold mode, hold the last known horizontal velocity vector if (!staticMode && !velHoldMode) { for (uint8_t i=0; i<=2; i++) observation[i] = velNED[i]; observation[3] = gpsPosNE.x + gpsPosGlitchOffsetNE.x; observation[4] = gpsPosNE.y + gpsPosGlitchOffsetNE.y; } else if (staticMode){ for (uint8_t i=0; i<=4; i++) observation[i] = 0.0f; } else if (velHoldMode) { 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 velocity caused by manoeuvring NEvelErr = _gpsNEVelVarAccScale * accNavMag; DvelErr = _gpsDVelVarAccScale * accNavMag; // calculate additional error in GPS position caused by manoeuvring posErr = _gpsPosVarAccScale * accNavMag; // estimate the GPS Velocity, GPS horiz position and height measurement variances. R_OBS[0] = sq(constrain_float(_gpsHorizVelNoise, 0.05f, 5.0f)) + sq(NEvelErr); R_OBS[1] = R_OBS[0]; R_OBS[2] = sq(constrain_float(_gpsVertVelNoise, 0.05f, 5.0f)) + sq(DvelErr); 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)); // 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. bool badIMUdata = false; if (_fusionModeGPS == 0 && fuseVelData && (imuSampleTime_ms - lastHgtTime_ms) < (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[5])) && (sq(velDErr) > 9.0f * (P[6][6] + R_OBS[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 posInnov[0] = statesAtPosTime.position.x - observation[3]; posInnov[1] = statesAtPosTime.position.y - observation[4]; varInnovVelPos[3] = P[7][7] + R_OBS[3]; varInnovVelPos[4] = P[8][8] + R_OBS[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 + 0.005f * accelScale * float(_gpsGlitchAccelMax) * sq(0.001f * float(imuSampleTime_ms - posFailTime))); posTestRatio = (sq(posInnov[0]) + sq(posInnov[1])) / maxPosInnov2; posHealth = ((posTestRatio < 1.0f) || badIMUdata); // declare a timeout condition if we have been too long without data posTimeout = ((imuSampleTime_ms - posFailTime) > gpsRetryTime); // use position data if healthy, timed out, or in static mode if (posHealth || posTimeout || staticMode) { posHealth = true; posFailTime = 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 += posInnov[0]; gpsPosGlitchOffsetNE.y += posInnov[1]; // limit the radius of the offset to 100m and decay the offset to zero radially decayGpsOffset(); // reset the position to the current GPS position which will include the glitch correction offset ResetPosition(); // don't fuse data on this time step fusePosData = false; } } else { posHealth = false; } } // test velocity measurements if (fuseVelData) { // test velocity measurements uint8_t imax = 2; if (_fusionModeGPS == 1 || velHoldMode) { 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[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 IMU1_weighting = 1.0f * (K1 / (K1 + K2)) + 0.0f * IMU1_weighting; // filter currently inactive // 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 velTimeout = (imuSampleTime_ms - velFailTime) > gpsRetryTime; // if data is healthy or in static mode we fuse it if (velHealth || staticMode || velHoldMode) { velHealth = true; velFailTime = imuSampleTime_ms; } else if (velTimeout && !posHealth) { // if data is not healthy and timed out and position is unhealthy we reset the velocity, but do not fuse data on this time step ResetVelocity(); StoreStatesReset(); fuseVelData = false; } else { // if data is unhealthy and position is healthy, we do not fuse it velHealth = false; } } // test height measurements if (fuseHgtData) { // set the height data timeout depending on whether vertical velocity data is being used uint32_t hgtRetryTime; if (_fusionModeGPS == 0) hgtRetryTime = _hgtRetryTimeMode0; else hgtRetryTime = _hgtRetryTimeMode12; // calculate height innovations hgtInnov = statesAtHgtTime.position.z - observation[5]; varInnovVelPos[5] = P[9][9] + R_OBS[5]; // calculate the innovation consistency test ratio hgtTestRatio = sq(hgtInnov) / (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 - hgtFailTime) > hgtRetryTime; // Fuse height data if healthy or timed out or in static mode if (hgtHealth || hgtTimeout || staticMode) { hgtHealth = true; hgtFailTime = imuSampleTime_ms; // if timed out, reset the height, but do not fuse data on this time step if (hgtTimeout) { ResetHeight(); StoreStatesReset(); 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 && _fusionModeGPS == 0 && velHealth && !staticMode) { fuseData[0] = true; fuseData[1] = true; fuseData[2] = true; } if (fuseVelData && _fusionModeGPS == 1 && velHealth && !staticMode) { fuseData[0] = true; fuseData[1] = true; } if ((fusePosData && _fusionModeGPS <= 2 && posHealth) || staticMode) { fuseData[3] = true; fuseData[4] = true; } if ((fuseHgtData && hgtHealth) || staticMode) { fuseData[5] = true; } if (velHoldMode) { 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]; } // 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 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 if (obsIndex == 5 && prevTnb.c.z > 0.5f) { 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[22] = Kfusion[13]; // IMU2 Z accel bias 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 } // 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]; // Correct single IMU prediction states using height measurement, limiting rate of change of bias to 0.02 m/s3 float correctionLimit = 0.02f * dtIMU *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 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 bool highRates = ((gpsUpdateCountMax * correctedDelAng.length()) > 0.1f); for (uint8_t i = 0; i<=21; i++) { if ((i <= 3 && highRates) || i >= 10 || staticMode || velHoldMode) { 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() { // start performance timer perf_begin(_perf_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 if (fuseMagData || obsIndex == 1 || obsIndex == 2) { // calculate observation jacobians and Kalman gains if (fuseMagData) { // 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() / dtIMU); // 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 increase the state variances and try again next time P[19][19] += 0.1f*R_MAG; 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] = 0.0; Kfusion[15] = 0.0; } // 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 increase the state variances and try again next time P[20][20] += 0.1f*R_MAG; 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] = 0.0; Kfusion[15] = 0.0; } // 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 increase the state variances and try again next time P[21][21] += 0.1f*R_MAG; 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] = 0.0; Kfusion[15] = 0.0; } // 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, we reduce the weighting by a factor of 4 if (!magHealth) { Kfusion[j] *= 0.25f; } if ((j <= 3 && highRates) || j >= 10 || staticMode || 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]; } } } obsIndex = obsIndex + 1; } else { // set flags to indicate to other processes that fusion has not been performed and is not required on the next time step magFusePerformed = false; magFuseRequired = false; } // force the covariance matrix to be symmetrical and limit the variances to prevent // ill-condiioning. ForceSymmetry(); ConstrainVariances(); // stop performance timer perf_end(_perf_FuseMagnetometer); } /* Estimation of optical flow sensor focal length scale factor and terrain offset using a two state EKF This fiter requires optical flow rates that are not motion compensated */ void NavEKF::RunAuxiliaryEKF() { // start performance timer perf_begin(_perf_OpticalFlowEKF); // calculate a predicted LOS rate squared float losRateSq = (sq(state.velocity.x) + sq(state.velocity.y)) / sq(flowStates[1] - state.position[2]); // 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 ((losRateSq < 0.01f || _fusionModeGPS == 3) && !fuseRngData) { inhibitGndState = true; } else { inhibitGndState = false; } // Don't update focal length offset if there is no range finder or not using GPS, or we are not flying fast enough to generate a useful LOS rate if (!fuseRngData || _fusionModeGPS == 3 || losRateSq < 0.1f || gpsGndSpd < 5.0f) { fScaleInhibit = true; } else { fScaleInhibit = false; } // 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 if (!inhibitGndState) { float distanceTravelledSq; if (fuseRngData) { distanceTravelledSq = sq(statesAtRngTime.position[0] - prevPosN) + sq(statesAtRngTime.position[1] - prevPosE); prevPosN = statesAtRngTime.position[0]; prevPosE = statesAtRngTime.position[1]; } else if (fuseOptFlowData) { distanceTravelledSq = sq(statesAtFlowTime.position[0] - prevPosN) + sq(statesAtFlowTime.position[1] - prevPosE); prevPosN = statesAtFlowTime.position[0]; prevPosE = statesAtFlowTime.position[1]; } else { return; } distanceTravelledSq = min(distanceTravelledSq, 100.0f); float timeLapsed = min(0.001f * (imuSampleTime_ms - timeAtLastAuxEKF_ms), 1.0f); Popt[1][1] += (distanceTravelledSq * sq(0.01f*float(_gndGradientSigma))) + sq(2.0f * timeLapsed); timeAtLastAuxEKF_ms = imuSampleTime_ms; } // fuse range finder data if (fuseRngData) { float range; // range from camera to centre of image float q0; // quaternion at optical flow measurement time float q1; // quaternion at optical flow measurement time float q2; // quaternion at optical flow measurement time float q3; // quaternion at optical flow measurement time float R_RNG = 0.5; // range measurement variance (m^2) TODO make this a function of range and tilt to allow for sensor, alignment and AHRS errors // Copy required states to local variable names q0 = statesAtRngTime.quat[0]; q1 = statesAtRngTime.quat[1]; q2 = statesAtRngTime.quat[2]; q3 = statesAtRngTime.quat[3]; // calculate Kalman gains float SK_RNG[3]; SK_RNG[0] = sq(q0) - sq(q1) - sq(q2) + sq(q3); SK_RNG[1] = 1/(R_RNG + Popt[1][1]/sq(SK_RNG[0])); SK_RNG[2] = 1/SK_RNG[0]; float K_RNG[2]; if (!fScaleInhibit) { K_RNG[0] = Popt[0][1]*SK_RNG[1]*SK_RNG[2]; } else { K_RNG[0] = 0.0f; } if (!inhibitGndState) { K_RNG[1] = Popt[1][1]*SK_RNG[1]*SK_RNG[2]; } else { K_RNG[1] = 0.0f; } // Calculate the innovation variance for data logging varInnovRng = 1.0f/SK_RNG[1]; // constrain terrain height to be below the vehicle flowStates[1] = max(flowStates[1], statesAtRngTime.position[2] + 0.1f); // estimate range to centre of image range = (flowStates[1] - statesAtRngTime.position[2]) * SK_RNG[2]; // Calculate the measurement innovation innovRng = range - 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[1]) < 25.0f) { // correct the state for (uint8_t i = 0; i < 2 ; i++) { flowStates[i] -= K_RNG[i] * innovRng; } // constrain the states flowStates[0] = constrain_float(flowStates[0], 0.8f, 1.25f); flowStates[1] = max(flowStates[1], statesAtRngTime.position[2] + 0.1f); // correct the covariance matrix float nextPopt[2][2]; nextPopt[0][0] = Popt[0][0] - (Popt[0][1]*Popt[1][0]*SK_RNG[1]*SK_RNG[2]) * SK_RNG[2]; nextPopt[0][1] = Popt[0][1] - (Popt[0][1]*Popt[1][1]*SK_RNG[1]*SK_RNG[2]) * SK_RNG[2]; nextPopt[1][0] = -Popt[1][0]*((Popt[1][1]*SK_RNG[1]*SK_RNG[2]) * SK_RNG[2] - 1.0f); nextPopt[1][1] = -Popt[1][1]*((Popt[1][1]*SK_RNG[1]*SK_RNG[2]) * SK_RNG[2] - 1.0f); // prevent the state variances from becoming negative and maintain symmetry Popt[0][0] = max(nextPopt[0][0],0.0f); Popt[1][1] = max(nextPopt[1][1],0.0f); Popt[0][1] = 0.5f * (nextPopt[0][1] + nextPopt[1][0]); Popt[1][0] = Popt[0][1]; } } 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[2]; // predicted optical flow angular rate measurements float range; // range from camera to centre of image float q0; // quaternion at optical flow measurement time float q1; // quaternion at optical flow measurement time float q2; // quaternion at optical flow measurement time float q3; // quaternion at optical flow measurement time float HP[2]; float SH_OPT[6]; float SK_OPT[3]; float K_OPT[2][2]; float H_OPT[2][2]; float nextPopt[2][2]; float SH015; float SH025; float SH014; float SH024; // propagate scale factor state noise if (!fScaleInhibit) { Popt[0][0] += 1e-8f; } else { Popt[0][0] = 0.0f; } // Copy required states to local variable names q0 = statesAtFlowTime.quat[0]; q1 = statesAtFlowTime.quat[1]; q2 = statesAtFlowTime.quat[2]; q3 = statesAtFlowTime.quat[3]; vel.x = statesAtFlowTime.velocity[0]; vel.y = statesAtFlowTime.velocity[1]; vel.z = statesAtFlowTime.velocity[2]; // constrain terrain height to be below the vehicle flowStates[1] = max(flowStates[1], statesAtFlowTime.position[2] + 0.1f); // estimate range to centre of image range = (flowStates[1] - statesAtFlowTime.position[2]) / Tnb_flow.c.z; // 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[0] = flowStates[0]*( relVelSensor.y/range) - omegaAcrossFlowTime.x; losPred[1] = flowStates[0]*(-relVelSensor.x/range) - omegaAcrossFlowTime.y; // calculate innovations auxFlowObsInnov[0] = losPred[0] - flowRadXY[0]; auxFlowObsInnov[1] = losPred[1] - flowRadXY[1]; // calculate Kalman gains SH_OPT[0] = sq(q0) - sq(q1) - sq(q2) + sq(q3); SH_OPT[1] = vel.x*(sq(q0) + sq(q1) - sq(q2) - sq(q3)) + vel.y*(2*q0*q3 + 2*q1*q2) - vel.z*(2*q0*q2 - 2*q1*q3); SH_OPT[2] = vel.y*(sq(q0) - sq(q1) + sq(q2) - sq(q3)) - vel.x*(2*q0*q3 - 2*q1*q2) + vel.z*(2*q0*q1 + 2*q2*q3); SH_OPT[3] = statesAtFlowTime.position[2] - flowStates[1]; SH_OPT[4] = 1.0f/sq(SH_OPT[3]); SH_OPT[5] = 1.0f/SH_OPT[3]; SH015 = SH_OPT[0]*SH_OPT[1]*SH_OPT[5]; SH025 = SH_OPT[0]*SH_OPT[2]*SH_OPT[5]; SH014 = SH_OPT[0]*SH_OPT[1]*SH_OPT[4]; SH024 = SH_OPT[0]*SH_OPT[2]*SH_OPT[4]; SK_OPT[0] = 1.0f/(R_LOS + SH015*(Popt[0][0]*SH015 + Popt[1][0]*flowStates[0]*SH014) + flowStates[0]*SH014*(Popt[0][1]*SH015 + Popt[1][1]*flowStates[0]*SH014)); SK_OPT[1] = 1.0f/(R_LOS + SH025*(Popt[0][0]*SH025 + Popt[1][0]*flowStates[0]*SH024) + flowStates[0]*SH024*(Popt[0][1]*SH025 + Popt[1][1]*flowStates[0]*SH024)); SK_OPT[2] = SH_OPT[0]; if (!fScaleInhibit) { K_OPT[0][0] = -SK_OPT[1]*(Popt[0][0]*SH_OPT[2]*SH_OPT[5]*SK_OPT[2] + Popt[0][1]*flowStates[0]*SH_OPT[2]*SH_OPT[4]*SK_OPT[2]); K_OPT[0][1] = SK_OPT[0]*(Popt[0][0]*SH_OPT[1]*SH_OPT[5]*SK_OPT[2] + Popt[0][1]*flowStates[0]*SH_OPT[1]*SH_OPT[4]*SK_OPT[2]); } else { K_OPT[0][0] = 0.0f; K_OPT[0][1] = 0.0f; } if (!inhibitGndState) { K_OPT[1][0] = -SK_OPT[1]*(Popt[1][0]*SH_OPT[2]*SH_OPT[5]*SK_OPT[2] + Popt[1][1]*flowStates[0]*SH_OPT[2]*SH_OPT[4]*SK_OPT[2]); K_OPT[1][1] = SK_OPT[0]*(Popt[1][0]*SH_OPT[1]*SH_OPT[5]*SK_OPT[2] + Popt[1][1]*flowStates[0]*SH_OPT[1]*SH_OPT[4]*SK_OPT[2]); } else { K_OPT[1][0] = 0.0f; K_OPT[1][1] = 0.0f; } // calculate observations jacobians H_OPT[0][0] = -SH025; H_OPT[0][1] = -flowStates[0]*SH024; H_OPT[1][0] = SH015; H_OPT[1][1] = flowStates[0]*SH014; // calculate innovation variances auxFlowObsInnovVar[0] = 1.0f/SK_OPT[1]; auxFlowObsInnovVar[1] = 1.0f/SK_OPT[0]; // Check the innovation for consistency and don't fuse if > threshold for (uint8_t obsIndex = 0; obsIndex < 2; obsIndex++) { // calculate the innovation consistency test ratio auxFlowTestRatio[obsIndex] = sq(auxFlowObsInnov[obsIndex]) / (sq(_flowInnovGate) * auxFlowObsInnovVar[obsIndex]); if ((auxFlowTestRatio[obsIndex] < 1.0f) && (flowRadXY[obsIndex] < _maxFlowRate)) { // correct the state for (uint8_t i = 0; i < 2 ; i++) { flowStates[i] -= K_OPT[i][obsIndex] * auxFlowObsInnov[obsIndex]; } // constrain the states flowStates[0] = constrain_float(flowStates[0], 0.8f, 1.25f); flowStates[1] = max(flowStates[1], statesAtFlowTime.position[2] + 0.1f); // correct the covariance matrix for (uint8_t i = 0; i < 2 ; i++) { HP[i] = 0.0f; for (uint8_t j = 0; j < 2 ; j++) { HP[i] += H_OPT[obsIndex][j] * P[j][i]; } } for (uint8_t i = 0; i < 2 ; i++) { for (uint8_t j = 0; j < 2 ; j++) { nextPopt[i][j] = P[i][j] - K_OPT[i][obsIndex] * HP[j]; } } // prevent the state variances from becoming negative and maintain symmetry Popt[0][0] = max(nextPopt[0][0],0.0f); Popt[1][1] = max(nextPopt[1][1],0.0f); Popt[0][1] = 0.5f * (nextPopt[0][1] + nextPopt[1][0]); Popt[1][0] = Popt[0][1]; } } } // stop the performance timer perf_end(_perf_OpticalFlowEKF); } void NavEKF::FuseOptFlow() { // start performance timer perf_begin(_perf_FuseOptFlow); float H_LOS[22]; float tempVar[9]; 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]; velNED_local.x = vn; velNED_local.y = ve; velNED_local.z = vd; // constrain terrain to be below vehicle flowStates[1] = max(flowStates[1], pd + 0.1f); float heightAboveGndEst = flowStates[1] - pd; // 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),0.1f,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/(pd - flowStates[1]); SH_LOS[4] = sq(SH_LOS[3]); // Calculate common expressions for Kalman gains float temp = (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]*SH_LOS[4] + 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]*SH_LOS[4] + 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]*SH_LOS[4] + 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]*SH_LOS[4] + P[4][3]*SH_LOS[0]*SH_LOS[3]*(sq(q0) + sq(q1) - sq(q2) - sq(q3))) - SH_LOS[0]*SH_LOS[1]*SH_LOS[4]*(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]*SH_LOS[4] + P[4][9]*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]*SH_LOS[4] + 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]*SH_LOS[4] + 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]*SH_LOS[4] + P[4][6]*SH_LOS[0]*SH_LOS[3]*(sq(q0) + sq(q1) - sq(q2) - sq(q3)))); if (fabsf(temp) < 1e-9f) return; SK_LOS[0] = 1.0f/temp; temp = (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]*SH_LOS[4] + 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]*SH_LOS[4] + 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]*SH_LOS[4] + 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]*SH_LOS[4] + P[5][3]*SH_LOS[0]*SH_LOS[3]*(sq(q0) - sq(q1) + sq(q2) - sq(q3))) - SH_LOS[0]*SH_LOS[2]*SH_LOS[4]*(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]*SH_LOS[4] + P[5][9]*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]*SH_LOS[4] + 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]*SH_LOS[4] + 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]*SH_LOS[4] + P[5][6]*SH_LOS[0]*SH_LOS[3]*(sq(q0) - sq(q1) + sq(q2) - sq(q3)))); if (fabsf(temp) < 1e-9f) return; SK_LOS[1] = 1.0f/temp; 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] = sq(q0) + sq(q1) - sq(q2) - sq(q3); SK_LOS[8] = SH_LOS[3]; // Calculate common intermediate terms tempVar[0] = SH_LOS[0]*SK_LOS[6]*SK_LOS[8]; tempVar[1] = SH_LOS[0]*SH_LOS[2]*SH_LOS[4]; tempVar[2] = 2.0f*SH_LOS[2]*SK_LOS[8]; tempVar[3] = SH_LOS[0]*SK_LOS[8]*(2.0f*q0*q1 + 2.0f*q2*q3); tempVar[4] = SH_LOS[0]*SK_LOS[8]*(2.0f*q0*q3 - 2.0f*q1*q2); tempVar[5] = (SK_LOS[5] - q2*tempVar[2]); tempVar[6] = (SK_LOS[2] - q3*tempVar[2]); tempVar[7] = (SK_LOS[3] - q1*tempVar[2]); tempVar[8] = (SK_LOS[4] + q0*tempVar[2]); // calculate observation jacobians for X LOS rate for (uint8_t i = 0; i < 23; i++) H_LOS[i] = 0; 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] = tempVar[1]; // calculate Kalman gains for X LOS rate Kfusion[0] = -(P[0][0]*tempVar[8] + P[0][1]*tempVar[7] - P[0][3]*tempVar[6] + P[0][2]*tempVar[5] - P[0][4]*tempVar[4] + P[0][6]*tempVar[3] - P[0][9]*tempVar[1] + P[0][5]*tempVar[0])/(R_LOS + tempVar[8]*(P[0][0]*tempVar[8] + P[1][0]*tempVar[7] + P[2][0]*tempVar[5] - P[3][0]*tempVar[6] - P[4][0]*tempVar[4] + P[6][0]*tempVar[3] - P[9][0]*tempVar[1] + P[5][0]*tempVar[0]) + tempVar[7]*(P[0][1]*tempVar[8] + P[1][1]*tempVar[7] + P[2][1]*tempVar[5] - P[3][1]*tempVar[6] - P[4][1]*tempVar[4] + P[6][1]*tempVar[3] - P[9][1]*tempVar[1] + P[5][1]*tempVar[0]) + tempVar[5]*(P[0][2]*tempVar[8] + P[1][2]*tempVar[7] + P[2][2]*tempVar[5] - P[3][2]*tempVar[6] - P[4][2]*tempVar[4] + P[6][2]*tempVar[3] - P[9][2]*tempVar[1] + P[5][2]*tempVar[0]) - tempVar[6]*(P[0][3]*tempVar[8] + P[1][3]*tempVar[7] + P[2][3]*tempVar[5] - P[3][3]*tempVar[6] - P[4][3]*tempVar[4] + P[6][3]*tempVar[3] - P[9][3]*tempVar[1] + P[5][3]*tempVar[0]) - tempVar[4]*(P[0][4]*tempVar[8] + P[1][4]*tempVar[7] + P[2][4]*tempVar[5] - P[3][4]*tempVar[6] - P[4][4]*tempVar[4] + P[6][4]*tempVar[3] - P[9][4]*tempVar[1] + P[5][4]*tempVar[0]) + tempVar[3]*(P[0][6]*tempVar[8] + P[1][6]*tempVar[7] + P[2][6]*tempVar[5] - P[3][6]*tempVar[6] - P[4][6]*tempVar[4] + P[6][6]*tempVar[3] - P[9][6]*tempVar[1] + P[5][6]*tempVar[0]) - tempVar[1]*(P[0][9]*tempVar[8] + P[1][9]*tempVar[7] + P[2][9]*tempVar[5] - P[3][9]*tempVar[6] - P[4][9]*tempVar[4] + P[6][9]*tempVar[3] - P[9][9]*tempVar[1] + P[5][9]*tempVar[0]) + tempVar[0]*(P[0][5]*tempVar[8] + P[1][5]*tempVar[7] + P[2][5]*tempVar[5] - P[3][5]*tempVar[6] - P[4][5]*tempVar[4] + P[6][5]*tempVar[3] - P[9][5]*tempVar[1] + P[5][5]*tempVar[0])); Kfusion[1] = -SK_LOS[1]*(P[1][0]*tempVar[8] + P[1][1]*tempVar[7] - P[1][3]*tempVar[6] + P[1][2]*tempVar[5] - P[1][4]*tempVar[4] + P[1][6]*tempVar[3] - P[1][9]*tempVar[1] + P[1][5]*tempVar[0]); Kfusion[2] = -SK_LOS[1]*(P[2][0]*tempVar[8] + P[2][1]*tempVar[7] - P[2][3]*tempVar[6] + P[2][2]*tempVar[5] - P[2][4]*tempVar[4] + P[2][6]*tempVar[3] - P[2][9]*tempVar[1] + P[2][5]*tempVar[0]); Kfusion[3] = -SK_LOS[1]*(P[3][0]*tempVar[8] + P[3][1]*tempVar[7] - P[3][3]*tempVar[6] + P[3][2]*tempVar[5] - P[3][4]*tempVar[4] + P[3][6]*tempVar[3] - P[3][9]*tempVar[1] + P[3][5]*tempVar[0]); Kfusion[4] = -SK_LOS[1]*(P[4][0]*tempVar[8] + P[4][1]*tempVar[7] - P[4][3]*tempVar[6] + P[4][2]*tempVar[5] - P[4][4]*tempVar[4] + P[4][6]*tempVar[3] - P[4][9]*tempVar[1] + P[4][5]*tempVar[0]); Kfusion[5] = -SK_LOS[1]*(P[5][0]*tempVar[8] + P[5][1]*tempVar[7] - P[5][3]*tempVar[6] + P[5][2]*tempVar[5] - P[5][4]*tempVar[4] + P[5][6]*tempVar[3] - P[5][9]*tempVar[1] + P[5][5]*tempVar[0]); Kfusion[6] = -SK_LOS[1]*(P[6][0]*tempVar[8] + P[6][1]*tempVar[7] - P[6][3]*tempVar[6] + P[6][2]*tempVar[5] - P[6][4]*tempVar[4] + P[6][6]*tempVar[3] - P[6][9]*tempVar[1] + P[6][5]*tempVar[0]); Kfusion[7] = -SK_LOS[1]*(P[7][0]*tempVar[8] + P[7][1]*tempVar[7] - P[7][3]*tempVar[6] + P[7][2]*tempVar[5] - P[7][4]*tempVar[4] + P[7][6]*tempVar[3] - P[7][9]*tempVar[1] + P[7][5]*tempVar[0]); Kfusion[8] = -SK_LOS[1]*(P[8][0]*tempVar[8] + P[8][1]*tempVar[7] - P[8][3]*tempVar[6] + P[8][2]*tempVar[5] - P[8][4]*tempVar[4] + P[8][6]*tempVar[3] - P[8][9]*tempVar[1] + P[8][5]*tempVar[0]); Kfusion[9] = -SK_LOS[1]*(P[9][0]*tempVar[8] + P[9][1]*tempVar[7] - P[9][3]*tempVar[6] + P[9][2]*tempVar[5] - P[9][4]*tempVar[4] + P[9][6]*tempVar[3] - P[9][9]*tempVar[1] + P[9][5]*tempVar[0]); Kfusion[10] = -SK_LOS[1]*(P[10][0]*tempVar[8] + P[10][1]*tempVar[7] - P[10][3]*tempVar[6] + P[10][2]*tempVar[5] - P[10][4]*tempVar[4] + P[10][6]*tempVar[3] - P[10][9]*tempVar[1] + P[10][5]*tempVar[0]); Kfusion[11] = -SK_LOS[1]*(P[11][0]*tempVar[8] + P[11][1]*tempVar[7] - P[11][3]*tempVar[6] + P[11][2]*tempVar[5] - P[11][4]*tempVar[4] + P[11][6]*tempVar[3] - P[11][9]*tempVar[1] + P[11][5]*tempVar[0]); Kfusion[12] = -SK_LOS[1]*(P[12][0]*tempVar[8] + P[12][1]*tempVar[7] - P[12][3]*tempVar[6] + P[12][2]*tempVar[5] - P[12][4]*tempVar[4] + P[12][6]*tempVar[3] - P[12][9]*tempVar[1] + P[12][5]*tempVar[0]); // only height measurements are allowed to modify the Z bias state to improve the stability of the estimate Kfusion[13] = 0.0f;//-SK_LOS[1]*(P[13][0]*tempVar[8] + P[13][1]*tempVar[7] - P[13][3]*tempVar[6] + P[13][2]*tempVar[5] - P[13][4]*tempVar[4] + P[13][6]*tempVar[3] - P[13][9]*tempVar[1] + P[13][5]*tempVar[0]); if (inhibitWindStates) { Kfusion[14] = -SK_LOS[1]*(P[14][0]*tempVar[8] + P[14][1]*tempVar[7] - P[14][3]*tempVar[6] + P[14][2]*tempVar[5] - P[14][4]*tempVar[4] + P[14][6]*tempVar[3] - P[14][9]*tempVar[1] + P[14][5]*tempVar[0]); Kfusion[15] = -SK_LOS[1]*(P[15][0]*tempVar[8] + P[15][1]*tempVar[7] - P[15][3]*tempVar[6] + P[15][2]*tempVar[5] - P[15][4]*tempVar[4] + P[15][6]*tempVar[3] - P[15][9]*tempVar[1] + P[15][5]*tempVar[0]); } else { Kfusion[14] = 0.0f; Kfusion[15] = 0.0f; } if (inhibitMagStates) { Kfusion[16] = -SK_LOS[1]*(P[16][0]*tempVar[8] + P[16][1]*tempVar[7] - P[16][3]*tempVar[6] + P[16][2]*tempVar[5] - P[16][4]*tempVar[4] + P[16][6]*tempVar[3] - P[16][9]*tempVar[1] + P[16][5]*tempVar[0]); Kfusion[17] = -SK_LOS[1]*(P[17][0]*tempVar[8] + P[17][1]*tempVar[7] - P[17][3]*tempVar[6] + P[17][2]*tempVar[5] - P[17][4]*tempVar[4] + P[17][6]*tempVar[3] - P[17][9]*tempVar[1] + P[17][5]*tempVar[0]); Kfusion[18] = -SK_LOS[1]*(P[18][0]*tempVar[8] + P[18][1]*tempVar[7] - P[18][3]*tempVar[6] + P[18][2]*tempVar[5] - P[18][4]*tempVar[4] + P[18][6]*tempVar[3] - P[18][9]*tempVar[1] + P[18][5]*tempVar[0]); Kfusion[19] = -SK_LOS[1]*(P[19][0]*tempVar[8] + P[19][1]*tempVar[7] - P[19][3]*tempVar[6] + P[19][2]*tempVar[5] - P[19][4]*tempVar[4] + P[19][6]*tempVar[3] - P[19][9]*tempVar[1] + P[19][5]*tempVar[0]); Kfusion[20] = -SK_LOS[1]*(P[20][0]*tempVar[8] + P[20][1]*tempVar[7] - P[20][3]*tempVar[6] + P[20][2]*tempVar[5] - P[20][4]*tempVar[4] + P[20][6]*tempVar[3] - P[20][9]*tempVar[1] + P[20][5]*tempVar[0]); Kfusion[21] = -SK_LOS[1]*(P[21][0]*tempVar[8] + P[21][1]*tempVar[7] - P[21][3]*tempVar[6] + P[21][2]*tempVar[5] - P[21][4]*tempVar[4] + P[21][6]*tempVar[3] - P[21][9]*tempVar[1] + P[21][5]*tempVar[0]); } else { for (uint8_t i = 16; i <= 21; i++) { Kfusion[i] = 0.0f; } } // calculate innovation variance and innovation for X axis observation varInnovOptFlow[0] = 1.0f/SK_LOS[0]; innovOptFlow[0] = losPred[0] - flowRadXYcomp[0]; } else if (obsIndex == 1) { // calculate intermediate common variables tempVar[0] = 2.0f*SH_LOS[1]*SK_LOS[8]; tempVar[1] = (SK_LOS[2] + q0*tempVar[0]); tempVar[2] = (SK_LOS[5] - q1*tempVar[0]); tempVar[3] = (SK_LOS[3] + q2*tempVar[0]); tempVar[4] = (SK_LOS[4] + q3*tempVar[0]); tempVar[5] = SH_LOS[0]*SK_LOS[8]*(2*q0*q3 + 2*q1*q2); tempVar[6] = SH_LOS[0]*SK_LOS[8]*(2*q0*q2 - 2*q1*q3); tempVar[7] = SH_LOS[0]*SH_LOS[1]*SH_LOS[4]; tempVar[8] = SH_LOS[0]*SK_LOS[7]*SK_LOS[8]; // Calculate observation jacobians for Y LOS rate for (uint8_t i = 0; i < 23; i++) H_LOS[i] = 0; 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] = -tempVar[7]; // Calculate Kalman gains for Y LOS rate Kfusion[0] = SK_LOS[0]*(P[0][0]*tempVar[1] + P[0][1]*tempVar[2] - P[0][2]*tempVar[3] + P[0][3]*tempVar[4] + P[0][5]*tempVar[5] - P[0][6]*tempVar[6] - P[0][9]*tempVar[7] + P[0][4]*tempVar[8]); Kfusion[1] = SK_LOS[0]*(P[1][0]*tempVar[1] + P[1][1]*tempVar[2] - P[1][2]*tempVar[3] + P[1][3]*tempVar[4] + P[1][5]*tempVar[5] - P[1][6]*tempVar[6] - P[1][9]*tempVar[7] + P[1][4]*tempVar[8]); Kfusion[2] = SK_LOS[0]*(P[2][0]*tempVar[1] + P[2][1]*tempVar[2] - P[2][2]*tempVar[3] + P[2][3]*tempVar[4] + P[2][5]*tempVar[5] - P[2][6]*tempVar[6] - P[2][9]*tempVar[7] + P[2][4]*tempVar[8]); Kfusion[3] = SK_LOS[0]*(P[3][0]*tempVar[1] + P[3][1]*tempVar[2] - P[3][2]*tempVar[3] + P[3][3]*tempVar[4] + P[3][5]*tempVar[5] - P[3][6]*tempVar[6] - P[3][9]*tempVar[7] + P[3][4]*tempVar[8]); Kfusion[4] = SK_LOS[0]*(P[4][0]*tempVar[1] + P[4][1]*tempVar[2] - P[4][2]*tempVar[3] + P[4][3]*tempVar[4] + P[4][5]*tempVar[5] - P[4][6]*tempVar[6] - P[4][9]*tempVar[7] + P[4][4]*tempVar[8]); Kfusion[5] = SK_LOS[0]*(P[5][0]*tempVar[1] + P[5][1]*tempVar[2] - P[5][2]*tempVar[3] + P[5][3]*tempVar[4] + P[5][5]*tempVar[5] - P[5][6]*tempVar[6] - P[5][9]*tempVar[7] + P[5][4]*tempVar[8]); Kfusion[6] = SK_LOS[0]*(P[6][0]*tempVar[1] + P[6][1]*tempVar[2] - P[6][2]*tempVar[3] + P[6][3]*tempVar[4] + P[6][5]*tempVar[5] - P[6][6]*tempVar[6] - P[6][9]*tempVar[7] + P[6][4]*tempVar[8]); Kfusion[7] = SK_LOS[0]*(P[7][0]*tempVar[1] + P[7][1]*tempVar[2] - P[7][2]*tempVar[3] + P[7][3]*tempVar[4] + P[7][5]*tempVar[5] - P[7][6]*tempVar[6] - P[7][9]*tempVar[7] + P[7][4]*tempVar[8]); Kfusion[8] = SK_LOS[0]*(P[8][0]*tempVar[1] + P[8][1]*tempVar[2] - P[8][2]*tempVar[3] + P[8][3]*tempVar[4] + P[8][5]*tempVar[5] - P[8][6]*tempVar[6] - P[8][9]*tempVar[7] + P[8][4]*tempVar[8]); Kfusion[9] = SK_LOS[0]*(P[9][0]*tempVar[1] + P[9][1]*tempVar[2] - P[9][2]*tempVar[3] + P[9][3]*tempVar[4] + P[9][5]*tempVar[5] - P[9][6]*tempVar[6] - P[9][9]*tempVar[7] + P[9][4]*tempVar[8]); Kfusion[10] = SK_LOS[0]*(P[10][0]*tempVar[1] + P[10][1]*tempVar[2] - P[10][2]*tempVar[3] + P[10][3]*tempVar[4] + P[10][5]*tempVar[5] - P[10][6]*tempVar[6] - P[10][9]*tempVar[7] + P[10][4]*tempVar[8]); Kfusion[11] = SK_LOS[0]*(P[11][0]*tempVar[1] + P[11][1]*tempVar[2] - P[11][2]*tempVar[3] + P[11][3]*tempVar[4] + P[11][5]*tempVar[5] - P[11][6]*tempVar[6] - P[11][9]*tempVar[7] + P[11][4]*tempVar[8]); Kfusion[12] = SK_LOS[0]*(P[12][0]*tempVar[1] + P[12][1]*tempVar[2] - P[12][2]*tempVar[3] + P[12][3]*tempVar[4] + P[12][5]*tempVar[5] - P[12][6]*tempVar[6] - P[12][9]*tempVar[7] + P[12][4]*tempVar[8]); // 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[1] + P[13][1]*tempVar[2] - P[13][2]*tempVar[3] + P[13][3]*tempVar[4] + P[13][5]*tempVar[5] - P[13][6]*tempVar[6] - P[13][9]*tempVar[7] + P[13][4]*tempVar[8]); if (inhibitWindStates) { Kfusion[14] = SK_LOS[0]*(P[14][0]*tempVar[1] + P[14][1]*tempVar[2] - P[14][2]*tempVar[3] + P[14][3]*tempVar[4] + P[14][5]*tempVar[5] - P[14][6]*tempVar[6] - P[14][9]*tempVar[7] + P[14][4]*tempVar[8]); Kfusion[15] = SK_LOS[0]*(P[15][0]*tempVar[1] + P[15][1]*tempVar[2] - P[15][2]*tempVar[3] + P[15][3]*tempVar[4] + P[15][5]*tempVar[5] - P[15][6]*tempVar[6] - P[15][9]*tempVar[7] + P[15][4]*tempVar[8]); } else { Kfusion[14] = 0.0f; Kfusion[15] = 0.0f; } if (inhibitMagStates) { Kfusion[16] = SK_LOS[0]*(P[16][0]*tempVar[1] + P[16][1]*tempVar[2] - P[16][2]*tempVar[3] + P[16][3]*tempVar[4] + P[16][5]*tempVar[5] - P[16][6]*tempVar[6] - P[16][9]*tempVar[7] + P[16][4]*tempVar[8]); Kfusion[17] = SK_LOS[0]*(P[17][0]*tempVar[1] + P[17][1]*tempVar[2] - P[17][2]*tempVar[3] + P[17][3]*tempVar[4] + P[17][5]*tempVar[5] - P[17][6]*tempVar[6] - P[17][9]*tempVar[7] + P[17][4]*tempVar[8]); Kfusion[18] = SK_LOS[0]*(P[18][0]*tempVar[1] + P[18][1]*tempVar[2] - P[18][2]*tempVar[3] + P[18][3]*tempVar[4] + P[18][5]*tempVar[5] - P[18][6]*tempVar[6] - P[18][9]*tempVar[7] + P[18][4]*tempVar[8]); Kfusion[19] = SK_LOS[0]*(P[19][0]*tempVar[1] + P[19][1]*tempVar[2] - P[19][2]*tempVar[3] + P[19][3]*tempVar[4] + P[19][5]*tempVar[5] - P[19][6]*tempVar[6] - P[19][9]*tempVar[7] + P[19][4]*tempVar[8]); Kfusion[20] = SK_LOS[0]*(P[20][0]*tempVar[1] + P[20][1]*tempVar[2] - P[20][2]*tempVar[3] + P[20][3]*tempVar[4] + P[20][5]*tempVar[5] - P[20][6]*tempVar[6] - P[20][9]*tempVar[7] + P[20][4]*tempVar[8]); Kfusion[21] = SK_LOS[0]*(P[21][0]*tempVar[1] + P[21][1]*tempVar[2] - P[21][2]*tempVar[3] + P[21][3]*tempVar[4] + P[21][5]*tempVar[5] - P[21][6]*tempVar[6] - P[21][9]*tempVar[7] + P[21][4]*tempVar[8]); } else { for (uint8_t i = 16; i <= 21; i++) { Kfusion[i] = 0.0f; } } // calculate variance and innovation for Y observation varInnovOptFlow[1] = 1.0f/SK_LOS[1]; 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)) { // Reset the timer for velocity fusion timeout. This prevents a velocity timeout from being declared if we have to momentarily go into velocity hold mode. velFailTime = imuSampleTime_ms; // correct the state vector for (uint8_t j = 0; j <= 21; j++) { states[j] = states[j] - Kfusion[j] * innovOptFlow[obsIndex]; } // 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. This is required because flow fusion is applied across two consecutive prediction cycles // 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]; } } } ForceSymmetry(); ConstrainVariances(); // stop the performance timer perf_end(_perf_FuseOptFlow); } // 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; // 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 VtasPred = pythagorous3((ve - vwe) , (vn - 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); // test the ratio before fusing data if (tasTestRatio < 1.0f) { // 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] = 0.0; 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] = 0.0; 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] = 0.0; } 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 float SH_BETA[13]; float SK_BETA[8]; 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 vel_rel_wind.x = vn - vwn; vel_rel_wind.y = ve - vwe; 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] = 0.0; 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] = 0.0; } 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 { omegaAvg = correctedDelAng * (1.0f * dtIMUinv); } } // 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). // return false if no position is available bool NavEKF::getPosNED(Vector3f &pos) const { pos = state.position; return true; } // return body axis gyro bias estimates in rad/sec void NavEKF::getGyroBias(Vector3f &gyroBias) const { if (dtIMU == 0) { gyroBias.zero(); return; } gyroBias = state.gyro_bias / dtIMU; } // 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(INIT_GYRO_BIAS_UNCERTAINTY * dtIMU)); P[11][11] = P[10][10]; P[12][12] = P[10][10]; } // 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 (dtIMU == 0) { zbias1 = 0; zbias2 = 0; } else { zbias1 = state.accel_zbias1 * dtIMUinv; zbias2 = state.accel_zbias2 * dtIMUinv; } } // 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 the last calculated latitude, longitude and height bool NavEKF::getLLH(struct Location &loc) const { loc.lat = _ahrs->get_home().lat; loc.lng = _ahrs->get_home().lng; loc.alt = _ahrs->get_home().alt - state.position.z*100; loc.flags.relative_alt = 0; loc.flags.terrain_alt = 0; location_offset(loc, state.position.x, state.position.y); return true; } // return data for debugging optical flow fusion void NavEKF::getFlowDebug(float &scaleFactor, float &gndPos, float &flowInnovX, float &flowInnovY, float &augFlowInnovX, float &augFlowInnovY, float &rngInnov, float &range) const { scaleFactor = flowStates[0]; gndPos = flowStates[1]; flowInnovX = innovOptFlow[0]; flowInnovY = innovOptFlow[1]; augFlowInnovX = auxFlowObsInnov[0]; augFlowInnovY = auxFlowObsInnov[1]; rngInnov = innovRng; range = rngMea; } // 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 const AP_Airspeed *airspeed = _ahrs->get_airspeed(); float gndSpdSq = sq(velNED[0]) + sq(velNED[1]); uint8_t inAirSum = 0; bool highGndSpdStage2 = false; // trigger at 8 m/s airspeed if (airspeed && airspeed->use() && airspeed->get_airspeed() * airspeed->get_EAS2TAS() > 8.0f) { inAirSum++; } // this will trigger during change in baro height if (fabsf(_baro.get_climb_rate()) > 0.5f) { inAirSum++; } // trigger at 3 m/s GPS velocity if (gndSpdSq > 9.0f) { inAirSum++; } // trigger at 6 m/s GPS velocity if (gndSpdSq > 36.0f) { highGndSpdStage2 = true; inAirSum++; } // trigger at 9 m/s GPS velocity if (gndSpdSq > 81.0f) { inAirSum++; } // trigger if more than 15m away from initial height if (fabsf(hgtMea) > 15.0f) { inAirSum++; } // this will trigger due to air turbulence during flight if (accNavMag > 0.5f) { inAirSum++; } // if we on-ground then 4 or more out of 7 criteria are required to transition to the // in-air mode and we also need enough GPS velocity to be able to calculate a reliable ground track heading if (onGround && (inAirSum >= 4) && highGndSpdStage2) { onGround = false; } // if is possible we are in flight, set the time this condition was last detected if (inAirSum >= 1) { 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 // 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 static mode, or don't have the right vehicle and sensing to estimate wind, inhibit wind states inhibitWindStates = ((!useAirspeed() && !assume_zero_sideslip()) || onGround || staticMode); // request mag calibration for both in-air and manoeuvre threshold options bool magCalRequested = ((_magCal == 0) && !onGround) || ((_magCal == 1) && manoeuvring); // deny mag calibration request if we aren't using the compass, are in the pre-arm static mode or it has been inhibited by the user bool magCalDenied = (!use_compass() || staticMode || (_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(5.0f); // delta angle biases P[10][10] = sq(radians(INIT_GYRO_BIAS_UNCERTAINTY * dtIMU)); P[11][11] = P[10][10]; P[12][12] = P[10][10]; // Z delta velocity bias P[13][13] = 0.0f; // 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 focal length scale factor Popt[0][0] = 0.0f; // ground height Popt[0][0] = 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 * dtIMU)); // delta angle biases P[13][13] = constrain_float(P[13][13],0.0f,sq(10.0f * dtIMU)); // 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 states[9] = constrain_float(states[9],-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*dtIMU,0.1f*dtIMU); // 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*dtIMU,1.0f*dtIMU); states[22] = constrain_float(states[22],-1.0f*dtIMU,1.0f*dtIMU); // 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); } // update IMU delta angle and delta velocity measurements void NavEKF::readIMUData() { Vector3f angRate; // angular rate vector in XYZ body axes measured by the IMU (rad/s) Vector3f accel1; // acceleration vector in XYZ body axes measured by IMU1 (m/s^2) Vector3f accel2; // acceleration vector in XYZ body axes measured by IMU2 (m/s^2) // the imu sample time is sued as a common time reference throughout the filter imuSampleTime_ms = hal.scheduler->millis(); // limit IMU delta time to prevent numerical problems elsewhere dtIMU = constrain_float(_ahrs->get_ins().get_delta_time(), 0.001f, 1.0f); // get accel and gyro data from dual sensors if healthy if (_ahrs->get_ins().get_accel_health(0) && _ahrs->get_ins().get_accel_health(1)) { accel1 = _ahrs->get_ins().get_accel(0); accel2 = _ahrs->get_ins().get_accel(1); } else { accel1 = _ahrs->get_ins().get_accel(); accel2 = accel1; } // average the available gyro sensors angRate.zero(); uint8_t gyro_count = 0; for (uint8_t i = 0; i<_ahrs->get_ins().get_gyro_count(); i++) { if (_ahrs->get_ins().get_gyro_health(i)) { angRate += _ahrs->get_ins().get_gyro(i); gyro_count++; } } if (gyro_count != 0) { angRate /= gyro_count; } // trapezoidal integration dAngIMU = (angRate + lastAngRate) * dtIMU * 0.5f; lastAngRate = angRate; dVelIMU1 = (accel1 + lastAccel1) * dtIMU * 0.5f; lastAccel1 = accel1; dVelIMU2 = (accel2 + lastAccel2) * dtIMU * 0.5f; lastAccel2 = accel2; } // check for new valid GPS data and update stored measurement if available void NavEKF::readGpsData() { // 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(); // check if we have enough GPS satellites and increase the gps noise scaler if we don't if (_ahrs->get_gps().num_sats() >= 6) { gpsNoiseScaler = 1.0f; } else if (_ahrs->get_gps().num_sats() == 5) { gpsNoiseScaler = 1.4f; } else { // <= 4 satellites gpsNoiseScaler = 2.0f; } // Check if GPS can output vertical velocity and set GPS fusion mode accordingly if (!_ahrs->get_gps().have_vertical_velocity()) { // vertical velocity should not be fused if (_fusionModeGPS == 0) { _fusionModeGPS = 1; } } // read latitutde and longitude from GPS and convert to NE position const struct Location &gpsloc = _ahrs->get_gps().location(); gpsPosNE = location_diff(_ahrs->get_home(), gpsloc); // decay and limit the position offset which is applied to NE position wherever it is used throughout code to allow GPS position jumps to be accommodated gradually decayGpsOffset(); } } // 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) { // time stamp used to check for new measurement lastHgtMeasTime = _baro.get_last_update(); // time stamp used to check for timeout lastHgtTime_ms = imuSampleTime_ms; // get measurement and set flag to let other functions know new data has arrived hgtMea = _baro.get_altitude(); newDataHgt = true; // get states that wer stored at the time closest to the measurement time, taking measurement delay into account RecallStates(statesAtHgtTime, (imuSampleTime_ms - _msecHgtDelay)); } 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 != lastMagUpdate) { // store time of last measurement update lastMagUpdate = _ahrs->get_compass()->last_update; // 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; } 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, uint8_t &rangeHealth, float &rawSonarRange) { // 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 velocity over ground in the X direction // A positive Y rate is produced by a positive velocity over ground in the Y direction // 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 flowQuality = rawFlowQuality; // recall vehicle states at mid sample time for flow observations allowing for delays RecallStates(statesAtFlowTime, imuSampleTime_ms - _msecFLowDelay - flowTimeDeltaAvg_ms/2); // recall angular rates averaged across flow observation period allowing for processing, transmission and intersample delays RecallOmega(omegaAcrossFlowTime, imuSampleTime_ms - flowTimeDeltaAvg_ms - _msecFLowDelay, flowMeaTime_ms - _msecFLowDelay); // calculate bias errors on flow sensor gyro rates flowGyroBias.x = 0.99f * flowGyroBias.x + 0.01f * (rawGyroRates.x - omegaAcrossFlowTime.x); flowGyroBias.y = 0.99f * flowGyroBias.y + 0.01f * (rawGyroRates.y - omegaAcrossFlowTime.y); // correct flow sensor rates for bias omegaAcrossFlowTime.x = rawGyroRates.x - flowGyroBias.x; omegaAcrossFlowTime.y = rawGyroRates.y - flowGyroBias.y; // calculate rotation matrices at mid sample time for flow observations Quaternion q(statesAtFlowTime.quat[0],statesAtFlowTime.quat[1],statesAtFlowTime.quat[2],statesAtFlowTime.quat[3]); q.rotation_matrix(Tbn_flow); Tnb_flow = Tbn_flow.transposed(); // 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 focal length scale factor errors and body rates flowRadXYcomp[0] = flowStates[0]*flowRadXY[0] + omegaAcrossFlowTime.x; flowRadXYcomp[1] = flowStates[0]*flowRadXY[1] + omegaAcrossFlowTime.y; if (rawFlowQuality > 100){ // set flag that will trigger observations newDataFlow = true; velHoldMode = false; flowMeaTime_ms = imuSampleTime_ms; } else { newDataFlow = false; } // Use range finder if 3 or more consecutive good samples. This reduces likelihood of using bad data. if (rangeHealth >= 3) { statesAtRngTime = statesAtFlowTime; rngMea = rawSonarRange; newDataRng = true; rngMeaTime_ms = imuSampleTime_ms; } else { newDataRng = 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) { 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); initMagNED = Tbn * magData; // write to earth magnetic field state vector state.earth_magfield = initMagNED; // 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 static 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 static 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) { calcQuatAndFieldStates(_ahrs->roll, _ahrs->pitch); } } } // 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; } // zero stored variables - this needs to be called before a full filter initialisation void NavEKF::ZeroVariables() { // initialise time stamps imuSampleTime_ms = hal.scheduler->millis(); lastHealthyMagTime_ms = imuSampleTime_ms; TASmsecPrev = imuSampleTime_ms; BETAmsecPrev = imuSampleTime_ms; lastMagUpdate = imuSampleTime_ms; lastHgtMeasTime = imuSampleTime_ms; lastHgtTime_ms = imuSampleTime_ms; lastAirspeedUpdate = imuSampleTime_ms; velFailTime = imuSampleTime_ms; posFailTime = imuSampleTime_ms; hgtFailTime = imuSampleTime_ms; lastStateStoreTime_ms = imuSampleTime_ms; lastFixTime_ms = imuSampleTime_ms; secondLastFixTime_ms = imuSampleTime_ms; lastDecayTime_ms = imuSampleTime_ms; timeAtLastAuxEKF_ms = imuSampleTime_ms; flowMeaTime_ms = imuSampleTime_ms; prevFlowFusionTime_ms = imuSampleTime_ms; rngMeaTime_ms = imuSampleTime_ms; gpsNoiseScaler = 1.0f; velTimeout = false; posTimeout = false; hgtTimeout = false; magTimeout = false; badMag = false; firstArmComplete = false; finalMagYawInit = false; storeIndex = 0; dtIMU = 0; dt = 0; hgtMea = 0; firstArmPosD = 0.0f; storeIndex = 0; lastGyroBias.zero(); prevDelAng.zero(); lastAngRate.zero(); lastAccel1.zero(); lastAccel2.zero(); velDotNEDfilt.zero(); summedDelAng.zero(); summedDelVel.zero(); velNED.zero(); gpsPosGlitchOffsetNE.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)); gpsPosGlitchOffsetNE.zero(); // optical flow variables newDataFlow = false; newDataRng = false; flowFusePerformed = false; fuseOptFlowData = false; memset(&Popt[0][0], 0, sizeof(Popt)); flowStates[0] = 1.0f; flowStates[1] = 0.0f; prevPosN = gpsPosNE.x; prevPosE = gpsPosNE.y; fuseRngData = false; inhibitGndState = true; flowGyroBias.x = 0; flowGyroBias.y = 0; velHoldMode = false; heldVelNE.zero(); } // return true if we should use the airspeed sensor bool NavEKF::useAirspeed(void) const { if (_ahrs->get_airspeed() == NULL) { return false; } return _ahrs->get_airspeed()->use(); } // 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 we should use the optical flow sensor bool NavEKF::useOptFlow(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 the vehicle code has requested use of static mode // in static mode, position and height are constrained to zero, allowing an attitude // reference to be initialised and maintained when on the ground and without GPS lock bool NavEKF::static_mode_demanded(void) const { return !_ahrs->get_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 // limit radius to a maximum of 100m // apply glitch offset to GPS measurements void NavEKF::decayGpsOffset() { 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 velocity of 1.0 multiplied by lapsed time (plus a margin to prevent divide by zero) if (offsetRadius > (lapsedTime + 0.1f)) { // calculate scale factor to be applied to both offset components float scaleFactor = constrain_float((offsetRadius - lapsedTime), 0.0f, 100.0f) / offsetRadius; gpsPosGlitchOffsetNE.x *= scaleFactor; gpsPosGlitchOffsetNE.y *= scaleFactor; } } /* 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; } /* 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 5 = unassigned 6 = unassigned 7 = unassigned 7 = unassigned */ void NavEKF::getFilterTimeouts(uint8_t &timeouts) const { timeouts = (posTimeout<<0 | velTimeout<<1 | hgtTimeout<<2 | magTimeout<<3); } #endif // HAL_CPU_CLASS