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ardupilot/libraries/AP_NavEKF/AP_NavEKF.cpp

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/// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: nil -*-
#include <AP_HAL.h>
#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 <AP_AHRS.h>
#include <AP_Param.h>
#include <AP_Vehicle.h>
#include <stdio.h>
/*
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
#define FLOW_NOISE_DEFAULT 0.15f
#define FLOW_GATE_DEFAULT 5
#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
#define FLOW_NOISE_DEFAULT 0.15f
#define FLOW_GATE_DEFAULT 5
#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 0.5f
#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 30
#define HGT_GATE_DEFAULT 20
#define MAG_GATE_DEFAULT 3
#define MAG_CAL_DEFAULT 0
#define GLITCH_ACCEL_DEFAULT 150
#define GLITCH_RADIUS_DEFAULT 20
#define FLOW_MEAS_DELAY 25
#define FLOW_NOISE_DEFAULT 0.3f
#define FLOW_GATE_DEFAULT 3
#endif // APM_BUILD_DIRECTORY
extern const AP_HAL::HAL& hal;
#define earthRate 0.000072921f // earth rotation rate (rad/sec)
// when the wind estimation first starts with no airspeed sensor,
// assume 3m/s to start
#define STARTUP_WIND_SPEED 3.0f
// initial 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, FLOW_NOISE_DEFAULT),
// @Param: FLOW_GATE
// @DisplayName: Optical Flow measurement gate size
// @Description: This parameter sets the number of standard deviations applied to the optical flow innovation consistency check. Decreasing it makes it more likely that good measurements will be rejected. Increasing it makes it more likely that bad measurements will be accepted.
// @Range: 1 - 100
// @Increment: 1
// @User: advanced
AP_GROUPINFO("FLOW_GATE", 27, NavEKF, _flowInnovGate, FLOW_GATE_DEFAULT),
// @Param: FLOW_DELAY
// @DisplayName: Optical Flow measurement delay (msec)
// @Description: This is the number of msec that the optical flow measurements lag behind the inertial measurements. It is the time from the end of the optical flow averaging period and does not include the time delay due to the 100msec of averaging within the flow sensor.
// @Range: 0 - 500
// @Increment: 10
// @User: advanced
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<struct state_elements *>(&states)),
gpsNEVelVarAccScale(0.05f), // Scale factor applied to horizontal 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(10000), // GPS retry time with airspeed measurements (msec)
gpsRetryTimeNoTAS(10000), // GPS retry time without airspeed measurements (msec)
gpsFailTimeWithFlow(5000), // If we have no GPS for longer than this and we have optical flow, then we will switch across to using optical flow (msec)
hgtRetryTimeMode0(10000), // Height retry time with vertical velocity measurement (msec)
hgtRetryTimeMode12(5000), // Height retry time without vertical velocity measurement (msec)
tasRetryTime(5000), // True airspeed timeout and retry interval (msec)
magFailTimeLimit_ms(10000), // number of msec before a magnetometer failing innovation consistency checks is declared failed (msec)
magVarRateScale(0.05f), // scale factor applied to magnetometer variance due to angular rate
gyroBiasNoiseScaler(2.0f), // scale factor applied to 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(0.2f), // number of seconds between position and velocity corrections. This should be a multiple of the imu update interval.
covTimeStepMax(0.07f), // maximum time (sec) between covariance prediction updates
covDelAngMax(0.05f), // maximum delta angle between covariance prediction updates
TASmsecMax(200), // maximum allowed interval between airspeed measurement updates
DCM33FlowMin(0.71f), // If Tbn(3,3) is less than this number, optical flow measurements will not be fused as tilt is too high.
fScaleFactorPnoise(1e-10f), // Process noise added to focal length scale factor state variance at each time step
flowTimeDeltaAvg_ms(100), // average interval between optical flow measurements (msec)
flowIntervalMax_ms(100) // maximum allowable time between flow fusion events
#if CONFIG_HAL_BOARD == HAL_BOARD_PX4 || CONFIG_HAL_BOARD == HAL_BOARD_VRBRAIN
,_perf_UpdateFilter(perf_alloc(PC_ELAPSED, "EKF_UpdateFilter")),
_perf_CovariancePrediction(perf_alloc(PC_ELAPSED, "EKF_CovariancePrediction")),
_perf_FuseVelPosNED(perf_alloc(PC_ELAPSED, "EKF_FuseVelPosNED")),
_perf_FuseMagnetometer(perf_alloc(PC_ELAPSED, "EKF_FuseMagnetometer")),
_perf_FuseAirspeed(perf_alloc(PC_ELAPSED, "EKF_FuseAirspeed")),
_perf_FuseSideslip(perf_alloc(PC_ELAPSED, "EKF_FuseSideslip"))
#endif
{
AP_Param::setup_object_defaults(this, var_info);
}
// Check basic filter health metrics and return a consolidated health status
bool NavEKF::healthy(void) const
{
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;
}
// Give the filter 10 seconds to settle before use
if ((imuSampleTime_ms - ekfStartTime_ms) < 10000) {
return false;
}
// all OK
return true;
}
// resets position states to last GPS measurement or to zero if in constant position mode
void NavEKF::ResetPosition(void)
{
if (constPosMode || (PV_AidingMode != AID_ABSOLUTE)) {
state.position.x = 0;
state.position.y = 0;
} else if (!gpsNotAvailable) {
// write to state vector and compensate for GPS latency
state.position.x = gpsPosNE.x + gpsPosGlitchOffsetNE.x + 0.001f*velNED.x*float(_msecPosDelay);
state.position.y = gpsPosNE.y + gpsPosGlitchOffsetNE.y + 0.001f*velNED.y*float(_msecPosDelay);
// the estimated states at the last GPS measurement are set equal to the GPS measurement to prevent transients on the first fusion
statesAtPosTime.position.x = gpsPosNE.x;
statesAtPosTime.position.y = gpsPosNE.y;
}
// stored horizontal position states to prevent subsequent GPS measurements from being rejected
for (uint8_t i=0; i<=49; i++){
storedStates[i].position.x = state.position.x;
storedStates[i].position.y = state.position.y;
}
}
// Reset velocity states to last GPS measurement if available or to zero if in constant position mode or if PV aiding is not absolute
// Do not reset vertical velocity using GPS as there is baro alt available to constrain drift
void NavEKF::ResetVelocity(void)
{
if (constPosMode || PV_AidingMode != AID_ABSOLUTE) {
state.velocity.zero();
state.vel1.zero();
state.vel2.zero();
} else if (!gpsNotAvailable) {
// reset horizontal velocity states, applying an offset to the GPS velocity to prevent the GPS position being rejected when the GPS position offset is being decayed to zero.
state.velocity.x = velNED.x + gpsVelGlitchOffset.x; // north velocity from blended accel data
state.velocity.y = velNED.y + gpsVelGlitchOffset.y; // east velocity from blended accel data
state.vel1.x = velNED.x + gpsVelGlitchOffset.x; // north velocity from IMU1 accel data
state.vel1.y = velNED.y + gpsVelGlitchOffset.y; // east velocity from IMU1 accel data
state.vel2.x = velNED.x + gpsVelGlitchOffset.x; // north velocity from IMU2 accel data
state.vel2.y = velNED.y + gpsVelGlitchOffset.y; // east velocity from IMU2 accel data
// over write stored horizontal velocity states to prevent subsequent GPS measurements from being rejected
for (uint8_t i=0; i<=49; i++){
storedStates[i].velocity.x = velNED.x + gpsVelGlitchOffset.x;
storedStates[i].velocity.y = velNED.y + gpsVelGlitchOffset.y;
}
}
}
// reset the vertical position state using the last height measurement
void NavEKF::ResetHeight(void)
{
// read the altimeter
readHgtData();
// write to the state vector
state.position.z = -hgtMea; // down position from blended accel data
state.posD1 = -hgtMea; // down position from IMU1 accel data
state.posD2 = -hgtMea; // down position from IMU2 accel data
// reset stored vertical position states to prevent subsequent GPS measurements from being rejected
for (uint8_t i=0; i<=49; i++){
storedStates[i].position.z = -hgtMea;
}
terrainState = 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
bool NavEKF::InitialiseFilterDynamic(void)
{
// this forces healthy() to be false so that when we ask for ahrs
// attitude we get the DCM attitude regardless of the state of AHRS_EKF_USE
statesInitialised = false;
// If we are a plane and don't have GPS lock then don't initialise
if (assume_zero_sideslip() && _ahrs->get_gps().status() < AP_GPS::GPS_OK_FIX_3D) {
return false;
}
// Set re-used variables to zero
InitialiseVariables();
// 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();
// read the GPS and set the position and velocity states
readGpsData();
ResetVelocity();
ResetPosition();
// read the barometer and set the height state
readHgtData();
ResetHeight();
// set stored states to current state
StoreStatesReset();
// set to true now that states have be initialised
statesInitialised = true;
// 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();
return true;
}
// Initialise the states from accelerometer and magnetometer data (if present)
// This method can only be used when the vehicle is static
bool NavEKF::InitialiseFilterBootstrap(void)
{
// If we are a plane and don't have GPS lock then don't initialise
if (assume_zero_sideslip() && _ahrs->get_gps().status() < AP_GPS::GPS_OK_FIX_3D) {
statesInitialised = false;
return false;
}
// set re-used variables to zero
InitialiseVariables();
// get initial time deltat between IMU measurements (sec)
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);
// check on ground status
SetFlightAndFusionModes();
// write to state vector
state.quat = initQuat;
state.gyro_bias.zero();
state.accel_zbias1 = 0;
state.accel_zbias2 = 0;
state.wind_vel.zero();
state.body_magfield.zero();
// read the GPS and set the position and velocity states
readGpsData();
ResetVelocity();
ResetPosition();
// read the barometer and set the height state
readHgtData();
ResetHeight();
// set stored states to current state
StoreStatesReset();
// set to true now we have intialised the states
statesInitialised = true;
// 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();
return true;
}
// 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();
// Check arm status and perform required checks and mode changes
performArmingChecks();
// run the strapdown INS equations every IMU update
UpdateStrapdownEquationsNED();
// store the predicted states for subsequent use by measurement fusion
StoreStates();
// sum delta angles and time used by covariance prediction
summedDelAng = summedDelAng + correctedDelAng;
summedDelVel = summedDelVel + 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 and read new GPS data
readGpsData();
// Specify which measurements should be used and check data for freshness
if (PV_AidingMode == AID_ABSOLUTE) {
// check if we can use opticalflow as a backup
bool optFlowBackup = (flowDataValid && !hgtTimeout);
// Set GPS time-out threshold depending on whether we have an airspeed sensor to constrain drift
uint16_t gpsRetryTimeout = useAirspeed() ? gpsRetryTimeUseTAS : gpsRetryTimeNoTAS;
// Set the time that copters will fly without a GPS lock before failing the GPS and switching to a non GPS mode
uint16_t gpsFailTimeout = optFlowBackup ? gpsFailTimeWithFlow : gpsRetryTimeout;
// If we haven't received GPS data for a while, then declare the position and velocity data as being timed out
if (imuSampleTime_ms - lastFixTime_ms > gpsFailTimeout) {
posTimeout = true;
velTimeout = true;
// If this happens in flight and we don't have airspeed or sideslip assumption or optical flow to constrain drift, then go into constant position mode.
// Stay in that mode until the vehicle is re-armed.
// If we can do optical flow nav (valid flow data and hieght above ground estimate, then go into flow nav mode.
// Stay in that mode until the vehicle is dis-armed.
if (vehicleArmed && !useAirspeed() && !assume_zero_sideslip()) {
if (optFlowBackup) {
// we can do optical flow only nav
_fusionModeGPS = 3;
PV_AidingMode = AID_RELATIVE;
constVelMode = false;
constPosMode = false;
} else {
constVelMode = false; // always clear constant velocity mode if constant velocity mode is active
constPosMode = true;
PV_AidingMode = AID_NONE;
posTimeout = true;
velTimeout = true;
// reset the velocity
ResetVelocity();
// store the current position to be used to keep reporting the last known position
lastKnownPositionNE.x = state.position.x;
lastKnownPositionNE.y = state.position.y;
// reset the position
ResetPosition();
}
// set the position and velocity timeouts to indicate we are not using GPS data
posTimeout = true;
velTimeout = true;
}
}
// command fusion of GPS data and reset states as required
if (newDataGps && (PV_AidingMode == AID_ABSOLUTE)) {
// reset data arrived flag
newDataGps = false;
// reset state updates and counter used to spread fusion updates across several frames to reduce 10Hz pulsing
memset(&gpsIncrStateDelta[0], 0, sizeof(gpsIncrStateDelta));
gpsUpdateCount = 0;
// use both if GPS use is enabled
fuseVelData = true;
fusePosData = true;
// If a long time since last GPS update, then reset position and velocity and reset stored state history
if (imuSampleTime_ms - secondLastFixTime_ms > gpsRetryTimeout) {
// Apply an offset to the GPS position so that the position can be corrected gradually
gpsPosGlitchOffsetNE.x = statesAtPosTime.position.x - gpsPosNE.x;
gpsPosGlitchOffsetNE.y = statesAtPosTime.position.y - gpsPosNE.y;
// limit the radius of the offset to 100m and decay the offset to zero radially
decayGpsOffset();
ResetPosition();
ResetVelocity();
}
} else {
fuseVelData = false;
fusePosData = false;
}
} else if (constPosMode && covPredStep) {
// in constant position mode use synthetic position measurements set to zero
// only fuse synthetic measurements when rate of change of velocity is less than 0.5g to reduce attitude errors due to launch acceleration
// do not use velocity fusion to reduce the effect of movement on attitude
if (accNavMag < 4.9f) {
fusePosData = true;
} else {
fusePosData = false;
}
fuseVelData = false;
} else if (constVelMode && covPredStep) {
// In constant velocity mode we fuse the last valid velocity vector
// Reset the stored velocity vector when we enter the mode
if (constVelMode && !lastConstVelMode) {
heldVelNE.x = state.velocity.x;
heldVelNE.y = state.velocity.y;
}
lastConstVelMode = constVelMode;
// We do not fuse when manoeuvring to avoid corrupting the attitude
if (accNavMag < 4.9f) {
fuseVelData = true;
} else {
fuseVelData = false;
}
fusePosData = false;
} else {
fuseVelData = false;
fusePosData = false;
}
// check for and read new height data
readHgtData();
// If we haven't received height data for a while, then declare the height data as being timed out
// set timeout period based on whether we have vertical GPS velocity available to constrain drift
hgtRetryTime = (_fusionModeGPS == 0 && !velTimeout) ? hgtRetryTimeMode0 : hgtRetryTimeMode12;
if (imuSampleTime_ms - lastHgtMeasTime > hgtRetryTime) {
hgtTimeout = true;
}
// command fusion of height data
if (newDataHgt)
{
// reset data arrived flag
newDataHgt = false;
// reset state updates and counter used to spread fusion updates across several frames to reduce 10Hz pulsing
memset(&hgtIncrStateDelta[0], 0, sizeof(hgtIncrStateDelta));
hgtUpdateCount = 0;
// enable fusion
fuseHgtData = true;
} else {
fuseHgtData = false;
}
// perform fusion
if (fuseVelData || fusePosData || fuseHgtData) {
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()
{
// Perform Data Checks
// Check if the optical flow data is still valid
flowDataValid = ((imuSampleTime_ms - flowValidMeaTime_ms) < 1000);
// Check if the fusion has timed out (flow measurements have been rejected for too long)
bool flowFusionTimeout = ((imuSampleTime_ms - prevFlowUseTime_ms) > 5000);
// check is the terrain offset estimate is still valid
gndOffsetValid = ((imuSampleTime_ms - gndHgtValidTime_ms) < 5000);
// Perform tilt check
bool tiltOK = (Tnb_flow.c.z > DCM33FlowMin);
// if we have waited too long, set a timeout flag which will force fusion to occur regardless of load spreading
bool flowFuseNow = ((imuSampleTime_ms - flowValidMeaTime_ms) >= flowIntervalMax_ms/2);
// check if fusion should be delayed to spread load. Setting fuseMeNow to true disables this load spreading feature.
bool delayFusion = ((covPredStep || magFusePerformed) && !(flowFuseNow || inhibitLoadLeveling));
// if we don't have valid flow measurements and are relying on them, dead reckon using current velocity vector
// If the flow measurements have been rejected for too long and we are relying on them, then reset the velocities to an estimate based on the flow and range data
if (!flowDataValid && PV_AidingMode == AID_RELATIVE) {
constVelMode = true;
constPosMode = false; // always clear constant position mode if constant velocity mode is active
} else if (flowDataValid && flowFusionTimeout && PV_AidingMode == AID_RELATIVE) {
// we need to reset the velocities to a value estimated from the flow data
// estimate the range
float initPredRng = max((terrainState - state.position[2]),0.1f) / Tnb_flow.c.z;
// multiply the range by the LOS rates to get an estimated XY velocity in body frame
Vector3f initVel;
initVel.x = -flowRadXYcomp[1]*initPredRng;
initVel.y = flowRadXYcomp[0]*initPredRng;
// rotate into earth frame
initVel = Tbn_flow*initVel;
// set horizontal velocity states
state.velocity.x = initVel.x;
state.velocity.y = initVel.y;
// clear any hold modes
constVelMode = false;
lastConstVelMode = false;
} else if (flowDataValid) {
// clear the constant velocity mode now we have good data
constVelMode = false;
lastConstVelMode = false;
}
// if we do have valid flow measurements
// Fuse data into a 1-state EKF to estimate terrain height
if ((newDataFlow || newDataRng) && tiltOK) {
// fuse range data into the terrain estimator if available
fuseRngData = newDataRng;
// fuse optical flow data into the terrain estimator if available and if there is no range data (range data is better)
fuseOptFlowData = (newDataFlow && !fuseRngData);
// Estimate the terrain offset (runs a one state EKF)
EstimateTerrainOffset();
// Indicate we have used the range data
newDataRng = false;
// we don't do subsequent fusion of optical flow data into the main filter if GPS is good and terrain offset data is invalid
// because an invalid height above ground estimate will casue the optical flow measurements to fight the GPS
if (!gpsNotAvailable && !gndOffsetValid) {
// turn of fusion permissions
// reset the measurement axis index
flow_state.obsIndex = 0;
// reset the flags to indicate that no new range finder or flow data is available for fusion
newDataFlow = false;
}
}
// Fuse optical flow data into the main filter
// if the filter is initialised, we have data to fuse and the vehicle is not excessively tilted, then perform optical flow fusion
if (flowDataValid && newDataFlow && tiltOK && !delayFusion && !constPosMode)
{
// reset state updates and counter used to spread fusion updates across several frames to reduce 10Hz pulsing
memset(&flowIncrStateDelta[0], 0, sizeof(flowIncrStateDelta));
flowUpdateCount = 0;
// Set the flow noise used by the fusion processes
R_LOS = sq(max(_flowNoise, 0.05f));
// set the measurement axis index to fuse the X axis data
flow_state.obsIndex = 0;
// Fuse the optical flow X axis data into the main filter
FuseOptFlow();
// increment the measurement axis 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
prevFlowUseTime_ms = imuSampleTime_ms;
} else if (flowDataValid && flow_state.obsIndex == 1 && !delayFusion && !constPosMode && tiltOK) {
// Fuse the optical flow Y axis data into the main filter
FuseOptFlow();
// Reset the measurement axis index to prevent further fusion of this data
flow_state.obsIndex = 0;
// reset flag to indicate that no new flow data is available for fusion
newDataFlow = false;
// indicate that flow fusion has been performed. This is used for load spreading.
flowFusePerformed = true;
}
// Apply corrections to quaternion, position and velocity states across several time steps to reduce 10Hz pulsing in the output
if (flowUpdateCount < flowUpdateCountMax) {
flowUpdateCount ++;
for (uint8_t i = 0; i <= 9; i++) {
states[i] += flowIncrStateDelta[i];
}
}
}
// select fusion of true airspeed measurements
void NavEKF::SelectTasFusion()
{
// get true airspeed measurement
readAirSpdData();
// If we haven't received airspeed data for a while, then declare the airspeed data as being timed out
if (imuSampleTime_ms - lastAirspeedUpdate > tasRetryTime) {
tasTimeout = true;
}
// if the filter is initialised, wind states are not inhibited and we have data to fuse, then 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 disarmed to allow for faster bias estimation
for (uint8_t i=10; i<=12; i++) {
processNoise[i] = dAngBiasSigma;
if (!vehicleArmed) {
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 1e4 (100m), then stop covariance
// growth by setting the predicted to the previous values
// This prevent an ill conditioned matrix from occurring for long periods
// without GPS
if ((P[7][7] + P[8][8]) > 1e4f)
{
for (uint8_t i=7; i<=8; i++)
{
for (uint8_t j=0; j<=21; j++)
{
nextP[i][j] = P[i][j];
nextP[j][i] = P[j][i];
}
}
}
// copy covariances to output and fix numerical errors
CopyAndFixCovariances();
// constrain diagonals to prevent ill-conditioning
ConstrainVariances();
perf_end(_perf_CovariancePrediction);
}
// fuse selected position, velocity and height measurements
void NavEKF::FuseVelPosNED()
{
// start performance timer
perf_begin(_perf_FuseVelPosNED);
// health is set bad until test passed
velHealth = false;
posHealth = false;
hgtHealth = false;
// declare variables used to check measurement errors
Vector3f velInnov;
Vector3f velInnov1;
Vector3f velInnov2;
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 constant position or constant velocity mode use the current states to calculate the predicted
// measurement rather than use states from a previous time. We need to do this
// because there may be no stored states due to lack of real measurements.
if (constPosMode) {
statesAtPosTime = state;
} else if (constVelMode) {
statesAtVelTime = state;
}
// set the GPS data timeout depending on whether airspeed data is present
uint32_t gpsRetryTime;
if (useAirspeed()) gpsRetryTime = gpsRetryTimeUseTAS;
else gpsRetryTime = gpsRetryTimeNoTAS;
// form the observation vector and zero velocity and horizontal position observations if in constant position mode
// If in constant velocity mode, hold the last known horizontal velocity vector
if (!constPosMode && !constVelMode) {
observation[0] = velNED.x + gpsVelGlitchOffset.x;
observation[1] = velNED.y + gpsVelGlitchOffset.y;
observation[2] = velNED.z;
observation[3] = gpsPosNE.x + gpsPosGlitchOffsetNE.x;
observation[4] = gpsPosNE.y + gpsPosGlitchOffsetNE.y;
} else if (constPosMode){
for (uint8_t i=0; i<=4; i++) observation[i] = 0.0f;
} else if (constVelMode) {
observation[0] = heldVelNE.x;
observation[1] = heldVelNE.y;
for (uint8_t i=2; i<=4; i++) observation[i] = 0.0f;
}
observation[5] = -hgtMea;
// calculate additional error in GPS 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.
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 or not aiding
posTimeout = (((imuSampleTime_ms - posFailTime) > gpsRetryTime) || PV_AidingMode == AID_NONE);
// use position data if healthy, timed out, or in constant position mode
if (posHealth || posTimeout || constPosMode) {
posHealth = true;
// only reset the failed time and do glitch timeout checks if we are doing full aiding
if (PV_AidingMode == AID_ABSOLUTE) {
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 || constVelMode) {
imax = 1;
}
float K1 = 0; // innovation to error ratio for IMU1
float K2 = 0; // innovation to error ratio for IMU2
float innovVelSumSq = 0; // sum of squares of velocity innovations
float varVelSum = 0; // sum of velocity innovation variances
for (uint8_t i = 0; i<=imax; i++) {
// velocity states start at index 4
stateIndex = i + 4;
// calculate innovations using blended and single IMU predicted states
velInnov[i] = statesAtVelTime.velocity[i] - observation[i]; // blended
velInnov1[i] = statesAtVelTime.vel1[i] - observation[i]; // IMU1
velInnov2[i] = statesAtVelTime.vel2[i] - observation[i]; // IMU2
// calculate innovation variance
varInnovVelPos[i] = P[stateIndex][stateIndex] + R_OBS[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 or not aiding
velTimeout = (((imuSampleTime_ms - velFailTime) > gpsRetryTime) || PV_AidingMode == AID_NONE);
// if data is healthy or in constant velocity mode we fuse it
if (velHealth || velTimeout || constVelMode) {
velHealth = true;
// restart the timeout count
velFailTime = imuSampleTime_ms;
} else if (velTimeout && !posHealth && PV_AidingMode == AID_ABSOLUTE) {
// if data is not healthy and timed out and position is unhealthy and we are using aiding, we reset the velocity, but do not fuse data on this time step
ResetVelocity();
fuseVelData = false;
} else {
// if data is unhealthy and position is healthy, we do not fuse it
velHealth = false;
}
}
// test height measurements
if (fuseHgtData) {
// calculate height innovations
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 constant position mode
if (hgtHealth || hgtTimeout || constPosMode) {
hgtHealth = true;
hgtFailTime = imuSampleTime_ms;
// if timed out, reset the height, but do not fuse data on this time step
if (hgtTimeout) {
ResetHeight();
fuseHgtData = false;
}
}
else {
hgtHealth = false;
}
}
// set range for sequential fusion of velocity and position measurements depending on which data is available and its health
if (fuseVelData && _fusionModeGPS == 0 && velHealth && !constPosMode && PV_AidingMode == AID_ABSOLUTE) {
fuseData[0] = true;
fuseData[1] = true;
fuseData[2] = true;
}
if (fuseVelData && _fusionModeGPS == 1 && velHealth && !constPosMode && PV_AidingMode == AID_ABSOLUTE) {
fuseData[0] = true;
fuseData[1] = true;
}
if ((fusePosData && posHealth && PV_AidingMode == AID_ABSOLUTE) || constPosMode) {
fuseData[3] = true;
fuseData[4] = true;
}
if ((fuseHgtData && hgtHealth) || constPosMode) {
fuseData[5] = true;
}
if (constVelMode) {
fuseData[0] = true;
fuseData[1] = true;
}
// fuse measurements sequentially
for (obsIndex=0; obsIndex<=5; obsIndex++) {
if (fuseData[obsIndex]) {
stateIndex = 4 + obsIndex;
// calculate the measurement innovation, using states from a different time coordinate if fusing height data
// adjust scaling on GPS measurement noise variances if not enough satellites
if (obsIndex <= 2)
{
innovVelPos[obsIndex] = statesAtVelTime.velocity[obsIndex] - observation[obsIndex];
R_OBS[obsIndex] *= sq(gpsNoiseScaler);
}
else if (obsIndex == 3 || obsIndex == 4) {
innovVelPos[obsIndex] = statesAtPosTime.position[obsIndex-3] - observation[obsIndex];
R_OBS[obsIndex] *= sq(gpsNoiseScaler);
} else {
innovVelPos[obsIndex] = statesAtHgtTime.position[obsIndex-3] - observation[obsIndex];
}
// 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 0.002 m/s3
float correctionLimit = 0.002f * 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 || constPosMode || constVelMode) {
states[i] = states[i] - Kfusion[i] * innovVelPos[obsIndex];
} else {
if (obsIndex == 5) {
hgtIncrStateDelta[i] -= Kfusion[i] * innovVelPos[obsIndex] * hgtUpdateCountMaxInv;
} else {
gpsIncrStateDelta[i] -= Kfusion[i] * innovVelPos[obsIndex] * gpsUpdateCountMaxInv;
}
}
}
state.quat.normalize();
// update the covariance - take advantage of direct observation of a single state at index = stateIndex to reduce computations
// this is a numerically optimised implementation of standard equation P = (I - K*H)*P;
for (uint8_t i= 0; i<=21; i++) {
for (uint8_t j= 0; j<=21; j++)
{
KHP[i][j] = Kfusion[i] * P[stateIndex][j];
}
}
for (uint8_t i= 0; i<=21; i++) {
for (uint8_t j= 0; j<=21; j++) {
P[i][j] = P[i][j] - KHP[i][j];
}
}
}
}
}
// force the covariance matrix to be symmetrical and limit the variances to prevent ill-condiioning.
ForceSymmetry();
ConstrainVariances();
// stop performance timer
perf_end(_perf_FuseVelPosNED);
}
// fuse magnetometer measurements and apply innovation consistency checks
// fuse each axis on consecutive time steps to spread computional load
void NavEKF::FuseMagnetometer()
{
// 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 || constPosMode || minorFramesToGo < 1.5f ) {
states[j] = states[j] - Kfusion[j] * innovMag[obsIndex];
} else {
// scale the correction based on the number of averaging frames left to go
magIncrStateDelta[j] -= Kfusion[j] * innovMag[obsIndex] * (magUpdateCountMaxInv * float(magUpdateCountMax) / minorFramesToGo);
}
}
// normalise the quaternion states
state.quat.normalize();
// correct the covariance P = (I - K*H)*P
// take advantage of the empty columns in KH to reduce the
// number of operations
for (uint8_t i = 0; i<=21; i++) {
for (uint8_t j = 0; j<=3; j++) {
KH[i][j] = Kfusion[i] * H_MAG[j];
}
for (uint8_t j = 4; j<=15; j++) {
KH[i][j] = 0.0f;
}
if (!inhibitMagStates) {
for (uint8_t j = 16; j<=21; j++) {
KH[i][j] = Kfusion[i] * H_MAG[j];
}
} else {
for (uint8_t j = 16; j<=21; j++) {
KH[i][j] = 0.0f;
}
}
}
for (uint8_t i = 0; i<=21; i++) {
for (uint8_t j = 0; j<=21; j++) {
KHP[i][j] = 0;
for (uint8_t k = 0; k<=3; k++) {
KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j];
}
if (!inhibitMagStates) {
for (uint8_t k = 16; k<=21; k++) {
KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j];
}
}
}
}
for (uint8_t i = 0; i<=21; i++) {
for (uint8_t j = 0; j<=21; j++) {
P[i][j] = P[i][j] - KHP[i][j];
}
}
}
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 terrain offset using a single state EKF
The filter can fuse motion compensated optiocal flow rates and range finder measurements
*/
void NavEKF::EstimateTerrainOffset()
{
// start performance timer
perf_begin(_perf_OpticalFlowEKF);
// calculate a predicted LOS rate squared
float velHorizSq = sq(state.velocity.x) + sq(state.velocity.y);
float losRateSq = velHorizSq / sq(terrainState - 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 (!fuseRngData && (gpsNotAvailable || PV_AidingMode == AID_RELATIVE || velHorizSq < 25.0f || losRateSq < 0.01f || onGround)) {
inhibitGndState = true;
} else {
inhibitGndState = false;
// record the time we last updated the terrain offset state
gndHgtValidTime_ms = imuSampleTime_ms;
// propagate ground position state noise each time this is called using the difference in position since the last observations and an RMS gradient assumption
// limit distance to prevent intialisation afer bad gps causing bad numerical conditioning
float distanceTravelledSq = sq(statesAtRngTime.position[0] - prevPosN) + sq(statesAtRngTime.position[1] - prevPosE);
distanceTravelledSq = min(distanceTravelledSq, 100.0f);
prevPosN = statesAtRngTime.position[0];
prevPosE = statesAtRngTime.position[1];
// in addition to a terrain gradient error model, we also have a time based error growth that is scaled using the gradient parameter
float timeLapsed = min(0.001f * (imuSampleTime_ms - timeAtLastAuxEKF_ms), 1.0f);
float Pincrement = (distanceTravelledSq * sq(0.01f*float(_gndGradientSigma))) + sq(float(_gndGradientSigma) * timeLapsed);
Popt += Pincrement;
timeAtLastAuxEKF_ms = imuSampleTime_ms;
// fuse range finder data
if (fuseRngData) {
// predict range
float predRngMeas = max((terrainState - statesAtRngTime.position[2]),0.1f) / Tnb_flow.c.z;
// Copy required states to local variable names
float q0 = statesAtRngTime.quat[0]; // quaternion at optical flow measurement time
float q1 = statesAtRngTime.quat[1]; // quaternion at optical flow measurement time
float q2 = statesAtRngTime.quat[2]; // quaternion at optical flow measurement time
float q3 = statesAtRngTime.quat[3]; // quaternion at optical flow measurement time
// Set range finder measurement noise variance. TODO make this a function of range and tilt to allow for sensor, alignment and AHRS errors
float R_RNG = 0.5;
// calculate Kalman gain
float SK_RNG = sq(q0) - sq(q1) - sq(q2) + sq(q3);
float K_RNG = Popt/(SK_RNG*(R_RNG + Popt/sq(SK_RNG)));
// Calculate the innovation variance for data logging
varInnovRng = (R_RNG + Popt/sq(SK_RNG));
// constrain terrain height to be below the vehicle
terrainState = max(terrainState, statesAtRngTime.position[2] + 0.1f);
// Calculate the measurement innovation
innovRng = predRngMeas - rngMea;
// calculate the innovation consistency test ratio
auxRngTestRatio = sq(innovRng) / (sq(_rngInnovGate) * varInnovRng);
// Check the innovation for consistency and don't fuse if > 5Sigma
if ((sq(innovRng)*SK_RNG) < 25.0f)
{
// correct the state
terrainState -= K_RNG * innovRng;
// constrain the state
terrainState = max(terrainState, statesAtRngTime.position[2] + 0.1f);
// correct the covariance
Popt = Popt - sq(Popt)/(SK_RNG*(R_RNG + Popt/sq(SK_RNG))*(sq(q0) - sq(q1) - sq(q2) + sq(q3)));
// prevent the state variance from becoming negative
Popt = max(Popt,0.0f);
}
}
if (fuseOptFlowData) {
Vector3f vel; // velocity of sensor relative to ground in NED axes
Vector3f relVelSensor; // velocity of sensor relative to ground in sensor axes
float losPred; // predicted optical flow angular rate measurement
float q0 = statesAtFlowTime.quat[0]; // quaternion at optical flow measurement time
float q1 = statesAtFlowTime.quat[1]; // quaternion at optical flow measurement time
float q2 = statesAtFlowTime.quat[2]; // quaternion at optical flow measurement time
float q3 = statesAtFlowTime.quat[3]; // quaternion at optical flow measurement time
float K_OPT;
float H_OPT;
// Correct velocities for GPS glitch recovery offset
vel.x = statesAtFlowTime.velocity[0] - gpsVelGlitchOffset.x;
vel.y = statesAtFlowTime.velocity[1] - gpsVelGlitchOffset.y;
vel.z = statesAtFlowTime.velocity[2];
// predict range to centre of image
float flowRngPred = max((terrainState - statesAtFlowTime.position[2]),0.1f) / Tnb_flow.c.z;
// constrain terrain height to be below the vehicle
terrainState = max(terrainState, statesAtFlowTime.position[2] + 0.1f);
// calculate relative velocity in sensor frame
relVelSensor = Tnb_flow*vel;
// divide velocity by range, subtract body rates and apply scale factor to
// get predicted sensed angular optical rates relative to X and Y sensor axes
losPred = relVelSensor.length()/flowRngPred;
// calculate innovations
auxFlowObsInnov = losPred - sqrtf(sq(flowRadXYcomp[0]) + sq(flowRadXYcomp[1]));
// calculate observation jacobian
float t3 = sq(q0);
float t4 = sq(q1);
float t5 = sq(q2);
float t6 = sq(q3);
float t10 = q0*q3*2.0f;
float t11 = q1*q2*2.0f;
float t14 = t3+t4-t5-t6;
float t15 = t14*vel.x;
float t16 = t10+t11;
float t17 = t16*vel.y;
float t18 = q0*q2*2.0f;
float t19 = q1*q3*2.0f;
float t20 = t18-t19;
float t21 = t20*vel.z;
float t2 = t15+t17-t21;
float t7 = t3-t4-t5+t6;
float t8 = statesAtFlowTime.position[2]-terrainState;
float t9 = 1.0f/sq(t8);
float t24 = t3-t4+t5-t6;
float t25 = t24*vel.y;
float t26 = t10-t11;
float t27 = t26*vel.x;
float t28 = q0*q1*2.0f;
float t29 = q2*q3*2.0f;
float t30 = t28+t29;
float t31 = t30*vel.z;
float t12 = t25-t27+t31;
float t13 = sq(t7);
float t22 = sq(t2);
float t23 = 1.0f/(t8*t8*t8);
float t32 = sq(t12);
H_OPT = 0.5f*(t13*t22*t23*2.0f+t13*t23*t32*2.0f)/sqrtf(t9*t13*t22+t9*t13*t32);
// calculate innovation variances
auxFlowObsInnovVar = H_OPT*Popt*H_OPT + R_LOS;
// calculate Kalman gain
K_OPT = Popt*H_OPT/auxFlowObsInnovVar;
// calculate the innovation consistency test ratio
auxFlowTestRatio = sq(auxFlowObsInnov) / (sq(_flowInnovGate) * auxFlowObsInnovVar);
// don't fuse if optical flow data is outside valid range
if (max(flowRadXY[0],flowRadXY[1]) < _maxFlowRate) {
// correct the state
terrainState -= K_OPT * auxFlowObsInnov;
// constrain the state
terrainState = max(terrainState, statesAtFlowTime.position[2] + 0.1f);
// correct the covariance
Popt = Popt - K_OPT * H_OPT * Popt;
// prevent the state variances from becoming negative
Popt = max(Popt,0.0f);
}
}
}
// stop the performance timer
perf_end(_perf_OpticalFlowEKF);
}
void NavEKF::FuseOptFlow()
{
// start performance timer
perf_begin(_perf_FuseOptFlow);
Vector22 H_LOS;
Vector9 tempVar;
Vector3f velNED_local;
Vector3f relVelSensor;
uint8_t &obsIndex = flow_state.obsIndex;
ftype &q0 = flow_state.q0;
ftype &q1 = flow_state.q1;
ftype &q2 = flow_state.q2;
ftype &q3 = flow_state.q3;
ftype *SH_LOS = &flow_state.SH_LOS[0];
ftype *SK_LOS = &flow_state.SK_LOS[0];
ftype &vn = flow_state.vn;
ftype &ve = flow_state.ve;
ftype &vd = flow_state.vd;
ftype &pd = flow_state.pd;
ftype *losPred = &flow_state.losPred[0];
// Copy required states to local variable names
q0 = statesAtFlowTime.quat[0];
q1 = statesAtFlowTime.quat[1];
q2 = statesAtFlowTime.quat[2];
q3 = statesAtFlowTime.quat[3];
vn = statesAtFlowTime.velocity[0];
ve = statesAtFlowTime.velocity[1];
vd = statesAtFlowTime.velocity[2];
pd = statesAtFlowTime.position[2];
// Correct velocities for GPS glitch recovery offset
velNED_local.x = vn - gpsVelGlitchOffset.x;
velNED_local.y = ve - gpsVelGlitchOffset.y;
velNED_local.z = vd;
// constrain terrain to be below vehicle
terrainState = max(terrainState, pd + 0.1f);
float heightAboveGndEst = terrainState - 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 - terrainState);
SH_LOS[4] = sq(SH_LOS[3]);
// Calculate common expressions for Kalman gains
// calculate innovation variance for Y axis observation
varInnovOptFlow[1] = (R_LOS + (SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) + 2*q0*SH_LOS[1]*SH_LOS[3])*(P[0][0]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) + 2*q0*SH_LOS[1]*SH_LOS[3]) + P[1][0]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q1*SH_LOS[1]*SH_LOS[3]) - P[2][0]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) + 2*q2*SH_LOS[1]*SH_LOS[3]) + P[3][0]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q3*SH_LOS[1]*SH_LOS[3]) + P[5][0]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 + 2*q1*q2) - P[6][0]*SH_LOS[0]*SH_LOS[3]*(2*q0*q2 - 2*q1*q3) - P[9][0]*SH_LOS[0]*SH_LOS[1]*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(varInnovOptFlow[1]) > R_LOS) {
SK_LOS[0] = 1.0f/varInnovOptFlow[1];
} else {
SK_LOS[0] = 1.0f/R_LOS;
}
// calculate innovation variance for X axis observation
varInnovOptFlow[0] = (R_LOS + (SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q0*SH_LOS[2]*SH_LOS[3])*(P[0][0]*(SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn) + 2*q0*SH_LOS[2]*SH_LOS[3]) + P[1][0]*(SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn) - 2*q1*SH_LOS[2]*SH_LOS[3]) + P[2][0]*(SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn) - 2*q2*SH_LOS[2]*SH_LOS[3]) - P[3][0]*(SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn) - 2*q3*SH_LOS[2]*SH_LOS[3]) - P[4][0]*SH_LOS[0]*SH_LOS[3]*(2*q0*q3 - 2*q1*q2) + P[6][0]*SH_LOS[0]*SH_LOS[3]*(2*q0*q1 + 2*q2*q3) - P[9][0]*SH_LOS[0]*SH_LOS[2]*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(varInnovOptFlow[0]) > R_LOS) {
SK_LOS[1] = 1.0f/varInnovOptFlow[0];
} else {
SK_LOS[1] = 1.0f/R_LOS;
}
SK_LOS[2] = SH_LOS[0]*SH_LOS[3]*(2*q3*ve - 2*q2*vd + 2*q0*vn);
SK_LOS[3] = SH_LOS[0]*SH_LOS[3]*(2*q0*vd - 2*q1*ve + 2*q2*vn);
SK_LOS[4] = SH_LOS[0]*SH_LOS[3]*(2*q1*vd + 2*q0*ve - 2*q3*vn);
SK_LOS[5] = SH_LOS[0]*SH_LOS[3]*(2*q3*vd + 2*q2*ve + 2*q1*vn);
SK_LOS[6] = sq(q0) - sq(q1) + sq(q2) - sq(q3);
SK_LOS[7] = 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 < 22; 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 for X axis observation
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 < 22; 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 {
memset(&H_LOS[0], 0, sizeof(H_LOS));
memset(&Kfusion[0], 0, sizeof(Kfusion));
}
// calculate innovation for Y observation
innovOptFlow[1] = losPred[1] - flowRadXYcomp[1];
}
// calculate the innovation consistency test ratio
flowTestRatio[obsIndex] = sq(innovOptFlow[obsIndex]) / (sq(_flowInnovGate) * varInnovOptFlow[obsIndex]);
// Check the innovation for consistency and don't fuse if out of bounds or flow is too fast to be reliable
if ((flowTestRatio[obsIndex]) < 1.0f && (flowRadXY[obsIndex] < _maxFlowRate)) {
// record the last time both X and Y observations were accepted for fusion
if (obsIndex == 0) {
flowXfailed = false;
} else if (!flowXfailed) {
prevFlowFuseTime_ms = imuSampleTime_ms;
}
// Attitude, velocity and position corrections are averaged across multiple prediction cycles between now and the anticipated time for the next measurement.
// Don't do averaging of quaternion state corrections if total angle change across predicted interval is going to exceed 0.1 rad
bool highRates = ((flowUpdateCountMax * correctedDelAng.length()) > 0.1f);
// Calculate the number of averaging frames left to go. 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];
}
}
} else if (obsIndex == 0) {
// store the fact we have failed the X conponent so that a combined X and Y axis pass/fail can be calculated next time round
flowXfailed = true;
}
ForceSymmetry();
ConstrainVariances();
// 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;
// health is set bad until test passed
tasHealth = false;
// copy required states to local variable names
vn = statesAtVtasMeasTime.velocity.x;
ve = statesAtVtasMeasTime.velocity.y;
vd = statesAtVtasMeasTime.velocity.z;
vwn = statesAtVtasMeasTime.wind_vel.x;
vwe = statesAtVtasMeasTime.wind_vel.y;
// calculate the predicted airspeed, compensating for bias in GPS velocity when we are pulling a glitch offset back in
VtasPred = pythagorous3((ve - gpsVelGlitchOffset.y - vwe) , (vn - gpsVelGlitchOffset.x - vwn) , vd);
// perform fusion of True Airspeed measurement
if (VtasPred > 1.0f)
{
// calculate observation jacobians
SH_TAS[0] = 1.0f/VtasPred;
SH_TAS[1] = (SH_TAS[0]*(2*ve - 2*vwe))/2;
SH_TAS[2] = (SH_TAS[0]*(2*vn - 2*vwn))/2;
for (uint8_t i=0; i<=21; i++) H_TAS[i] = 0.0f;
H_TAS[4] = SH_TAS[2];
H_TAS[5] = SH_TAS[1];
H_TAS[6] = vd*SH_TAS[0];
H_TAS[14] = -SH_TAS[2];
H_TAS[15] = -SH_TAS[1];
// calculate Kalman gains
float temp = (R_TAS + SH_TAS[2]*(P[4][4]*SH_TAS[2] + P[5][4]*SH_TAS[1] - P[14][4]*SH_TAS[2] - P[15][4]*SH_TAS[1] + P[6][4]*vd*SH_TAS[0]) + SH_TAS[1]*(P[4][5]*SH_TAS[2] + P[5][5]*SH_TAS[1] - P[14][5]*SH_TAS[2] - P[15][5]*SH_TAS[1] + P[6][5]*vd*SH_TAS[0]) - SH_TAS[2]*(P[4][14]*SH_TAS[2] + P[5][14]*SH_TAS[1] - P[14][14]*SH_TAS[2] - P[15][14]*SH_TAS[1] + P[6][14]*vd*SH_TAS[0]) - SH_TAS[1]*(P[4][15]*SH_TAS[2] + P[5][15]*SH_TAS[1] - P[14][15]*SH_TAS[2] - P[15][15]*SH_TAS[1] + P[6][15]*vd*SH_TAS[0]) + vd*SH_TAS[0]*(P[4][6]*SH_TAS[2] + P[5][6]*SH_TAS[1] - P[14][6]*SH_TAS[2] - P[15][6]*SH_TAS[1] + P[6][6]*vd*SH_TAS[0]));
if (temp >= R_TAS) {
SK_TAS = 1.0f / temp;
faultStatus.bad_airspeed = false;
} else {
// the calculation is badly conditioned, so we cannot perform fusion on this step
// we increase the wind state variances and try again next time
P[14][14] += 0.05f*R_TAS;
P[15][15] += 0.05f*R_TAS;
faultStatus.bad_airspeed = true;
return;
}
Kfusion[0] = SK_TAS*(P[0][4]*SH_TAS[2] - P[0][14]*SH_TAS[2] + P[0][5]*SH_TAS[1] - P[0][15]*SH_TAS[1] + P[0][6]*vd*SH_TAS[0]);
Kfusion[1] = SK_TAS*(P[1][4]*SH_TAS[2] - P[1][14]*SH_TAS[2] + P[1][5]*SH_TAS[1] - P[1][15]*SH_TAS[1] + P[1][6]*vd*SH_TAS[0]);
Kfusion[2] = SK_TAS*(P[2][4]*SH_TAS[2] - P[2][14]*SH_TAS[2] + P[2][5]*SH_TAS[1] - P[2][15]*SH_TAS[1] + P[2][6]*vd*SH_TAS[0]);
Kfusion[3] = SK_TAS*(P[3][4]*SH_TAS[2] - P[3][14]*SH_TAS[2] + P[3][5]*SH_TAS[1] - P[3][15]*SH_TAS[1] + P[3][6]*vd*SH_TAS[0]);
Kfusion[4] = SK_TAS*(P[4][4]*SH_TAS[2] - P[4][14]*SH_TAS[2] + P[4][5]*SH_TAS[1] - P[4][15]*SH_TAS[1] + P[4][6]*vd*SH_TAS[0]);
Kfusion[5] = SK_TAS*(P[5][4]*SH_TAS[2] - P[5][14]*SH_TAS[2] + P[5][5]*SH_TAS[1] - P[5][15]*SH_TAS[1] + P[5][6]*vd*SH_TAS[0]);
Kfusion[6] = SK_TAS*(P[6][4]*SH_TAS[2] - P[6][14]*SH_TAS[2] + P[6][5]*SH_TAS[1] - P[6][15]*SH_TAS[1] + P[6][6]*vd*SH_TAS[0]);
Kfusion[7] = SK_TAS*(P[7][4]*SH_TAS[2] - P[7][14]*SH_TAS[2] + P[7][5]*SH_TAS[1] - P[7][15]*SH_TAS[1] + P[7][6]*vd*SH_TAS[0]);
Kfusion[8] = SK_TAS*(P[8][4]*SH_TAS[2] - P[8][14]*SH_TAS[2] + P[8][5]*SH_TAS[1] - P[8][15]*SH_TAS[1] + P[8][6]*vd*SH_TAS[0]);
Kfusion[9] = SK_TAS*(P[9][4]*SH_TAS[2] - P[9][14]*SH_TAS[2] + P[9][5]*SH_TAS[1] - P[9][15]*SH_TAS[1] + P[9][6]*vd*SH_TAS[0]);
Kfusion[10] = SK_TAS*(P[10][4]*SH_TAS[2] - P[10][14]*SH_TAS[2] + P[10][5]*SH_TAS[1] - P[10][15]*SH_TAS[1] + P[10][6]*vd*SH_TAS[0]);
Kfusion[11] = SK_TAS*(P[11][4]*SH_TAS[2] - P[11][14]*SH_TAS[2] + P[11][5]*SH_TAS[1] - P[11][15]*SH_TAS[1] + P[11][6]*vd*SH_TAS[0]);
Kfusion[12] = SK_TAS*(P[12][4]*SH_TAS[2] - P[12][14]*SH_TAS[2] + P[12][5]*SH_TAS[1] - P[12][15]*SH_TAS[1] + P[12][6]*vd*SH_TAS[0]);
// this term has been zeroed to improve stability of the Z accel bias
Kfusion[13] = 0.0f;//SK_TAS*(P[13][4]*SH_TAS[2] - P[13][14]*SH_TAS[2] + P[13][5]*SH_TAS[1] - P[13][15]*SH_TAS[1] + P[13][6]*vd*SH_TAS[0]);
Kfusion[14] = SK_TAS*(P[14][4]*SH_TAS[2] - P[14][14]*SH_TAS[2] + P[14][5]*SH_TAS[1] - P[14][15]*SH_TAS[1] + P[14][6]*vd*SH_TAS[0]);
Kfusion[15] = SK_TAS*(P[15][4]*SH_TAS[2] - P[15][14]*SH_TAS[2] + P[15][5]*SH_TAS[1] - P[15][15]*SH_TAS[1] + P[15][6]*vd*SH_TAS[0]);
// zero Kalman gains to inhibit magnetic field state estimation
if (!inhibitMagStates) {
Kfusion[16] = SK_TAS*(P[16][4]*SH_TAS[2] - P[16][14]*SH_TAS[2] + P[16][5]*SH_TAS[1] - P[16][15]*SH_TAS[1] + P[16][6]*vd*SH_TAS[0]);
Kfusion[17] = SK_TAS*(P[17][4]*SH_TAS[2] - P[17][14]*SH_TAS[2] + P[17][5]*SH_TAS[1] - P[17][15]*SH_TAS[1] + P[17][6]*vd*SH_TAS[0]);
Kfusion[18] = SK_TAS*(P[18][4]*SH_TAS[2] - P[18][14]*SH_TAS[2] + P[18][5]*SH_TAS[1] - P[18][15]*SH_TAS[1] + P[18][6]*vd*SH_TAS[0]);
Kfusion[19] = SK_TAS*(P[19][4]*SH_TAS[2] - P[19][14]*SH_TAS[2] + P[19][5]*SH_TAS[1] - P[19][15]*SH_TAS[1] + P[19][6]*vd*SH_TAS[0]);
Kfusion[20] = SK_TAS*(P[20][4]*SH_TAS[2] - P[20][14]*SH_TAS[2] + P[20][5]*SH_TAS[1] - P[20][15]*SH_TAS[1] + P[20][6]*vd*SH_TAS[0]);
Kfusion[21] = SK_TAS*(P[21][4]*SH_TAS[2] - P[21][14]*SH_TAS[2] + P[21][5]*SH_TAS[1] - P[21][15]*SH_TAS[1] + P[21][6]*vd*SH_TAS[0]);
} else {
for (uint8_t i=16; i<=21; i++) {
Kfusion[i] = 0.0f;
}
}
// calculate measurement innovation variance
varInnovVtas = 1.0f/SK_TAS;
// calculate measurement innovation
innovVtas = VtasPred - VtasMeas;
// calculate the innovation consistency test ratio
tasTestRatio = sq(innovVtas) / (sq(_tasInnovGate) * varInnovVtas);
// fail if the ratio is > 1, but don't fail if bad IMU data
tasHealth = ((tasTestRatio < 1.0f) || badIMUdata);
tasTimeout = (imuSampleTime_ms - tasFailTime) > tasRetryTime;
// test the ratio before fusing data, forcing fusion if airspeed and position are timed out as we have no choice but to try and use airspeed to constrain error growth
if (tasHealth || (tasTimeout && posTimeout))
{
// restart the counter
tasFailTime = imuSampleTime_ms;
// correct the state vector
for (uint8_t j=0; j<=21; j++)
{
states[j] = states[j] - Kfusion[j] * innovVtas;
}
state.quat.normalize();
// correct the covariance P = (I - K*H)*P
// take advantage of the empty columns in H to reduce the number of operations
for (uint8_t i = 0; i<=21; i++)
{
for (uint8_t j = 0; j<=3; j++) KH[i][j] = 0.0;
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
Vector13 SH_BETA;
Vector8 SK_BETA;
Vector3f vel_rel_wind;
Vector22 H_BETA;
float innovBeta;
// copy required states to local variable names
q0 = state.quat[0];
q1 = state.quat[1];
q2 = state.quat[2];
q3 = state.quat[3];
vn = state.velocity.x;
ve = state.velocity.y;
vd = state.velocity.z;
vwn = state.wind_vel.x;
vwe = state.wind_vel.y;
// calculate predicted wind relative velocity in NED, compensating for offset in velcity when we are pulling a GPS glitch offset back in
vel_rel_wind.x = vn - vwn - gpsVelGlitchOffset.x;
vel_rel_wind.y = ve - vwe - gpsVelGlitchOffset.y;
vel_rel_wind.z = vd;
// rotate into body axes
vel_rel_wind = prevTnb * vel_rel_wind;
// perform fusion of assumed sideslip = 0
if (vel_rel_wind.x > 5.0f)
{
// Calculate observation jacobians
SH_BETA[0] = (vn - vwn)*(sq(q0) + sq(q1) - sq(q2) - sq(q3)) - vd*(2*q0*q2 - 2*q1*q3) + (ve - vwe)*(2*q0*q3 + 2*q1*q2);
if (fabsf(SH_BETA[0]) <= 1e-9f) {
faultStatus.bad_sideslip = true;
return;
} else {
faultStatus.bad_sideslip = false;
}
SH_BETA[1] = (ve - vwe)*(sq(q0) - sq(q1) + sq(q2) - sq(q3)) + vd*(2*q0*q1 + 2*q2*q3) - (vn - vwn)*(2*q0*q3 - 2*q1*q2);
SH_BETA[2] = vn - vwn;
SH_BETA[3] = ve - vwe;
SH_BETA[4] = 1/sq(SH_BETA[0]);
SH_BETA[5] = 1/SH_BETA[0];
SH_BETA[6] = SH_BETA[5]*(sq(q0) - sq(q1) + sq(q2) - sq(q3));
SH_BETA[7] = sq(q0) + sq(q1) - sq(q2) - sq(q3);
SH_BETA[8] = 2*q0*SH_BETA[3] - 2*q3*SH_BETA[2] + 2*q1*vd;
SH_BETA[9] = 2*q0*SH_BETA[2] + 2*q3*SH_BETA[3] - 2*q2*vd;
SH_BETA[10] = 2*q2*SH_BETA[2] - 2*q1*SH_BETA[3] + 2*q0*vd;
SH_BETA[11] = 2*q1*SH_BETA[2] + 2*q2*SH_BETA[3] + 2*q3*vd;
SH_BETA[12] = 2*q0*q3;
for (uint8_t i=0; i<=21; i++) {
H_BETA[i] = 0.0f;
}
H_BETA[0] = SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9];
H_BETA[1] = SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11];
H_BETA[2] = SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10];
H_BETA[3] = - SH_BETA[5]*SH_BETA[9] - SH_BETA[1]*SH_BETA[4]*SH_BETA[8];
H_BETA[4] = - SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) - SH_BETA[1]*SH_BETA[4]*SH_BETA[7];
H_BETA[5] = SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2);
H_BETA[6] = SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3);
H_BETA[14] = SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7];
H_BETA[15] = SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2) - SH_BETA[6];
// Calculate Kalman gains
float temp = (R_BETA - (SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7])*(P[14][4]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][4]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][4]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][4]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][4]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][4]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][4]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][4]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][4]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) + (SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7])*(P[14][14]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][14]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][14]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][14]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][14]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][14]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][14]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][14]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][14]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) + (SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2))*(P[14][5]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][5]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][5]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][5]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][5]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][5]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][5]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][5]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][5]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) - (SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2))*(P[14][15]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][15]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][15]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][15]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][15]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][15]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][15]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][15]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][15]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) + (SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9])*(P[14][0]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][0]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][0]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][0]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][0]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][0]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][0]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][0]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][0]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) + (SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11])*(P[14][1]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][1]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][1]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][1]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][1]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][1]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][1]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][1]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][1]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) + (SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10])*(P[14][2]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][2]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][2]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][2]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][2]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][2]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][2]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][2]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][2]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) - (SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8])*(P[14][3]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][3]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][3]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][3]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][3]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][3]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][3]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][3]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][3]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))) + (SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))*(P[14][6]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) - P[4][6]*(SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7]) + P[5][6]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) - P[15][6]*(SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2)) + P[0][6]*(SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9]) + P[1][6]*(SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11]) + P[2][6]*(SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10]) - P[3][6]*(SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8]) + P[6][6]*(SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3))));
if (temp >= R_BETA) {
SK_BETA[0] = 1.0f / temp;
faultStatus.bad_sideslip = false;
} else {
// the calculation is badly conditioned, so we cannot perform fusion on this step
faultStatus.bad_sideslip = true;
return;
}
SK_BETA[1] = SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7];
SK_BETA[2] = SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2);
SK_BETA[3] = SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3);
SK_BETA[4] = SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11];
SK_BETA[5] = SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9];
SK_BETA[6] = SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10];
SK_BETA[7] = SH_BETA[5]*SH_BETA[9] + SH_BETA[1]*SH_BETA[4]*SH_BETA[8];
Kfusion[0] = SK_BETA[0]*(P[0][0]*SK_BETA[5] + P[0][1]*SK_BETA[4] - P[0][4]*SK_BETA[1] + P[0][5]*SK_BETA[2] + P[0][2]*SK_BETA[6] + P[0][6]*SK_BETA[3] - P[0][3]*SK_BETA[7] + P[0][14]*SK_BETA[1] - P[0][15]*SK_BETA[2]);
Kfusion[1] = SK_BETA[0]*(P[1][0]*SK_BETA[5] + P[1][1]*SK_BETA[4] - P[1][4]*SK_BETA[1] + P[1][5]*SK_BETA[2] + P[1][2]*SK_BETA[6] + P[1][6]*SK_BETA[3] - P[1][3]*SK_BETA[7] + P[1][14]*SK_BETA[1] - P[1][15]*SK_BETA[2]);
Kfusion[2] = SK_BETA[0]*(P[2][0]*SK_BETA[5] + P[2][1]*SK_BETA[4] - P[2][4]*SK_BETA[1] + P[2][5]*SK_BETA[2] + P[2][2]*SK_BETA[6] + P[2][6]*SK_BETA[3] - P[2][3]*SK_BETA[7] + P[2][14]*SK_BETA[1] - P[2][15]*SK_BETA[2]);
Kfusion[3] = SK_BETA[0]*(P[3][0]*SK_BETA[5] + P[3][1]*SK_BETA[4] - P[3][4]*SK_BETA[1] + P[3][5]*SK_BETA[2] + P[3][2]*SK_BETA[6] + P[3][6]*SK_BETA[3] - P[3][3]*SK_BETA[7] + P[3][14]*SK_BETA[1] - P[3][15]*SK_BETA[2]);
Kfusion[4] = SK_BETA[0]*(P[4][0]*SK_BETA[5] + P[4][1]*SK_BETA[4] - P[4][4]*SK_BETA[1] + P[4][5]*SK_BETA[2] + P[4][2]*SK_BETA[6] + P[4][6]*SK_BETA[3] - P[4][3]*SK_BETA[7] + P[4][14]*SK_BETA[1] - P[4][15]*SK_BETA[2]);
Kfusion[5] = SK_BETA[0]*(P[5][0]*SK_BETA[5] + P[5][1]*SK_BETA[4] - P[5][4]*SK_BETA[1] + P[5][5]*SK_BETA[2] + P[5][2]*SK_BETA[6] + P[5][6]*SK_BETA[3] - P[5][3]*SK_BETA[7] + P[5][14]*SK_BETA[1] - P[5][15]*SK_BETA[2]);
Kfusion[6] = SK_BETA[0]*(P[6][0]*SK_BETA[5] + P[6][1]*SK_BETA[4] - P[6][4]*SK_BETA[1] + P[6][5]*SK_BETA[2] + P[6][2]*SK_BETA[6] + P[6][6]*SK_BETA[3] - P[6][3]*SK_BETA[7] + P[6][14]*SK_BETA[1] - P[6][15]*SK_BETA[2]);
Kfusion[7] = SK_BETA[0]*(P[7][0]*SK_BETA[5] + P[7][1]*SK_BETA[4] - P[7][4]*SK_BETA[1] + P[7][5]*SK_BETA[2] + P[7][2]*SK_BETA[6] + P[7][6]*SK_BETA[3] - P[7][3]*SK_BETA[7] + P[7][14]*SK_BETA[1] - P[7][15]*SK_BETA[2]);
Kfusion[8] = SK_BETA[0]*(P[8][0]*SK_BETA[5] + P[8][1]*SK_BETA[4] - P[8][4]*SK_BETA[1] + P[8][5]*SK_BETA[2] + P[8][2]*SK_BETA[6] + P[8][6]*SK_BETA[3] - P[8][3]*SK_BETA[7] + P[8][14]*SK_BETA[1] - P[8][15]*SK_BETA[2]);
Kfusion[9] = SK_BETA[0]*(P[9][0]*SK_BETA[5] + P[9][1]*SK_BETA[4] - P[9][4]*SK_BETA[1] + P[9][5]*SK_BETA[2] + P[9][2]*SK_BETA[6] + P[9][6]*SK_BETA[3] - P[9][3]*SK_BETA[7] + P[9][14]*SK_BETA[1] - P[9][15]*SK_BETA[2]);
Kfusion[10] = SK_BETA[0]*(P[10][0]*SK_BETA[5] + P[10][1]*SK_BETA[4] - P[10][4]*SK_BETA[1] + P[10][5]*SK_BETA[2] + P[10][2]*SK_BETA[6] + P[10][6]*SK_BETA[3] - P[10][3]*SK_BETA[7] + P[10][14]*SK_BETA[1] - P[10][15]*SK_BETA[2]);
Kfusion[11] = SK_BETA[0]*(P[11][0]*SK_BETA[5] + P[11][1]*SK_BETA[4] - P[11][4]*SK_BETA[1] + P[11][5]*SK_BETA[2] + P[11][2]*SK_BETA[6] + P[11][6]*SK_BETA[3] - P[11][3]*SK_BETA[7] + P[11][14]*SK_BETA[1] - P[11][15]*SK_BETA[2]);
Kfusion[12] = SK_BETA[0]*(P[12][0]*SK_BETA[5] + P[12][1]*SK_BETA[4] - P[12][4]*SK_BETA[1] + P[12][5]*SK_BETA[2] + P[12][2]*SK_BETA[6] + P[12][6]*SK_BETA[3] - P[12][3]*SK_BETA[7] + P[12][14]*SK_BETA[1] - P[12][15]*SK_BETA[2]);
// this term has been zeroed to improve stability of the Z accel bias
Kfusion[13] = 0.0f;//SK_BETA[0]*(P[13][0]*SK_BETA[5] + P[13][1]*SK_BETA[4] - P[13][4]*SK_BETA[1] + P[13][5]*SK_BETA[2] + P[13][2]*SK_BETA[6] + P[13][6]*SK_BETA[3] - P[13][3]*SK_BETA[7] + P[13][14]*SK_BETA[1] - P[13][15]*SK_BETA[2]);
Kfusion[14] = SK_BETA[0]*(P[14][0]*SK_BETA[5] + P[14][1]*SK_BETA[4] - P[14][4]*SK_BETA[1] + P[14][5]*SK_BETA[2] + P[14][2]*SK_BETA[6] + P[14][6]*SK_BETA[3] - P[14][3]*SK_BETA[7] + P[14][14]*SK_BETA[1] - P[14][15]*SK_BETA[2]);
Kfusion[15] = SK_BETA[0]*(P[15][0]*SK_BETA[5] + P[15][1]*SK_BETA[4] - P[15][4]*SK_BETA[1] + P[15][5]*SK_BETA[2] + P[15][2]*SK_BETA[6] + P[15][6]*SK_BETA[3] - P[15][3]*SK_BETA[7] + P[15][14]*SK_BETA[1] - P[15][15]*SK_BETA[2]);
// zero Kalman gains to inhibit magnetic field state estimation
if (!inhibitMagStates) {
Kfusion[16] = SK_BETA[0]*(P[16][0]*SK_BETA[5] + P[16][1]*SK_BETA[4] - P[16][4]*SK_BETA[1] + P[16][5]*SK_BETA[2] + P[16][2]*SK_BETA[6] + P[16][6]*SK_BETA[3] - P[16][3]*SK_BETA[7] + P[16][14]*SK_BETA[1] - P[16][15]*SK_BETA[2]);
Kfusion[17] = SK_BETA[0]*(P[17][0]*SK_BETA[5] + P[17][1]*SK_BETA[4] - P[17][4]*SK_BETA[1] + P[17][5]*SK_BETA[2] + P[17][2]*SK_BETA[6] + P[17][6]*SK_BETA[3] - P[17][3]*SK_BETA[7] + P[17][14]*SK_BETA[1] - P[17][15]*SK_BETA[2]);
Kfusion[18] = SK_BETA[0]*(P[18][0]*SK_BETA[5] + P[18][1]*SK_BETA[4] - P[18][4]*SK_BETA[1] + P[18][5]*SK_BETA[2] + P[18][2]*SK_BETA[6] + P[18][6]*SK_BETA[3] - P[18][3]*SK_BETA[7] + P[18][14]*SK_BETA[1] - P[18][15]*SK_BETA[2]);
Kfusion[19] = SK_BETA[0]*(P[19][0]*SK_BETA[5] + P[19][1]*SK_BETA[4] - P[19][4]*SK_BETA[1] + P[19][5]*SK_BETA[2] + P[19][2]*SK_BETA[6] + P[19][6]*SK_BETA[3] - P[19][3]*SK_BETA[7] + P[19][14]*SK_BETA[1] - P[19][15]*SK_BETA[2]);
Kfusion[20] = SK_BETA[0]*(P[20][0]*SK_BETA[5] + P[20][1]*SK_BETA[4] - P[20][4]*SK_BETA[1] + P[20][5]*SK_BETA[2] + P[20][2]*SK_BETA[6] + P[20][6]*SK_BETA[3] - P[20][3]*SK_BETA[7] + P[20][14]*SK_BETA[1] - P[20][15]*SK_BETA[2]);
Kfusion[21] = SK_BETA[0]*(P[21][0]*SK_BETA[5] + P[21][1]*SK_BETA[4] - P[21][4]*SK_BETA[1] + P[21][5]*SK_BETA[2] + P[21][2]*SK_BETA[6] + P[21][6]*SK_BETA[3] - P[21][3]*SK_BETA[7] + P[21][14]*SK_BETA[1] - P[21][15]*SK_BETA[2]);
} else {
for (uint8_t i=16; i<=21; i++) {
Kfusion[i] = 0.0f;
}
}
// calculate predicted sideslip angle and innovation using small angle approximation
innovBeta = vel_rel_wind.y / vel_rel_wind.x;
// reject measurement if greater than 3-sigma inconsistency
if (innovBeta > 0.5f) {
return;
}
// correct the state vector
for (uint8_t j=0; j<=21; j++)
{
states[j] = states[j] - Kfusion[j] * innovBeta;
}
state.quat.normalize();
// correct the covariance P = (I - K*H)*P
// take advantage of the empty columns in H to reduce the
// number of operations
for (uint8_t i = 0; i<=21; i++)
{
for (uint8_t j = 0; j<=6; j++)
{
KH[i][j] = Kfusion[i] * H_BETA[j];
}
for (uint8_t j = 7; j<=13; j++) KH[i][j] = 0.0;
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
{
if (constPosMode) {
pos.x = state.position.x + lastKnownPositionNE.x;
pos.y = state.position.y + lastKnownPositionNE.y;
} else {
pos.x = state.position.x;
pos.y = state.position.y;
}
// If relying on optical flow, then output ground relative position so that the vehicle does terain following
if (_fusionModeGPS == 3) {
pos.z = state.position.z - terrainState;
} else {
pos.z = state.position.z;
}
return true;
}
// return body axis gyro bias estimates in rad/sec
void NavEKF::getGyroBias(Vector3f &gyroBias) const
{
if (dtIMU < 1e-6f) {
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];
}
// Commands the EKF to not use GPS.
// This command must be sent prior to arming
// This command is forgotten by the EKF each time the vehicle disarms
// Returns 0 if command rejected
// Returns 1 if attitude, vertical velocity and vertical position will be provided
// Returns 2 if attitude, 3D-velocity, vertical position and relative horizontal position will be provided
uint8_t NavEKF::setInhibitGPS(void)
{
if(!vehicleArmed) {
return 0;
}
if (optFlowDataPresent()) {
return 2;
} else {
return 1;
}
_fusionModeGPS = 3;
}
// return the horizontal speed limit in m/s set by optical flow sensor limits
// return the scale factor to be applied to navigation velocity gains to compensate for increase in velocity noise with height when using optical flow
void NavEKF::getEkfControlLimits(float &ekfGndSpdLimit, float &ekfNavVelGainScaler) const
{
if (PV_AidingMode == AID_RELATIVE) {
// allow 1.0 rad/sec margin for angular motion
ekfGndSpdLimit = max((_maxFlowRate - 1.0f), 0.0f) * max((terrainState - state.position[2]), 0.1f);
// use standard gains up to 5.0 metres height and reduce above that
ekfNavVelGainScaler = 4.0f / max((terrainState - state.position[2]),4.0f);
} else {
ekfGndSpdLimit = 400.0f; //return 80% of max filter speed
ekfNavVelGainScaler = 1.0f;
}
}
// return weighting of first IMU in blending function
void NavEKF::getIMU1Weighting(float &ret) const
{
ret = IMU1_weighting;
}
// return the individual Z-accel bias estimates in m/s^2
void NavEKF::getAccelZBias(float &zbias1, float &zbias2) const {
if (dtIMU < 1e-6f) {
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
{
if(validOrigin) {
loc.lat = EKF_origin.lat;
loc.lng = EKF_origin.lng;
loc.alt = EKF_origin.alt - state.position.z*100;
loc.flags.relative_alt = 0;
loc.flags.terrain_alt = 0;
if (constPosMode) {
location_offset(loc, lastKnownPositionNE.x, lastKnownPositionNE.y);
} else {
location_offset(loc, state.position.x, state.position.y);
}
return true;
} else {
return false;
}
}
// return the estimated height above ground level
bool NavEKF::getHAGL(float &HAGL) const
{
HAGL = terrainState - state.position.z;
return !inhibitGndState;
}
// return data for debugging optical flow fusion
void NavEKF::getFlowDebug(float &varFlow, float &gndOffset, float &flowInnovX, float &flowInnovY, float &auxInnov, float &HAGL, float &rngInnov, float &range, float &gndOffsetErr) const
{
varFlow = max(flowTestRatio[0],flowTestRatio[1]);
gndOffset = terrainState;
flowInnovX = innovOptFlow[0];
flowInnovY = innovOptFlow[1];
auxInnov = auxFlowObsInnov;
HAGL = terrainState - state.position.z;
rngInnov = innovRng;
range = rngMea;
gndOffsetErr = sqrtf(Popt); // note Popt is constrained to be non-negative in EstimateTerrainOffset()
}
// calculate whether the flight vehicle is on the ground or flying from height, airspeed and GPS speed
void NavEKF::SetFlightAndFusionModes()
{
// determine if the vehicle is manoevring
if (accNavMagHoriz > 0.5f){
manoeuvring = true;
} else {
manoeuvring = false;
}
// if we are a fly forward type vehicle, then in-air mode can be determined through a combination of speed and height criteria
if (assume_zero_sideslip()) {
// Evaluate a numerical score that defines the likelihood we are in the air
float gndSpdSq = sq(velNED[0]) + sq(velNED[1]);
uint8_t inAirSum = 0;
bool highGndSpdStage2 = false;
// trigger at 8 m/s airspeed
if (_ahrs->airspeed_sensor_enabled()) {
const AP_Airspeed *airspeed = _ahrs->get_airspeed();
if (airspeed->get_airspeed() * airspeed->get_EAS2TAS() > 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 constant position mode, or don't have the right vehicle and sensing to estimate wind, inhibit wind states
inhibitWindStates = ((!useAirspeed() && !assume_zero_sideslip()) || onGround || constPosMode);
// request mag calibration for both in-air and manoeuvre threshold options
bool magCalRequested = ((_magCal == 0) && !onGround) || ((_magCal == 1) && manoeuvring);
// deny mag calibration request if we aren't using the compass, are in the pre-arm constant position mode or it has been inhibited by the user
bool magCalDenied = (!use_compass() || constPosMode || (_magCal == 2));
// inhibit the magnetic field calibration if not requested or denied
inhibitMagStates = (!magCalRequested || magCalDenied);
}
// initialise the covariance matrix
void NavEKF::CovarianceInit()
{
// zero the matrix
for (uint8_t i=1; i<=21; i++)
{
for (uint8_t j=0; j<=21; j++)
{
P[i][j] = 0.0f;
}
}
// quaternions - TODO better maths for initial quaternion covariances that uses roll, pitch and yaw
P[0][0] = 1.0e-9f;
P[1][1] = 0.25f*sq(radians(1.0f));
P[2][2] = 0.25f*sq(radians(1.0f));
P[3][3] = 0.25f*sq(radians(1.0f));
// velocities
P[4][4] = sq(0.7f);
P[5][5] = P[4][4];
P[6][6] = sq(0.7f);
// positions
P[7][7] = sq(15.0f);
P[8][8] = P[7][7];
P[9][9] = sq(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 ground height covariance
Popt = 0.25f;
}
// force symmetry on the covariance matrix to prevent ill-conditioning
void NavEKF::ForceSymmetry()
{
for (uint8_t i=1; i<=21; i++)
{
for (uint8_t j=0; j<=i-1; j++)
{
float temp = 0.5f*(P[i][j] + P[j][i]);
P[i][j] = temp;
P[j][i] = temp;
}
}
}
// copy covariances across from covariance prediction calculation and fix numerical errors
void NavEKF::CopyAndFixCovariances()
{
// copy predicted variances
for (uint8_t i=0; i<=21; i++) {
P[i][i] = nextP[i][i];
}
// copy predicted covariances and force symmetry
for (uint8_t i=1; i<=21; i++) {
for (uint8_t j=0; j<=i-1; j++)
{
P[i][j] = 0.5f*(nextP[i][j] + nextP[j][i]);
P[j][i] = P[i][j];
}
}
}
// constrain variances (diagonal terms) in the state covariance matrix to prevent ill-conditioning
void NavEKF::ConstrainVariances()
{
for (uint8_t i=0; i<=3; i++) P[i][i] = constrain_float(P[i][i],0.0f,1.0f); // quaternions
for (uint8_t i=4; i<=6; i++) P[i][i] = constrain_float(P[i][i],0.0f,1.0e3f); // velocities
for (uint8_t i=7; i<=9; i++) P[i][i] = constrain_float(P[i][i],0.0f,1.0e6f); // positions
for (uint8_t i=10; i<=12; i++) P[i][i] = constrain_float(P[i][i],0.0f,sq(0.175f * 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 local NE position relative to the stored origin
// If we don't have an origin, then set it to the current GPS coordinates
if (validOrigin) {
const struct Location &gpsloc = _ahrs->get_gps().location();
gpsPosNE = location_diff(EKF_origin, gpsloc);
} else {
setOrigin();
gpsPosNE.zero();
}
// calculate a position offset which is applied to NE position and velocity wherever it is used throughout code to allow GPS position jumps to be accommodated gradually
decayGpsOffset();
}
// If no previous GPS lock or told not to use it, we declare the GPS unavailable available for use
if ((_ahrs->get_gps().status() < AP_GPS::GPS_OK_FIX_3D) || _fusionModeGPS == 3) {
gpsNotAvailable = true;
} else {
gpsNotAvailable = false;
}
}
// check for new altitude measurement data and update stored measurement if available
void NavEKF::readHgtData()
{
// check to see if baro measurement has changed so we know if a new measurement has arrived
if (_baro.get_last_update() != lastHgtMeasTime) {
// 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_usec() != lastMagUpdate) {
// store time of last measurement update
lastMagUpdate = _ahrs->get_compass()->last_update_usec();
// read compass data and scale to improve numerical conditioning
magData = _ahrs->get_compass()->get_field() * 0.001f;
// get states stored at time closest to measurement time after allowance for measurement delay
RecallStates(statesAtMagMeasTime, (imuSampleTime_ms - msecMagDelay));
// let other processes know that new compass data has arrived
newDataMag = true;
} 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 sensor rotation about the X axis
// A positive Y rate is produced by a positive sensor rotation about the Y axis
// This filter uses a different definition of optical flow rates to the sensor with a positive optical flow rate produced by a
// negative rotation about that axis. For example a positive rotation of the flight vehicle about its X (roll) axis would produce a negative X flow rate
flowMeaTime_ms = imuSampleTime_ms;
flowQuality = rawFlowQuality;
// recall angular rates averaged across flow observation period allowing for processing, transmission and intersample delays
RecallOmega(omegaAcrossFlowTime, imuSampleTime_ms - flowTimeDeltaAvg_ms - _msecFLowDelay, imuSampleTime_ms - _msecFLowDelay);
// calculate bias errors on flow sensor gyro rates, but protect against spikes in data
flowGyroBias.x = 0.99f * flowGyroBias.x + 0.01f * constrain_float((rawGyroRates.x - omegaAcrossFlowTime.x),-0.1f,0.1f);
flowGyroBias.y = 0.99f * flowGyroBias.y + 0.01f * constrain_float((rawGyroRates.y - omegaAcrossFlowTime.y),-0.1f,0.1f);
// don't use data with a low quality indicator or extreme rates (helps catch corrupt sesnor data)
if (rawFlowQuality > 50 && rawFlowRates.length() < 4.2f && rawGyroRates.length() < 4.2f) {
// recall vehicle states at mid sample time for flow observations allowing for delays
RecallStates(statesAtFlowTime, imuSampleTime_ms - _msecFLowDelay - flowTimeDeltaAvg_ms/2);
// calculate rotation matrices at mid sample time for flow observations
statesAtFlowTime.quat.rotation_matrix(Tbn_flow);
Tnb_flow = Tbn_flow.transposed();
// correct flow sensor rates for bias
omegaAcrossFlowTime.x = rawGyroRates.x - flowGyroBias.x;
omegaAcrossFlowTime.y = rawGyroRates.y - flowGyroBias.y;
// write uncorrected flow rate measurements that will be used by the focal length scale factor estimator
// note correction for different axis and sign conventions used by the px4flow sensor
flowRadXY[0] = - rawFlowRates.x; // raw (non motion compensated) optical flow angular rate about the X axis (rad/sec)
flowRadXY[1] = - rawFlowRates.y; // raw (non motion compensated) optical flow angular rate about the Y axis (rad/sec)
// write flow rate measurements corrected for body rates
flowRadXYcomp[0] = flowRadXY[0] + omegaAcrossFlowTime.x;
flowRadXYcomp[1] = flowRadXY[1] + omegaAcrossFlowTime.y;
// set flag that will trigger observations
newDataFlow = true;
flowValidMeaTime_ms = imuSampleTime_ms;
} else {
newDataFlow = false;
}
// 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;
} 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 constant position mode due to GPS lag
P[4][4] = 400.0f;
P[5][5] = P[4][4];
P[6][6] = sq(0.7f);
// positions - we could have a big error coming out of constant position mode due to GPS lag
P[7][7] = 400.0f;
P[8][8] = P[7][7];
P[9][9] = sq(5.0f);
}
// Update magnetic field states if the magnetometer is bad
if (badMag) {
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;
}
// Use a function call rather than a constructor to initialise variables because it enables the filter to be re-started in flight if necessary.
void NavEKF::InitialiseVariables()
{
// initialise time stamps
imuSampleTime_ms = hal.scheduler->millis();
lastHealthyMagTime_ms = imuSampleTime_ms;
TASmsecPrev = imuSampleTime_ms;
BETAmsecPrev = imuSampleTime_ms;
lastMagUpdate = 0;
lastHgtMeasTime = imuSampleTime_ms;
lastHgtTime_ms = 0;
lastAirspeedUpdate = 0;
velFailTime = imuSampleTime_ms;
posFailTime = imuSampleTime_ms;
hgtFailTime = imuSampleTime_ms;
tasFailTime = imuSampleTime_ms;
lastStateStoreTime_ms = imuSampleTime_ms;
lastFixTime_ms = 0;
secondLastFixTime_ms = 0;
lastDecayTime_ms = imuSampleTime_ms;
timeAtLastAuxEKF_ms = imuSampleTime_ms;
flowValidMeaTime_ms = imuSampleTime_ms;
flowMeaTime_ms = 0;
prevFlowUseTime_ms = imuSampleTime_ms;
prevFlowFuseTime_ms = imuSampleTime_ms;
gndHgtValidTime_ms = 0;
ekfStartTime_ms = imuSampleTime_ms;
// initialise other variables
gpsNoiseScaler = 1.0f;
hgtTimeout = true;
magTimeout = true;
tasTimeout = true;
badMag = false;
badIMUdata = 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();
lastKnownPositionNE.zero();
gpsPosNE.zero();
prevTnb.zero();
memset(&P[0][0], 0, sizeof(P));
memset(&nextP[0][0], 0, sizeof(nextP));
memset(&processNoise[0], 0, sizeof(processNoise));
memset(&storedStates[0], 0, sizeof(storedStates));
memset(&statetimeStamp[0], 0, sizeof(statetimeStamp));
memset(&gpsIncrStateDelta[0], 0, sizeof(gpsIncrStateDelta));
memset(&hgtIncrStateDelta[0], 0, sizeof(hgtIncrStateDelta));
memset(&magIncrStateDelta[0], 0, sizeof(magIncrStateDelta));
memset(&flowIncrStateDelta[0], 0, sizeof(flowIncrStateDelta));
newDataFlow = false;
flowDataValid = false;
newDataRng = false;
flowFusePerformed = false;
fuseOptFlowData = false;
Popt = 0.0f;
terrainState = 0.0f;
prevPosN = gpsPosNE.x;
prevPosE = gpsPosNE.y;
fuseRngData = false;
inhibitGndState = true;
flowGyroBias.x = 0;
flowGyroBias.y = 0;
constVelMode = false;
lastConstVelMode = false;
heldVelNE.zero();
PV_AidingMode = AID_NONE;
posTimeout = true;
velTimeout = true;
gpsVelGlitchOffset.zero();
vehicleArmed = false;
prevVehicleArmed = false;
constPosMode = true;
memset(&faultStatus, 0, sizeof(faultStatus));
hgtRate = 0.0f;
mag_state.q0 = 1;
mag_state.DCM.identity();
IMU1_weighting = 0.5f;
onGround = true;
manoeuvring = false;
yawAligned = false;
inhibitWindStates = true;
inhibitMagStates = true;
gndOffsetValid = false;
flowXfailed = false;
validOrigin = false;
}
// return true if we should use the airspeed sensor
bool NavEKF::useAirspeed(void) const
{
return _ahrs->airspeed_sensor_enabled();
}
// return true if we should use the range finder sensor
bool NavEKF::useRngFinder(void) const
{
// TO-DO add code to set this based in setting of optical flow use parameter and presence of sensor
return true;
}
// return true if optical flow data is available
bool NavEKF::optFlowDataPresent(void) const
{
if (imuSampleTime_ms - flowMeaTime_ms < 5000) {
return true;
} else {
return false;
}
}
// return true if the vehicle is requesting the filter to be ready for flight
bool NavEKF::getVehicleArmStatus(void) const
{
return hal.util->get_soft_armed() || _ahrs->get_correct_centrifugal();
}
// return true if we should use the compass
bool NavEKF::use_compass(void) const
{
return _ahrs->get_compass() && _ahrs->get_compass()->use_for_yaw();
}
// decay GPS horizontal position offset to close to zero at a rate of 1 m/s for copters and 5 m/s for planes
// limit radius to a maximum of 100m
void NavEKF::decayGpsOffset()
{
float offsetDecaySpd;
if (assume_zero_sideslip()) {
offsetDecaySpd = 5.0f;
} else {
offsetDecaySpd = 1.0f;
}
float lapsedTime = 0.001f*float(imuSampleTime_ms - lastDecayTime_ms);
lastDecayTime_ms = imuSampleTime_ms;
float offsetRadius = pythagorous2(gpsPosGlitchOffsetNE.x, gpsPosGlitchOffsetNE.y);
// decay radius if larger than offset decay speed multiplied by lapsed time (plus a margin to prevent divide by zero)
if (offsetRadius > (offsetDecaySpd * lapsedTime + 0.1f)) {
// Calculate the GPS velocity offset required. This is necessary to prevent the position measurement being rejected for inconsistency when the radius is being pulled back in.
gpsVelGlitchOffset = -gpsPosGlitchOffsetNE*offsetDecaySpd/offsetRadius;
// calculate scale factor to be applied to both offset components
float scaleFactor = constrain_float((offsetRadius - offsetDecaySpd * lapsedTime), 0.0f, 100.0f) / offsetRadius;
gpsPosGlitchOffsetNE.x *= scaleFactor;
gpsPosGlitchOffsetNE.y *= scaleFactor;
} else {
gpsVelGlitchOffset.zero();
gpsPosGlitchOffsetNE.zero();
}
}
/*
should we assume zero sideslip?
*/
bool NavEKF::assume_zero_sideslip(void) const
{
// we don't assume zero sideslip for ground vehicles as EKF could
// be quite sensitive to a rapid spin of the ground vehicle if
// traction is lost
return _ahrs->get_fly_forward() && _ahrs->get_vehicle_class() != AHRS_VEHICLE_GROUND;
}
/*
return the filter fault status as a bitmasked integer
0 = quaternions are NaN
1 = velocities are NaN
2 = badly conditioned X magnetometer fusion
3 = badly conditioned Y magnetometer fusion
5 = badly conditioned Z magnetometer fusion
6 = badly conditioned airspeed fusion
7 = badly conditioned synthetic sideslip fusion
7 = filter is not initialised
*/
void NavEKF::getFilterFaults(uint8_t &faults) const
{
faults = (state.quat.is_nan()<<0 |
state.velocity.is_nan()<<1 |
faultStatus.bad_xmag<<2 |
faultStatus.bad_ymag<<3 |
faultStatus.bad_zmag<<4 |
faultStatus.bad_airspeed<<5 |
faultStatus.bad_sideslip<<6 |
!statesInitialised<<7);
}
/*
return filter timeout status as a bitmasked integer
0 = position measurement timeout
1 = velocity measurement timeout
2 = height measurement timeout
3 = magnetometer measurement timeout
4 = true airspeed measurement timeout
5 = unassigned
6 = unassigned
7 = unassigned
*/
void NavEKF::getFilterTimeouts(uint8_t &timeouts) const
{
timeouts = (posTimeout<<0 |
velTimeout<<1 |
hgtTimeout<<2 |
magTimeout<<3 |
tasTimeout<<4);
}
/*
return filter function status as a bitmasked integer
0 = attitude estimate valid
1 = horizontal velocity estimate valid
2 = vertical velocity estimate valid
3 = relative horizontal position estimate valid
4 = absolute horizontal position estimate valid
5 = vertical position estimate valid
6 = terrain height estimate valid
7 = constant position mode
*/
void NavEKF::getFilterStatus(nav_filter_status &status) const
{
// init return value
status.value = 0;
bool doingFlowNav = (PV_AidingMode == AID_RELATIVE) && flowDataValid;
bool doingWindRelNav = !tasTimeout && assume_zero_sideslip();
bool doingNormalGpsNav = !posTimeout && (PV_AidingMode == AID_ABSOLUTE);
bool notDeadReckoning = !constVelMode && !constPosMode;
bool someVertRefData = (!velTimeout && (_fusionModeGPS == 0)) || !hgtTimeout;
bool someHorizRefData = !(velTimeout && posTimeout && tasTimeout) || doingFlowNav;
bool optFlowNavPossible = flowDataValid && (_fusionModeGPS == 3);
bool gpsNavPossible = !gpsNotAvailable && (_fusionModeGPS <= 2);
// set individual flags
status.flags.attitude = !state.quat.is_nan(); // attitude valid (we need a better check)
status.flags.horiz_vel = someHorizRefData && notDeadReckoning; // horizontal velocity estimate valid
status.flags.vert_vel = someVertRefData; // vertical velocity estimate valid
status.flags.horiz_pos_rel = (doingFlowNav || doingWindRelNav || doingNormalGpsNav) && notDeadReckoning; // relative horizontal position estimate valid
status.flags.horiz_pos_abs = doingNormalGpsNav && notDeadReckoning; // absolute horizontal position estimate valid
status.flags.vert_pos = !hgtTimeout; // vertical position estimate valid
status.flags.terrain_alt = gndOffsetValid; // terrain height estimate valid
status.flags.const_pos_mode = constPosMode; // constant position mode
status.flags.pred_horiz_pos_rel = optFlowNavPossible || gpsNavPossible; // we should be able to estimate a relative position when we enter flight mode
status.flags.pred_horiz_pos_abs = gpsNavPossible; // we should be able to estimate an absolute position when we enter flight mode
}
// send an EKF_STATUS message to GCS
void NavEKF::send_status_report(mavlink_channel_t chan)
{
// get filter status
nav_filter_status filt_state;
getFilterStatus(filt_state);
// prepare flags
uint16_t flags = 0;
if (filt_state.flags.attitude) { flags |= EKF_ATTITUDE; }
if (filt_state.flags.horiz_vel) { flags |= EKF_VELOCITY_HORIZ; }
if (filt_state.flags.vert_vel) { flags |= EKF_VELOCITY_VERT; }
if (filt_state.flags.horiz_pos_rel) { flags |= EKF_POS_HORIZ_REL; }
if (filt_state.flags.horiz_pos_abs) { flags |= EKF_POS_HORIZ_ABS; }
if (filt_state.flags.vert_pos) { flags |= EKF_POS_VERT_ABS; }
if (filt_state.flags.terrain_alt) { flags |= EKF_POS_VERT_AGL; }
if (filt_state.flags.const_pos_mode) { flags |= EKF_CONST_POS_MODE; }
if (filt_state.flags.pred_horiz_pos_rel) { flags |= EKF_PRED_POS_HORIZ_REL; }
if (filt_state.flags.pred_horiz_pos_abs) { flags |= EKF_PRED_POS_HORIZ_ABS; }
// get variances
float velVar, posVar, hgtVar, tasVar;
Vector3f magVar;
Vector2f offset;
getVariances(velVar, posVar, hgtVar, magVar, tasVar, offset);
// send message
mavlink_msg_ekf_status_report_send(chan, flags, velVar, posVar, hgtVar, magVar.length(), tasVar);
}
// Check arm status and perform required checks and mode changes
void NavEKF::performArmingChecks()
{
// determine vehicle arm status and don't allow filter to arm until it has been running for long enough to stabilise
prevVehicleArmed = vehicleArmed;
vehicleArmed = (getVehicleArmStatus() && (imuSampleTime_ms - ekfStartTime_ms) > 10000);
// check to see if arm status has changed and reset states if it has
if (vehicleArmed != prevVehicleArmed) {
// only reset the magnetic field and heading on the first arm. This prevents in-flight learning being forgotten for vehicles that do multiple short flights and disarm in-between.
if (vehicleArmed && !firstArmComplete) {
firstArmComplete = true;
state.quat = calcQuatAndFieldStates(_ahrs->roll, _ahrs->pitch);
firstArmPosD = state.position.z;
}
// zero stored velocities used to do dead-reckoning
heldVelNE.zero();
// set various useage modes based on the condition at arming. These are then held until the vehicle is disarmed.
if (!vehicleArmed) {
PV_AidingMode = AID_NONE; // When dis-armed, we only estimate orientation & height using the constant position mode
posTimeout = true;
velTimeout = true;
constPosMode = true;
constVelMode = false; // always clear constant velocity mode if constant position mode is active
lastConstVelMode = false;
// store the current position to be used to keep reporting the last known position when disarmed
lastKnownPositionNE.x = state.position.x;
lastKnownPositionNE.y = state.position.y;
} else if (_fusionModeGPS == 3) { // arming when GPS useage has been prohibited
if (optFlowDataPresent()) {
PV_AidingMode = AID_RELATIVE; // we have optical flow data and can estimate all vehicle states
posTimeout = true;
velTimeout = true;
constPosMode = false;
constVelMode = false;
} else {
PV_AidingMode = AID_NONE; // we don't have optical flow data and will only be able to estimate orientation and height
posTimeout = true;
velTimeout = true;
constPosMode = true;
constVelMode = false; // always clear constant velocity mode if constant position mode is active
}
} else { // arming when GPS useage is allowed
if (gpsNotAvailable) {
PV_AidingMode = AID_NONE; // we don't have have GPS data and will only be able to estimate orientation and height
posTimeout = true;
velTimeout = true;
constPosMode = true;
constVelMode = false; // always clear constant velocity mode if constant position mode is active
} else {
PV_AidingMode = AID_ABSOLUTE; // we have GPS data and can estimate all vehicle states
posTimeout = false;
velTimeout = false;
constPosMode = false;
constVelMode = false;
// we need to reset the GPS timers to prevent GPS timeout logic being invoked on entry into GPS aiding
// this is becasue the EKF can be interrupted for an arbitrary amount of time during vehicle arming checks
lastFixTime_ms = imuSampleTime_ms;
secondLastFixTime_ms = imuSampleTime_ms;
// reset the last valid position fix time to prevent unwanted activation of GPS glitch logic
posFailTime = imuSampleTime_ms;
}
}
// Reset filter positon, height and velocity states on arming or disarming
ResetVelocity();
ResetPosition();
ResetHeight();
StoreStatesReset();
} else if (vehicleArmed && !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;
}
// Always turn aiding off when the vehicle is disarmed
if (!vehicleArmed) {
PV_AidingMode = AID_NONE;
posTimeout = true;
velTimeout = true;
// set constant position mode if aiding is inhibited
constPosMode = true;
constVelMode = false; // always clear constant velocity mode if constant position mode is active
lastConstVelMode = false;
}
}
// Set the NED origin to be used until the next filter reset
void NavEKF::setOrigin()
{
EKF_origin = _ahrs->get_gps().location();
validOrigin = true;
}
// return the LLH location of the filters NED origin
bool NavEKF::getOriginLLH(struct Location &loc) const
{
if (validOrigin) {
loc = EKF_origin;
}
return validOrigin;
}
// set the LLH location of the filters NED origin
bool NavEKF::setOriginLLH(struct Location &loc)
{
if (vehicleArmed) {
return false;
}
EKF_origin = loc;
validOrigin = true;
return true;
}
#endif // HAL_CPU_CLASS
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