mirror of https://github.com/ArduPilot/ardupilot
3447 lines
224 KiB
C++
3447 lines
224 KiB
C++
/// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: nil -*-
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#include <AP_HAL.h>
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#if HAL_CPU_CLASS >= HAL_CPU_CLASS_150
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// uncomment this to force the optimisation of this code, note that
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// this makes debugging harder
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#if CONFIG_HAL_BOARD == HAL_BOARD_AVR_SITL || CONFIG_HAL_BOARD == HAL_BOARD_LINUX
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#pragma GCC optimize("O0")
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#else
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#pragma GCC optimize("O3")
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#endif
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#include "AP_NavEKF.h"
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#include <AP_AHRS.h>
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#include <AP_Param.h>
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#include <AP_Vehicle.h>
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#include <stdio.h>
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/*
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parameter defaults for different types of vehicle. The
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APM_BUILD_DIRECTORY is taken from the main vehicle directory name
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where the code is built. Note that this trick won't work for arduino
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builds on APM2, but NavEKF doesn't run on APM2, so that's OK
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*/
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#if APM_BUILD_TYPE(APM_BUILD_ArduCopter)
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// copter defaults
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#define VELNE_NOISE_DEFAULT 0.5f
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#define VELD_NOISE_DEFAULT 0.7f
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#define POSNE_NOISE_DEFAULT 0.5f
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#define ALT_NOISE_DEFAULT 1.0f
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#define MAG_NOISE_DEFAULT 0.05f
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#define GYRO_PNOISE_DEFAULT 0.015f
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#define ACC_PNOISE_DEFAULT 0.25f
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#define GBIAS_PNOISE_DEFAULT 1E-06f
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#define ABIAS_PNOISE_DEFAULT 0.0001f
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#define MAGE_PNOISE_DEFAULT 0.0003f
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#define MAGB_PNOISE_DEFAULT 0.0003f
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#define VEL_GATE_DEFAULT 2
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#define POS_GATE_DEFAULT 10
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#define HGT_GATE_DEFAULT 5
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#define MAG_GATE_DEFAULT 3
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#define MAG_CAL_DEFAULT 1
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#define GLITCH_ACCEL_DEFAULT 150
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#define GLITCH_RADIUS_DEFAULT 15
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#elif APM_BUILD_TYPE(APM_BUILD_APMrover2)
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// rover defaults
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#define VELNE_NOISE_DEFAULT 0.5f
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#define VELD_NOISE_DEFAULT 0.7f
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#define POSNE_NOISE_DEFAULT 0.5f
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#define ALT_NOISE_DEFAULT 1.0f
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#define MAG_NOISE_DEFAULT 0.05f
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#define GYRO_PNOISE_DEFAULT 0.015f
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#define ACC_PNOISE_DEFAULT 0.25f
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#define GBIAS_PNOISE_DEFAULT 1E-06f
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#define ABIAS_PNOISE_DEFAULT 0.0002f
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#define MAGE_PNOISE_DEFAULT 0.0003f
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#define MAGB_PNOISE_DEFAULT 0.0003f
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#define VEL_GATE_DEFAULT 2
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#define POS_GATE_DEFAULT 10
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#define HGT_GATE_DEFAULT 5
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#define MAG_GATE_DEFAULT 3
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#define MAG_CAL_DEFAULT 1
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#define GLITCH_ACCEL_DEFAULT 150
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#define GLITCH_RADIUS_DEFAULT 15
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#else
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// generic defaults (and for plane)
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#define VELNE_NOISE_DEFAULT 0.3f
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#define VELD_NOISE_DEFAULT 0.5f
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#define POSNE_NOISE_DEFAULT 0.5f
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#define ALT_NOISE_DEFAULT 0.5f
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#define MAG_NOISE_DEFAULT 0.05f
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#define GYRO_PNOISE_DEFAULT 0.015f
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#define ACC_PNOISE_DEFAULT 0.25f
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#define GBIAS_PNOISE_DEFAULT 1E-06f
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#define ABIAS_PNOISE_DEFAULT 0.0002f
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#define MAGE_PNOISE_DEFAULT 0.0003f
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#define MAGB_PNOISE_DEFAULT 0.0003f
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#define VEL_GATE_DEFAULT 2
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#define POS_GATE_DEFAULT 10
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#define HGT_GATE_DEFAULT 10
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#define MAG_GATE_DEFAULT 3
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#define MAG_CAL_DEFAULT 0
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#define GLITCH_ACCEL_DEFAULT 150
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#define GLITCH_RADIUS_DEFAULT 15
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#endif // APM_BUILD_DIRECTORY
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extern const AP_HAL::HAL& hal;
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#define earthRate 0.000072921f // earth rotation rate (rad/sec)
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// maximum value for any element in the covariance matrix
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#define EKF_COVARIENCE_MAX 1.0e8f
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// when the wind estimation first starts with no airspeed sensor,
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// assume 3m/s to start
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#define STARTUP_WIND_SPEED 3.0f
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// Define tuning parameters
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const AP_Param::GroupInfo NavEKF::var_info[] PROGMEM = {
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// @Param: VELNE_NOISE
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// @DisplayName: GPS horizontal velocity measurement noise (m/s)
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// @Description: This is the RMS value of noise in the North and East GPS velocity measurements. Increasing it reduces the weighting on these measurements.
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// @Range: 0.05 - 5.0
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// @Increment: 0.05
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// @User: advanced
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AP_GROUPINFO("VELNE_NOISE", 0, NavEKF, _gpsHorizVelNoise, VELNE_NOISE_DEFAULT),
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// @Param: VELD_NOISE
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// @DisplayName: GPS vertical velocity measurement noise (m/s)
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// @Description: This is the RMS value of noise in the vertical GPS velocity measurement. Increasing it reduces the weighting on this measurement.
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// @Range: 0.05 - 5.0
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// @Increment: 0.05
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// @User: advanced
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AP_GROUPINFO("VELD_NOISE", 1, NavEKF, _gpsVertVelNoise, VELD_NOISE_DEFAULT),
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// @Param: POSNE_NOISE
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// @DisplayName: GPS horizontal position measurement noise (m)
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// @Description: This is the RMS value of noise in the GPS horizontal position measurements. Increasing it reduces the weighting on these measurements.
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// @Range: 0.1 - 10.0
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// @Increment: 0.1
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// @User: advanced
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AP_GROUPINFO("POSNE_NOISE", 2, NavEKF, _gpsHorizPosNoise, POSNE_NOISE_DEFAULT),
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// @Param: ALT_NOISE
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// @DisplayName: Altitude measurement noise (m)
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// @Description: This is the RMS value of noise in the altitude measurement. Increasing it reduces the weighting on this measurement.
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// @Range: 0.1 - 10.0
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// @Increment: 0.1
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// @User: advanced
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AP_GROUPINFO("ALT_NOISE", 3, NavEKF, _baroAltNoise, ALT_NOISE_DEFAULT),
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// @Param: MAG_NOISE
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// @DisplayName: Magnetometer measurement noise (Gauss)
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// @Description: This is the RMS value of noise in magnetometer measurements. Increasing it reduces the weighting on these measurements.
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// @Range: 0.01 - 0.5
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// @Increment: 0.01
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// @User: advanced
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AP_GROUPINFO("MAG_NOISE", 4, NavEKF, _magNoise, MAG_NOISE_DEFAULT),
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// @Param: EAS_NOISE
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// @DisplayName: Equivalent airspeed measurement noise (m/s)
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// @Description: This is the RMS value of noise in magnetometer measurements. Increasing it reduces the weighting on these measurements.
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// @Range: 0.5 - 5.0
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// @Increment: 0.1
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// @User: advanced
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AP_GROUPINFO("EAS_NOISE", 5, NavEKF, _easNoise, 1.4f),
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// @Param: WIND_PNOISE
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// @DisplayName: Wind velocity process noise (m/s^2)
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// @Description: This noise controls the growth of wind state error estimates. Increasing it makes wind estimation faster and noisier.
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// @Range: 0.01 - 1.0
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// @Increment: 0.1
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// @User: advanced
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AP_GROUPINFO("WIND_PNOISE", 6, NavEKF, _windVelProcessNoise, 0.1f),
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// @Param: WIND_PSCALE
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// @DisplayName: Height rate to wind procss noise scaler
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// @Description: Increasing this parameter increases how rapidly the wind states adapt when changing altitude, but does make wind speed estimation noiser.
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// @Range: 0.0 - 1.0
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// @Increment: 0.1
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// @User: advanced
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AP_GROUPINFO("WIND_PSCALE", 7, NavEKF, _wndVarHgtRateScale, 0.5f),
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// @Param: GYRO_PNOISE
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// @DisplayName: Rate gyro noise (rad/s)
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// @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.
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// @Range: 0.001 - 0.05
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// @Increment: 0.001
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// @User: advanced
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AP_GROUPINFO("GYRO_PNOISE", 8, NavEKF, _gyrNoise, GYRO_PNOISE_DEFAULT),
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// @Param: ACC_PNOISE
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// @DisplayName: Accelerometer noise (m/s^2)
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// @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.
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// @Range: 0.05 - 1.0 AP_Float _gpsNEVelVarAccScale; // scale factor applied to NE velocity measurement variance due to Vdot
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// @Increment: 0.01
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// @User: advanced
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AP_GROUPINFO("ACC_PNOISE", 9, NavEKF, _accNoise, ACC_PNOISE_DEFAULT),
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// @Param: GBIAS_PNOISE
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// @DisplayName: Rate gyro bias process noise (rad/s)
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// @Description: This noise controls the growth of gyro bias state error estimates. Increasing it makes rate gyro bias estimation faster and noisier.
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// @Range: 0.0000001 - 0.00001
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// @User: advanced
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AP_GROUPINFO("GBIAS_PNOISE", 10, NavEKF, _gyroBiasProcessNoise, GBIAS_PNOISE_DEFAULT),
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// @Param: ABIAS_PNOISE
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// @DisplayName: Accelerometer bias process noise (m/s^2)
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// @Description: This noise controls the growth of the vertical acelerometer bias state error estimate. Increasing it makes accelerometer bias estimation faster and noisier.
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// @Range: 0.00001 - 0.001
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// @User: advanced
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AP_GROUPINFO("ABIAS_PNOISE", 11, NavEKF, _accelBiasProcessNoise, ABIAS_PNOISE_DEFAULT),
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// @Param: MAGE_PNOISE
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// @DisplayName: Earth magnetic field process noise (gauss/s)
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// @Description: This noise controls the growth of earth magnetic field state error estimates. Increasing it makes earth magnetic field bias estimation faster and noisier.
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// @Range: 0.0001 - 0.01
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// @User: advanced
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AP_GROUPINFO("MAGE_PNOISE", 12, NavEKF, _magEarthProcessNoise, MAGE_PNOISE_DEFAULT),
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// @Param: MAGB_PNOISE
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// @DisplayName: Body magnetic field process noise (gauss/s)
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// @Description: This noise controls the growth of body magnetic field state error estimates. Increasing it makes compass offset estimation faster and noisier.
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// @Range: 0.0001 - 0.01
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// @User: advanced
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AP_GROUPINFO("MAGB_PNOISE", 13, NavEKF, _magBodyProcessNoise, MAGB_PNOISE_DEFAULT),
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// @Param: VEL_DELAY
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// @DisplayName: GPS velocity measurement delay (msec)
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// @Description: This is the number of msec that the GPS velocity measurements lag behind the inertial measurements.
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// @Range: 0 - 500
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// @Increment: 10
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// @User: advanced
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AP_GROUPINFO("VEL_DELAY", 14, NavEKF, _msecVelDelay, 220),
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// @Param: POS_DELAY
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// @DisplayName: GPS position measurement delay (msec)
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// @Description: This is the number of msec that the GPS position measurements lag behind the inertial measurements.
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// @Range: 0 - 500
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// @Increment: 10
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// @User: advancedScale factor applied to horizontal position measurement variance due to manoeuvre acceleration
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AP_GROUPINFO("POS_DELAY", 15, NavEKF, _msecPosDelay, 220),
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// @Param: GPS_TYPE
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// @DisplayName: GPS velocity mode control
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// @Description: This parameter controls use of GPS velocity measurements : 0 = use 3D velocity, 1 = use 2D velocity, 2 = use no velocity
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// @Range: 0 - 3
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// @Increment: 1
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// @User: advanced
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AP_GROUPINFO("GPS_TYPE", 16, NavEKF, _fusionModeGPS, 0),
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// @Param: VEL_GATE
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// @DisplayName: GPS velocity measurement gate size
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// @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.
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// @Range: 1 - 100
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// @Increment: 1
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// @User: advanced
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AP_GROUPINFO("VEL_GATE", 17, NavEKF, _gpsVelInnovGate, VEL_GATE_DEFAULT),
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// @Param: POS_GATE
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// @DisplayName: GPS position measurement gate size
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// @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.
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// @Range: 1 - 100
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// @Increment: 1
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// @User: advanced
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AP_GROUPINFO("POS_GATE", 18, NavEKF, _gpsPosInnovGate, POS_GATE_DEFAULT),
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// @Param: HGT_GATE
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// @DisplayName: Height measurement gate size
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// @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.
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// @Range: 1 - 100
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// @Increment: 1
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// @User: advanced
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AP_GROUPINFO("HGT_GATE", 19, NavEKF, _hgtInnovGate, HGT_GATE_DEFAULT),
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// @Param: MAG_GATE
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// @DisplayName: Magnetometer measurement gate size
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// @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.
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// @Range: 1 - 100
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// @Increment: 1
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// @User: advanced
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AP_GROUPINFO("MAG_GATE", 20, NavEKF, _magInnovGate, MAG_GATE_DEFAULT),
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// @Param: EAS_GATE
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// @DisplayName: Airspeed measurement gate size
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// @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.
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// @Range: 1 - 100
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// @Increment: 1
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// @User: advanced
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AP_GROUPINFO("EAS_GATE", 21, NavEKF, _tasInnovGate, 10),
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// @Param: MAG_CAL
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// @DisplayName: Magnetometer calibration mode
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// @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.
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// @Values: 0:Speed and Height,1:Acceleration,2:Never
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// @Increment: 1
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// @User: advanced
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AP_GROUPINFO("MAG_CAL", 22, NavEKF, _magCal, MAG_CAL_DEFAULT),
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// @Param: GLITCH_ACCEL
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// @DisplayName: GPS glitch accel gate size (cm/s^2)
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// @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.
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// @Range: 100 - 500
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// @Increment: 50
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// @User: advanced
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AP_GROUPINFO("GLITCH_ACCEL", 23, NavEKF, _gpsGlitchAccelMax, GLITCH_ACCEL_DEFAULT),
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// @Param: GLITCH_RAD
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// @DisplayName: GPS glitch radius gate size (m)
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// @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.
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// @Range: 10 - 50
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// @Increment: 5
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// @User: advanced
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AP_GROUPINFO("GLITCH_RAD", 24, NavEKF, _gpsGlitchRadiusMax, GLITCH_RADIUS_DEFAULT),
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AP_GROUPEND
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};
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// constructor
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NavEKF::NavEKF(const AP_AHRS *ahrs, AP_Baro &baro) :
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_ahrs(ahrs),
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_baro(baro),
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state(*reinterpret_cast<struct state_elements *>(&states)),
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covTimeStepMax(0.07f), // maximum time (sec) between covariance prediction updates
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covDelAngMax(0.05f), // maximum delta angle between covariance prediction updates
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TASmsecMax(200), // maximum allowed interval between airspeed measurement updates
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fuseMeNow(false), // forces airspeed and sythetic sideslip fusion to occur on the IMU frame that data arrives
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staticMode(true), // staticMode forces position and velocity fusion with zero values
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prevStaticMode(true), // staticMode from previous filter update
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yawAligned(false), // set true when heading or yaw angle has been aligned
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inhibitWindStates(true), // inhibit wind state updates on startup
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inhibitMagStates(true) // inhibit magnetometer state updates on startup
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#if CONFIG_HAL_BOARD == HAL_BOARD_PX4 || CONFIG_HAL_BOARD == HAL_BOARD_VRBRAIN
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,_perf_UpdateFilter(perf_alloc(PC_ELAPSED, "EKF_UpdateFilter")),
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_perf_CovariancePrediction(perf_alloc(PC_ELAPSED, "EKF_CovariancePrediction")),
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_perf_FuseVelPosNED(perf_alloc(PC_ELAPSED, "EKF_FuseVelPosNED")),
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_perf_FuseMagnetometer(perf_alloc(PC_ELAPSED, "EKF_FuseMagnetometer")),
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_perf_FuseAirspeed(perf_alloc(PC_ELAPSED, "EKF_FuseAirspeed")),
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_perf_FuseSideslip(perf_alloc(PC_ELAPSED, "EKF_FuseSideslip"))
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#endif
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{
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AP_Param::setup_object_defaults(this, var_info);
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// Tuning parameters
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_gpsNEVelVarAccScale = 0.05f; // Scale factor applied to NE velocity measurement variance due to manoeuvre acceleration
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_gpsDVelVarAccScale = 0.07f; // Scale factor applied to vertical velocity measurement variance due to manoeuvre acceleration
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_gpsPosVarAccScale = 0.05f; // Scale factor applied to horizontal position measurement variance due to manoeuvre acceleration
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_msecHgtDelay = 60; // Height measurement delay (msec)
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_msecMagDelay = 40; // Magnetometer measurement delay (msec)
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_msecTasDelay = 240; // Airspeed measurement delay (msec)
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_gpsRetryTimeUseTAS = 20000; // GPS retry time with airspeed measurements (msec)
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_gpsRetryTimeNoTAS = 10000; // GPS retry time without airspeed measurements (msec)
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_hgtRetryTimeMode0 = 10000; // Height retry time with vertical velocity measurement (msec)
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_hgtRetryTimeMode12 = 5000; // Height retry time without vertical velocity measurement (msec)
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_magFailTimeLimit_ms = 10000; // number of msec before a magnetometer failing innovation consistency checks is declared failed (msec)
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_magVarRateScale = 0.05f; // scale factor applied to magnetometer variance due to angular rate
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_gyroBiasNoiseScaler = 2.0f; // scale factor applied to gyro bias state process noise when on ground
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_msecGpsAvg = 200; // average number of msec between GPS measurements
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_msecHgtAvg = 100; // average number of msec between height measurements
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_msecBetaAvg = 100; // average number of msec between synthetic sideslip measurements
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dtVelPos = 0.02; // number of seconds between position and velocity corrections. This should be a multiple of the imu update interval.
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// Misc initial conditions
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hgtRate = 0.0f;
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mag_state.q0 = 1;
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mag_state.DCM.identity();
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IMU1_weighting = 0.5f;
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lastDivergeTime_ms = 0;
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memset(&faultStatus, 0, sizeof(faultStatus));
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}
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// Check basic filter health metrics and return a consolidated health status
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bool NavEKF::healthy(void) const
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{
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if (!statesInitialised) {
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return false;
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}
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if (state.quat.is_nan()) {
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return false;
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}
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if (state.velocity.is_nan()) {
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return false;
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}
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if (filterDiverged || (hal.scheduler->millis() - lastDivergeTime_ms < 10000)) {
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return false;
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}
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// If measurements have failed innovation consistency checks for long enough to time-out
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// and force fusion then the nav solution can be conidered to be unhealthy
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// This will only be set as a transient
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if (posTimeout || velTimeout || hgtTimeout) {
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return false;
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}
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// all OK
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return true;
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}
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// return true if filter is dead-reckoning height
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bool NavEKF::HeightDrifting(void) const
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{
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// Set to true if height measurements are failing the innovation consistency check
|
|
return !hgtHealth;
|
|
}
|
|
|
|
// return true if filter is dead-reckoning position
|
|
bool NavEKF::PositionDrifting(void) const
|
|
{
|
|
// Set to true if position measurements are failing the innovation consistency check
|
|
return !posHealth;
|
|
}
|
|
|
|
// resets position states to last GPS measurement or to zero if in static mode
|
|
void NavEKF::ResetPosition(void)
|
|
{
|
|
if (staticMode) {
|
|
states[7] = 0;
|
|
states[8] = 0;
|
|
} else if (_ahrs->get_gps().status() >= AP_GPS::GPS_OK_FIX_3D) {
|
|
|
|
// read the GPS
|
|
readGpsData();
|
|
// write to state vector
|
|
states[7] = gpsPosNE.x + gpsPosGlitchOffsetNE.x;
|
|
states[8] = gpsPosNE.y + gpsPosGlitchOffsetNE.y;
|
|
}
|
|
}
|
|
|
|
// resets velocity states to last GPS measurement or to zero if in static mode
|
|
void NavEKF::ResetVelocity(void)
|
|
{
|
|
if (staticMode) {
|
|
state.velocity.zero();
|
|
state.vel1.zero();
|
|
state.vel2.zero();
|
|
} else if (_ahrs->get_gps().status() >= AP_GPS::GPS_OK_FIX_3D) {
|
|
// read the GPS
|
|
readGpsData();
|
|
// reset horizontal velocity states
|
|
if (_fusionModeGPS <= 1) {
|
|
states[4] = velNED[0]; // north velocity from blended accel data
|
|
states[5] = velNED[1]; // east velocity from blended accel data
|
|
states[23] = velNED[0]; // north velocity from IMU1 accel data
|
|
states[24] = velNED[1]; // east velocity from IMU1 accel data
|
|
states[27] = velNED[0]; // north velocity from IMU2 accel data
|
|
states[28] = velNED[1]; // east velocity from IMU2 accel data
|
|
}
|
|
// reset vertical velocity states
|
|
if (_fusionModeGPS <= 0) {
|
|
states[6] = velNED[2]; // down velocity from blended accel data
|
|
states[25] = velNED[2]; // down velocity from IMU1 accel data
|
|
states[29] = velNED[2]; // down velocity from IMU2 accel data
|
|
}
|
|
}
|
|
}
|
|
|
|
// reset the vertical position state using the last height measurement
|
|
void NavEKF::ResetHeight(void)
|
|
{
|
|
// read the altimeter
|
|
readHgtData();
|
|
// write to the state vector
|
|
states[9] = -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
|
|
}
|
|
|
|
// this function is used to initialise the filter whilst moving, using the AHRS DCM solution
|
|
// it should NOT be used to re-initialise after a timeout as DCM will also be corrupted
|
|
void NavEKF::InitialiseFilterDynamic(void)
|
|
{
|
|
// this forces healthy() to be false so that when we ask for ahrs
|
|
// attitude we get the DCM attitude regardless of the state of AHRS_EKF_USE
|
|
statesInitialised = false;
|
|
|
|
// Set re-used variables to zero
|
|
ZeroVariables();
|
|
|
|
// get initial time deltat between IMU measurements (sec)
|
|
dtIMU = _ahrs->get_ins().get_delta_time();
|
|
|
|
// calculate initial orientation and earth magnetic field states
|
|
Quaternion initQuat;
|
|
initQuat = calcQuatAndFieldStates(_ahrs->roll, _ahrs->pitch);
|
|
|
|
// write to state vector
|
|
state.quat = initQuat;
|
|
state.gyro_bias.zero();
|
|
state.accel_zbias1 = 0;
|
|
state.accel_zbias2 = 0;
|
|
state.wind_vel.zero();
|
|
ResetVelocity();
|
|
ResetPosition();
|
|
ResetHeight();
|
|
state.body_magfield = magBias;
|
|
|
|
// set to true now that states have be initialised
|
|
statesInitialised = true;
|
|
|
|
// initialise the covariance matrix
|
|
CovarianceInit();
|
|
|
|
// define Earth rotation vector in the NED navigation frame
|
|
calcEarthRateNED(earthRateNED, _ahrs->get_home().lat);
|
|
|
|
// initialise IMU pre-processing states
|
|
readIMUData();
|
|
}
|
|
|
|
// Initialise the states from accelerometer and magnetometer data (if present)
|
|
// This method can only be used when the vehicle is static
|
|
void NavEKF::InitialiseFilterBootstrap(void)
|
|
{
|
|
// set re-used variables to zero
|
|
ZeroVariables();
|
|
|
|
// 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
|
|
initAccVec.normalize();
|
|
|
|
// calculate initial pitch angle
|
|
float pitch = asinf(initAccVec.x);
|
|
|
|
// calculate initial roll angle
|
|
float roll = -asinf(initAccVec.y / cosf(pitch));
|
|
|
|
// calculate initial orientation and earth magnetic field states
|
|
Quaternion initQuat;
|
|
initQuat = calcQuatAndFieldStates(roll, pitch);
|
|
|
|
// read the GPS
|
|
readGpsData();
|
|
|
|
// read the barometer
|
|
readHgtData();
|
|
|
|
// check on ground status
|
|
SetFlightAndFusionModes();
|
|
|
|
// write to state vector
|
|
state.quat = initQuat;
|
|
state.gyro_bias.zero();
|
|
state.accel_zbias1 = 0;
|
|
state.accel_zbias2 = 0;
|
|
state.wind_vel.zero();
|
|
state.body_magfield = magBias;
|
|
|
|
// set to true now we have intialised the states
|
|
statesInitialised = true;
|
|
|
|
// initialise the covariance matrix
|
|
CovarianceInit();
|
|
|
|
// define Earth rotation vector in the NED navigation frame
|
|
calcEarthRateNED(earthRateNED, _ahrs->get_home().lat);
|
|
|
|
// initialise IMU pre-processing states
|
|
readIMUData();
|
|
}
|
|
|
|
// Update Filter States - this should be called whenever new IMU data is available
|
|
void NavEKF::UpdateFilter()
|
|
{
|
|
// don't run filter updates if states have not been initialised
|
|
if (!statesInitialised) {
|
|
return;
|
|
}
|
|
|
|
// start the timer used for load measurement
|
|
perf_begin(_perf_UpdateFilter);
|
|
|
|
// read IMU data and convert to delta angles and velocities
|
|
readIMUData();
|
|
|
|
// detect if filter has diverged and do a dynamic reset using the DCM solution
|
|
checkDivergence();
|
|
if (filterDiverged) {
|
|
InitialiseFilterDynamic();
|
|
return;
|
|
}
|
|
|
|
// detect if the filter update has been delayed for too long
|
|
if (dtIMU > 0.2f) {
|
|
// we have stalled for too long - reset states
|
|
ResetVelocity();
|
|
ResetPosition();
|
|
ResetHeight();
|
|
StoreStatesReset();
|
|
//Initialise IMU pre-processing states
|
|
readIMUData();
|
|
// stop the timer used for load measurement
|
|
perf_end(_perf_UpdateFilter);
|
|
return;
|
|
}
|
|
|
|
// check if on ground
|
|
SetFlightAndFusionModes();
|
|
|
|
// define rules used to set staticMode
|
|
// staticMode enables ground operation without GPS by fusing zeros for position and height measurements
|
|
if (static_mode_demanded()) {
|
|
staticMode = true;
|
|
} else {
|
|
staticMode = false;
|
|
}
|
|
|
|
// check to see if static mode has changed and reset states if it has
|
|
if (prevStaticMode != staticMode) {
|
|
ResetVelocity();
|
|
ResetPosition();
|
|
ResetHeight();
|
|
StoreStatesReset();
|
|
calcQuatAndFieldStates(_ahrs->roll, _ahrs->pitch);
|
|
prevStaticMode = staticMode;
|
|
}
|
|
|
|
// 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();
|
|
SelectTasFusion();
|
|
SelectBetaFusion();
|
|
|
|
// stop the timer used for load measurement
|
|
perf_end(_perf_UpdateFilter);
|
|
}
|
|
|
|
// select fusion of velocity, position and height measurements
|
|
void NavEKF::SelectVelPosFusion()
|
|
{
|
|
// calculate ratio of VelPos fusion to state prediction steps
|
|
uint8_t velPosFuseStepRatio = floor(dtVelPos/dtIMU + 0.5f);
|
|
|
|
// calculate the scale factor to be applied to GPS measurement variance to account for
|
|
// the fact we repeat fusion of the same measurement to provide a smoother output
|
|
gpsVarScaler = _msecGpsAvg/(1000.0f*dtVelPos);
|
|
|
|
// calculate the scale factor to be applied to height measurement variance to account for
|
|
// the fact we repeat fusion of the same measurement to provide a smoother output
|
|
hgtVarScaler = _msecHgtAvg/(1000.0f*dtVelPos);
|
|
|
|
// check for new data, specify which measurements should be used and check data for freshness
|
|
if (!staticMode) {
|
|
|
|
// check for and read new GPS data
|
|
readGpsData();
|
|
|
|
// command fusion of GPS data and reset states as required
|
|
if (newDataGps) {
|
|
// reset data arrived flag
|
|
newDataGps = false;
|
|
// enable fusion
|
|
fuseVelData = true;
|
|
fusePosData = true;
|
|
// reset the counter used to schedule updates so that we always fuse data on the frame GPS data arrives
|
|
skipCounter = velPosFuseStepRatio;
|
|
// If a long time since last GPS update, then reset position and velocity and reset stored state history
|
|
|
|
uint32_t gpsRetryTimeout = useAirspeed() ? _gpsRetryTimeUseTAS : _gpsRetryTimeNoTAS;
|
|
if (hal.scheduler->millis() - secondLastFixTime_ms > gpsRetryTimeout) {
|
|
ResetPosition();
|
|
ResetVelocity();
|
|
StoreStatesReset();
|
|
}
|
|
} else if (hal.scheduler->millis() - lastFixTime_ms > (uint32_t)(_msecGpsAvg + 40)) {
|
|
// Timeout fusion of GPS data if stale. Needed because we repeatedly fuse the same
|
|
// measurement until the next one arrives to provide a smoother output
|
|
fuseVelData = false;
|
|
fusePosData = false;
|
|
}
|
|
|
|
// command fusion of height data
|
|
if (newDataHgt)
|
|
{
|
|
// reset data arrived flag
|
|
newDataHgt = false;
|
|
// enable fusion
|
|
fuseHgtData = true;
|
|
} else if (hal.scheduler->millis() - lastHgtTime_ms > (uint32_t)(_msecHgtAvg + 40)) {
|
|
// timeout fusion of height data if stale. Needed because we repeatedly fuse the same
|
|
// measurement until the next one arrives to provide a smoother output
|
|
fuseHgtData = false;
|
|
}
|
|
|
|
} else {
|
|
// in static mode use synthetic position measurements set to zero
|
|
// only fuse synthetic measurements when rate of change of velocity is less than 0.5g to reduce attitude errors due to launch acceleration
|
|
// do not use velocity fusion to reduce the effect of movement on attitude
|
|
if (accNavMag < 4.9f) {
|
|
fusePosData = true;
|
|
} else {
|
|
fusePosData = false;
|
|
}
|
|
fuseVelData = false;
|
|
fuseHgtData = true;
|
|
}
|
|
|
|
// check for and read new height data
|
|
readHgtData();
|
|
|
|
// perform fusion as commanded, and in accordance with specified time intervals
|
|
if (fuseVelData || fusePosData || fuseHgtData) {
|
|
// skip fusion as required to maintain ~dtVelPos time interval between corrections
|
|
if (skipCounter >= velPosFuseStepRatio) {
|
|
FuseVelPosNED();
|
|
// reset counter used to skip update frames
|
|
skipCounter = 1;
|
|
} else {
|
|
// increment counter used to skip update frames
|
|
skipCounter += 1;
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
// 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 it failed
|
|
if (magHealth) {
|
|
lastHealthyMagTime_ms = hal.scheduler->millis();
|
|
} else {
|
|
if ((hal.scheduler->millis() - lastHealthyMagTime_ms) > _magFailTimeLimit_ms && use_compass()) {
|
|
magTimeout = true;
|
|
} else {
|
|
magTimeout = false;
|
|
}
|
|
}
|
|
|
|
// determine if conditions are right to start a new fusion cycle
|
|
bool dataReady = statesInitialised && use_compass() && newDataMag;
|
|
if (dataReady)
|
|
{
|
|
MAGmsecPrev = IMUmsec;
|
|
fuseMagData = true;
|
|
}
|
|
else
|
|
{
|
|
fuseMagData = false;
|
|
}
|
|
|
|
// call the function that performs fusion of magnetometer data
|
|
FuseMagnetometer();
|
|
|
|
}
|
|
|
|
// select fusion of true airspeed measurements
|
|
void NavEKF::SelectTasFusion()
|
|
{
|
|
// get true airspeed measurement
|
|
readAirSpdData();
|
|
|
|
// if the filter is initialised, wind states are not inhibited and we have data to fuse, then queue TAS fusion
|
|
tasDataWaiting = (statesInitialised && !inhibitWindStates && (tasDataWaiting || newDataTas));
|
|
|
|
// if we have waited too long, set a timeout flag which will force fusion to occur
|
|
bool timeout = ((IMUmsec - 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 && (!magFusePerformed || timeout || fuseMeNow))
|
|
{
|
|
FuseAirspeed();
|
|
TASmsecPrev = IMUmsec;
|
|
tasDataWaiting = false;
|
|
}
|
|
}
|
|
|
|
// select fusion of synthetic sideslip measurements
|
|
void NavEKF::SelectBetaFusion()
|
|
{
|
|
// Determine if synthetic sidelsip data should be fused
|
|
// synthetic sidelip fusion only works for fixed wing aircraft and relies on the average sideslip being close to zero
|
|
// it requires a stable wind estimate for best results and should not be used for aerobatic flight
|
|
// we fuse synthetic sideslip measurements if:
|
|
// we are a fly forward vehicle type AND NOT using a full range of sensors with healthy position
|
|
// AND NOT on the ground AND enough time has lapsed since our last fusion
|
|
// AND (we have not fused magnetometer data on this time step OR the immediate fusion flag is set)
|
|
if (assume_zero_sideslip() && !(use_compass() && useAirspeed() && posHealth) && !inhibitWindStates && ((IMUmsec - BETAmsecPrev) >= _msecBetaAvg) && (!magFusePerformed || fuseMeNow)) {
|
|
FuseSideslip();
|
|
BETAmsecPrev = IMUmsec;
|
|
}
|
|
}
|
|
|
|
// 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);
|
|
|
|
// save current measurements
|
|
prevDelAng = correctedDelAng;
|
|
|
|
// apply corrections for earths rotation rate and coning errors
|
|
// % * - and + operators have been overloaded
|
|
correctedDelAng = correctedDelAng - prevTnb * earthRateNED*dtIMU + (prevDelAng % correctedDelAng) * 8.333333e-2f;
|
|
|
|
// 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
|
|
Quaternion q(states[0],states[1],states[2],states[3]);
|
|
Matrix3f Tbn_temp;
|
|
q.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);
|
|
|
|
// 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) - states[6] * alpha;
|
|
|
|
// use filtered height rate to increase wind process noise when climbing or descending
|
|
// this allows for wind gradient effects.
|
|
if (!inhibitWindStates) {
|
|
windVelSigma = dt * constrain_float(_windVelProcessNoise, 0.01f, 1.0f) * (1.0f + constrain_float(_wndVarHgtRateScale, 0.0f, 1.0f) * fabsf(hgtRate));
|
|
} else {
|
|
windVelSigma = 0.0f;
|
|
}
|
|
dAngBiasSigma = dt * constrain_float(_gyroBiasProcessNoise, 1e-7f, 1e-5f);
|
|
dVelBiasSigma = dt * constrain_float(_accelBiasProcessNoise, 1e-5f, 1e-3f);
|
|
if (!inhibitMagStates) {
|
|
magEarthSigma = dt * constrain_float(_magEarthProcessNoise, 1e-4f, 1e-2f);
|
|
magBodySigma = dt * constrain_float(_magBodyProcessNoise, 1e-4f, 1e-2f);
|
|
} else {
|
|
magEarthSigma = 0.0f;
|
|
magBodySigma = 0.0f;
|
|
}
|
|
for (uint8_t i= 0; i<=9; i++) processNoise[i] = 1.0e-9f;
|
|
for (uint8_t i=10; i<=12; i++) processNoise[i] = dAngBiasSigma;
|
|
// scale gyro bias noise when in static mode to allow for faster bias estimation
|
|
for (uint8_t i=10; i<=12; i++) {
|
|
processNoise[i] = dAngBiasSigma;
|
|
if (staticMode) {
|
|
processNoise[i] *= _gyroBiasNoiseScaler;
|
|
}
|
|
}
|
|
processNoise[13] = dVelBiasSigma;
|
|
for (uint8_t i=14; i<=15; i++) processNoise[i] = windVelSigma;
|
|
for (uint8_t i=16; i<=18; i++) processNoise[i] = magEarthSigma;
|
|
for (uint8_t i=19; i<=21; i++) processNoise[i] = magBodySigma;
|
|
for (uint8_t i= 0; i<=21; i++) processNoise[i] = sq(processNoise[i]);
|
|
|
|
// set variables used to calculate covariance growth
|
|
dvx = summedDelVel.x;
|
|
dvy = summedDelVel.y;
|
|
dvz = summedDelVel.z;
|
|
dax = summedDelAng.x;
|
|
day = summedDelAng.y;
|
|
daz = summedDelAng.z;
|
|
q0 = states[0];
|
|
q1 = states[1];
|
|
q2 = states[2];
|
|
q3 = states[3];
|
|
dax_b = states[10];
|
|
day_b = states[11];
|
|
daz_b = states[12];
|
|
dvz_b = IMU1_weighting * states[13] + (1.0f - IMU1_weighting) * states[22];
|
|
_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]);
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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]);
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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);
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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;
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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;
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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;
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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);
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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);
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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);
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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);
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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);
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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);
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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);
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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;
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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;
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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;
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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);
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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);
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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);
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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);
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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);
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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);
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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);
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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;
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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;
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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;
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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);
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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);
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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);
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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);
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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);
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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);
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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;
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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]);
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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;
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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;
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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;
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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]);
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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;
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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;
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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;
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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];
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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)));
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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;
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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;
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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;
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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)));
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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)));
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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]);
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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]);
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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]);
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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]);
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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];
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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];
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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];
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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];
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|
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];
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|
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];
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|
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];
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|
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];
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|
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];
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|
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];
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|
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];
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|
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];
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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);
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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;
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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;
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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;
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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);
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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);
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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);
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nextP[7][7] = P[7][7] + P[4][7]*dt + dt*(P[7][4] + P[4][4]*dt);
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nextP[7][8] = P[7][8] + P[4][8]*dt + dt*(P[7][5] + P[4][5]*dt);
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nextP[7][9] = P[7][9] + P[4][9]*dt + dt*(P[7][6] + P[4][6]*dt);
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nextP[7][10] = P[7][10] + P[4][10]*dt;
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nextP[7][11] = P[7][11] + P[4][11]*dt;
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nextP[7][12] = P[7][12] + P[4][12]*dt;
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nextP[7][13] = P[7][13] + P[4][13]*dt;
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nextP[7][14] = P[7][14] + P[4][14]*dt;
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nextP[7][15] = P[7][15] + P[4][15]*dt;
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nextP[7][16] = P[7][16] + P[4][16]*dt;
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nextP[7][17] = P[7][17] + P[4][17]*dt;
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nextP[7][18] = P[7][18] + P[4][18]*dt;
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nextP[7][19] = P[7][19] + P[4][19]*dt;
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nextP[7][20] = P[7][20] + P[4][20]*dt;
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nextP[7][21] = P[7][21] + P[4][21]*dt;
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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);
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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;
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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;
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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;
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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);
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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);
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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);
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nextP[8][7] = P[8][7] + P[5][7]*dt + dt*(P[8][4] + P[5][4]*dt);
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nextP[8][8] = P[8][8] + P[5][8]*dt + dt*(P[8][5] + P[5][5]*dt);
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nextP[8][9] = P[8][9] + P[5][9]*dt + dt*(P[8][6] + P[5][6]*dt);
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nextP[8][10] = P[8][10] + P[5][10]*dt;
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nextP[8][11] = P[8][11] + P[5][11]*dt;
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nextP[8][12] = P[8][12] + P[5][12]*dt;
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nextP[8][13] = P[8][13] + P[5][13]*dt;
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nextP[8][14] = P[8][14] + P[5][14]*dt;
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|
nextP[8][15] = P[8][15] + P[5][15]*dt;
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nextP[8][16] = P[8][16] + P[5][16]*dt;
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nextP[8][17] = P[8][17] + P[5][17]*dt;
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|
nextP[8][18] = P[8][18] + P[5][18]*dt;
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nextP[8][19] = P[8][19] + P[5][19]*dt;
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nextP[8][20] = P[8][20] + P[5][20]*dt;
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nextP[8][21] = P[8][21] + P[5][21]*dt;
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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);
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|
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;
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|
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;
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|
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;
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|
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);
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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);
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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);
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|
nextP[9][7] = P[9][7] + P[6][7]*dt + dt*(P[9][4] + P[6][4]*dt);
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|
nextP[9][8] = P[9][8] + P[6][8]*dt + dt*(P[9][5] + P[6][5]*dt);
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|
nextP[9][9] = P[9][9] + P[6][9]*dt + dt*(P[9][6] + P[6][6]*dt);
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|
nextP[9][10] = P[9][10] + P[6][10]*dt;
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|
nextP[9][11] = P[9][11] + P[6][11]*dt;
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|
nextP[9][12] = P[9][12] + P[6][12]*dt;
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|
nextP[9][13] = P[9][13] + P[6][13]*dt;
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|
nextP[9][14] = P[9][14] + P[6][14]*dt;
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|
nextP[9][15] = P[9][15] + P[6][15]*dt;
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|
nextP[9][16] = P[9][16] + P[6][16]*dt;
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|
nextP[9][17] = P[9][17] + P[6][17]*dt;
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|
nextP[9][18] = P[9][18] + P[6][18]*dt;
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|
nextP[9][19] = P[9][19] + P[6][19]*dt;
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|
nextP[9][20] = P[9][20] + P[6][20]*dt;
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|
nextP[9][21] = P[9][21] + P[6][21]*dt;
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|
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];
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|
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;
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|
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;
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|
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;
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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];
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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];
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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];
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nextP[10][7] = P[10][7] + P[10][4]*dt;
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|
nextP[10][8] = P[10][8] + P[10][5]*dt;
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|
nextP[10][9] = P[10][9] + P[10][6]*dt;
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|
nextP[10][10] = P[10][10];
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|
nextP[10][11] = P[10][11];
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|
nextP[10][12] = P[10][12];
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|
nextP[10][13] = P[10][13];
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|
nextP[10][14] = P[10][14];
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|
nextP[10][15] = P[10][15];
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|
nextP[10][16] = P[10][16];
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|
nextP[10][17] = P[10][17];
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|
nextP[10][18] = P[10][18];
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|
nextP[10][19] = P[10][19];
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|
nextP[10][20] = P[10][20];
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|
nextP[10][21] = P[10][21];
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|
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];
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|
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;
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|
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;
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|
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;
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|
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];
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|
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];
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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];
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|
nextP[11][7] = P[11][7] + P[11][4]*dt;
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|
nextP[11][8] = P[11][8] + P[11][5]*dt;
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|
nextP[11][9] = P[11][9] + P[11][6]*dt;
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|
nextP[11][10] = P[11][10];
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|
nextP[11][11] = P[11][11];
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|
nextP[11][12] = P[11][12];
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|
nextP[11][13] = P[11][13];
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|
nextP[11][14] = P[11][14];
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|
nextP[11][15] = P[11][15];
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|
nextP[11][16] = P[11][16];
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|
nextP[11][17] = P[11][17];
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|
nextP[11][18] = P[11][18];
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|
nextP[11][19] = P[11][19];
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|
nextP[11][20] = P[11][20];
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|
nextP[11][21] = P[11][21];
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|
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];
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|
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;
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|
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;
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|
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;
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|
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];
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|
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];
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|
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];
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|
nextP[12][7] = P[12][7] + P[12][4]*dt;
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|
nextP[12][8] = P[12][8] + P[12][5]*dt;
|
|
nextP[12][9] = P[12][9] + P[12][6]*dt;
|
|
nextP[12][10] = P[12][10];
|
|
nextP[12][11] = P[12][11];
|
|
nextP[12][12] = P[12][12];
|
|
nextP[12][13] = P[12][13];
|
|
nextP[12][14] = P[12][14];
|
|
nextP[12][15] = P[12][15];
|
|
nextP[12][16] = P[12][16];
|
|
nextP[12][17] = P[12][17];
|
|
nextP[12][18] = P[12][18];
|
|
nextP[12][19] = P[12][19];
|
|
nextP[12][20] = P[12][20];
|
|
nextP[12][21] = P[12][21];
|
|
nextP[13][0] = P[13][0] + P[13][1]*SF[7] + P[13][2]*SF[9] + P[13][3]*SF[8] + P[13][10]*SF[11] + P[13][11]*SPP[7] + P[13][12]*SPP[6];
|
|
nextP[13][1] = P[13][1] + P[13][0]*SF[6] + P[13][2]*SF[5] + P[13][3]*SF[9] + P[13][11]*SPP[6] - P[13][12]*SPP[7] - (P[13][10]*q0)/2;
|
|
nextP[13][2] = P[13][2] + P[13][0]*SF[4] + P[13][1]*SF[8] + P[13][3]*SF[6] + P[13][12]*SF[11] - P[13][10]*SPP[6] - (P[13][11]*q0)/2;
|
|
nextP[13][3] = P[13][3] + P[13][0]*SF[5] + P[13][1]*SF[4] + P[13][2]*SF[7] - P[13][11]*SF[11] + P[13][10]*SPP[7] - (P[13][12]*q0)/2;
|
|
nextP[13][4] = P[13][4] + P[13][1]*SF[1] + P[13][0]*SF[3] + P[13][2]*SPP[0] - P[13][3]*SPP[2] - P[13][13]*SPP[4];
|
|
nextP[13][5] = P[13][5] + P[13][0]*SF[2] + P[13][2]*SF[1] + P[13][3]*SF[3] - P[13][1]*SPP[0] + P[13][13]*SPP[3];
|
|
nextP[13][6] = P[13][6] + P[13][1]*SF[2] + P[13][3]*SF[1] + P[13][0]*SPP[0] - P[13][2]*SPP[1] - P[13][13]*SPP[5];
|
|
nextP[13][7] = P[13][7] + P[13][4]*dt;
|
|
nextP[13][8] = P[13][8] + P[13][5]*dt;
|
|
nextP[13][9] = P[13][9] + P[13][6]*dt;
|
|
nextP[13][10] = P[13][10];
|
|
nextP[13][11] = P[13][11];
|
|
nextP[13][12] = P[13][12];
|
|
nextP[13][13] = P[13][13];
|
|
nextP[13][14] = P[13][14];
|
|
nextP[13][15] = P[13][15];
|
|
nextP[13][16] = P[13][16];
|
|
nextP[13][17] = P[13][17];
|
|
nextP[13][18] = P[13][18];
|
|
nextP[13][19] = P[13][19];
|
|
nextP[13][20] = P[13][20];
|
|
nextP[13][21] = P[13][21];
|
|
nextP[14][0] = P[14][0] + P[14][1]*SF[7] + P[14][2]*SF[9] + P[14][3]*SF[8] + P[14][10]*SF[11] + P[14][11]*SPP[7] + P[14][12]*SPP[6];
|
|
nextP[14][1] = P[14][1] + P[14][0]*SF[6] + P[14][2]*SF[5] + P[14][3]*SF[9] + P[14][11]*SPP[6] - P[14][12]*SPP[7] - (P[14][10]*q0)/2;
|
|
nextP[14][2] = P[14][2] + P[14][0]*SF[4] + P[14][1]*SF[8] + P[14][3]*SF[6] + P[14][12]*SF[11] - P[14][10]*SPP[6] - (P[14][11]*q0)/2;
|
|
nextP[14][3] = P[14][3] + P[14][0]*SF[5] + P[14][1]*SF[4] + P[14][2]*SF[7] - P[14][11]*SF[11] + P[14][10]*SPP[7] - (P[14][12]*q0)/2;
|
|
nextP[14][4] = P[14][4] + P[14][1]*SF[1] + P[14][0]*SF[3] + P[14][2]*SPP[0] - P[14][3]*SPP[2] - P[14][13]*SPP[4];
|
|
nextP[14][5] = P[14][5] + P[14][0]*SF[2] + P[14][2]*SF[1] + P[14][3]*SF[3] - P[14][1]*SPP[0] + P[14][13]*SPP[3];
|
|
nextP[14][6] = P[14][6] + P[14][1]*SF[2] + P[14][3]*SF[1] + P[14][0]*SPP[0] - P[14][2]*SPP[1] - P[14][13]*SPP[5];
|
|
nextP[14][7] = P[14][7] + P[14][4]*dt;
|
|
nextP[14][8] = P[14][8] + P[14][5]*dt;
|
|
nextP[14][9] = P[14][9] + P[14][6]*dt;
|
|
nextP[14][10] = P[14][10];
|
|
nextP[14][11] = P[14][11];
|
|
nextP[14][12] = P[14][12];
|
|
nextP[14][13] = P[14][13];
|
|
nextP[14][14] = P[14][14];
|
|
nextP[14][15] = P[14][15];
|
|
nextP[14][16] = P[14][16];
|
|
nextP[14][17] = P[14][17];
|
|
nextP[14][18] = P[14][18];
|
|
nextP[14][19] = P[14][19];
|
|
nextP[14][20] = P[14][20];
|
|
nextP[14][21] = P[14][21];
|
|
nextP[15][0] = P[15][0] + P[15][1]*SF[7] + P[15][2]*SF[9] + P[15][3]*SF[8] + P[15][10]*SF[11] + P[15][11]*SPP[7] + P[15][12]*SPP[6];
|
|
nextP[15][1] = P[15][1] + P[15][0]*SF[6] + P[15][2]*SF[5] + P[15][3]*SF[9] + P[15][11]*SPP[6] - P[15][12]*SPP[7] - (P[15][10]*q0)/2;
|
|
nextP[15][2] = P[15][2] + P[15][0]*SF[4] + P[15][1]*SF[8] + P[15][3]*SF[6] + P[15][12]*SF[11] - P[15][10]*SPP[6] - (P[15][11]*q0)/2;
|
|
nextP[15][3] = P[15][3] + P[15][0]*SF[5] + P[15][1]*SF[4] + P[15][2]*SF[7] - P[15][11]*SF[11] + P[15][10]*SPP[7] - (P[15][12]*q0)/2;
|
|
nextP[15][4] = P[15][4] + P[15][1]*SF[1] + P[15][0]*SF[3] + P[15][2]*SPP[0] - P[15][3]*SPP[2] - P[15][13]*SPP[4];
|
|
nextP[15][5] = P[15][5] + P[15][0]*SF[2] + P[15][2]*SF[1] + P[15][3]*SF[3] - P[15][1]*SPP[0] + P[15][13]*SPP[3];
|
|
nextP[15][6] = P[15][6] + P[15][1]*SF[2] + P[15][3]*SF[1] + P[15][0]*SPP[0] - P[15][2]*SPP[1] - P[15][13]*SPP[5];
|
|
nextP[15][7] = P[15][7] + P[15][4]*dt;
|
|
nextP[15][8] = P[15][8] + P[15][5]*dt;
|
|
nextP[15][9] = P[15][9] + P[15][6]*dt;
|
|
nextP[15][10] = P[15][10];
|
|
nextP[15][11] = P[15][11];
|
|
nextP[15][12] = P[15][12];
|
|
nextP[15][13] = P[15][13];
|
|
nextP[15][14] = P[15][14];
|
|
nextP[15][15] = P[15][15];
|
|
nextP[15][16] = P[15][16];
|
|
nextP[15][17] = P[15][17];
|
|
nextP[15][18] = P[15][18];
|
|
nextP[15][19] = P[15][19];
|
|
nextP[15][20] = P[15][20];
|
|
nextP[15][21] = P[15][21];
|
|
nextP[16][0] = P[16][0] + P[16][1]*SF[7] + P[16][2]*SF[9] + P[16][3]*SF[8] + P[16][10]*SF[11] + P[16][11]*SPP[7] + P[16][12]*SPP[6];
|
|
nextP[16][1] = P[16][1] + P[16][0]*SF[6] + P[16][2]*SF[5] + P[16][3]*SF[9] + P[16][11]*SPP[6] - P[16][12]*SPP[7] - (P[16][10]*q0)/2;
|
|
nextP[16][2] = P[16][2] + P[16][0]*SF[4] + P[16][1]*SF[8] + P[16][3]*SF[6] + P[16][12]*SF[11] - P[16][10]*SPP[6] - (P[16][11]*q0)/2;
|
|
nextP[16][3] = P[16][3] + P[16][0]*SF[5] + P[16][1]*SF[4] + P[16][2]*SF[7] - P[16][11]*SF[11] + P[16][10]*SPP[7] - (P[16][12]*q0)/2;
|
|
nextP[16][4] = P[16][4] + P[16][1]*SF[1] + P[16][0]*SF[3] + P[16][2]*SPP[0] - P[16][3]*SPP[2] - P[16][13]*SPP[4];
|
|
nextP[16][5] = P[16][5] + P[16][0]*SF[2] + P[16][2]*SF[1] + P[16][3]*SF[3] - P[16][1]*SPP[0] + P[16][13]*SPP[3];
|
|
nextP[16][6] = P[16][6] + P[16][1]*SF[2] + P[16][3]*SF[1] + P[16][0]*SPP[0] - P[16][2]*SPP[1] - P[16][13]*SPP[5];
|
|
nextP[16][7] = P[16][7] + P[16][4]*dt;
|
|
nextP[16][8] = P[16][8] + P[16][5]*dt;
|
|
nextP[16][9] = P[16][9] + P[16][6]*dt;
|
|
nextP[16][10] = P[16][10];
|
|
nextP[16][11] = P[16][11];
|
|
nextP[16][12] = P[16][12];
|
|
nextP[16][13] = P[16][13];
|
|
nextP[16][14] = P[16][14];
|
|
nextP[16][15] = P[16][15];
|
|
nextP[16][16] = P[16][16];
|
|
nextP[16][17] = P[16][17];
|
|
nextP[16][18] = P[16][18];
|
|
nextP[16][19] = P[16][19];
|
|
nextP[16][20] = P[16][20];
|
|
nextP[16][21] = P[16][21];
|
|
nextP[17][0] = P[17][0] + P[17][1]*SF[7] + P[17][2]*SF[9] + P[17][3]*SF[8] + P[17][10]*SF[11] + P[17][11]*SPP[7] + P[17][12]*SPP[6];
|
|
nextP[17][1] = P[17][1] + P[17][0]*SF[6] + P[17][2]*SF[5] + P[17][3]*SF[9] + P[17][11]*SPP[6] - P[17][12]*SPP[7] - (P[17][10]*q0)/2;
|
|
nextP[17][2] = P[17][2] + P[17][0]*SF[4] + P[17][1]*SF[8] + P[17][3]*SF[6] + P[17][12]*SF[11] - P[17][10]*SPP[6] - (P[17][11]*q0)/2;
|
|
nextP[17][3] = P[17][3] + P[17][0]*SF[5] + P[17][1]*SF[4] + P[17][2]*SF[7] - P[17][11]*SF[11] + P[17][10]*SPP[7] - (P[17][12]*q0)/2;
|
|
nextP[17][4] = P[17][4] + P[17][1]*SF[1] + P[17][0]*SF[3] + P[17][2]*SPP[0] - P[17][3]*SPP[2] - P[17][13]*SPP[4];
|
|
nextP[17][5] = P[17][5] + P[17][0]*SF[2] + P[17][2]*SF[1] + P[17][3]*SF[3] - P[17][1]*SPP[0] + P[17][13]*SPP[3];
|
|
nextP[17][6] = P[17][6] + P[17][1]*SF[2] + P[17][3]*SF[1] + P[17][0]*SPP[0] - P[17][2]*SPP[1] - P[17][13]*SPP[5];
|
|
nextP[17][7] = P[17][7] + P[17][4]*dt;
|
|
nextP[17][8] = P[17][8] + P[17][5]*dt;
|
|
nextP[17][9] = P[17][9] + P[17][6]*dt;
|
|
nextP[17][10] = P[17][10];
|
|
nextP[17][11] = P[17][11];
|
|
nextP[17][12] = P[17][12];
|
|
nextP[17][13] = P[17][13];
|
|
nextP[17][14] = P[17][14];
|
|
nextP[17][15] = P[17][15];
|
|
nextP[17][16] = P[17][16];
|
|
nextP[17][17] = P[17][17];
|
|
nextP[17][18] = P[17][18];
|
|
nextP[17][19] = P[17][19];
|
|
nextP[17][20] = P[17][20];
|
|
nextP[17][21] = P[17][21];
|
|
nextP[18][0] = P[18][0] + P[18][1]*SF[7] + P[18][2]*SF[9] + P[18][3]*SF[8] + P[18][10]*SF[11] + P[18][11]*SPP[7] + P[18][12]*SPP[6];
|
|
nextP[18][1] = P[18][1] + P[18][0]*SF[6] + P[18][2]*SF[5] + P[18][3]*SF[9] + P[18][11]*SPP[6] - P[18][12]*SPP[7] - (P[18][10]*q0)/2;
|
|
nextP[18][2] = P[18][2] + P[18][0]*SF[4] + P[18][1]*SF[8] + P[18][3]*SF[6] + P[18][12]*SF[11] - P[18][10]*SPP[6] - (P[18][11]*q0)/2;
|
|
nextP[18][3] = P[18][3] + P[18][0]*SF[5] + P[18][1]*SF[4] + P[18][2]*SF[7] - P[18][11]*SF[11] + P[18][10]*SPP[7] - (P[18][12]*q0)/2;
|
|
nextP[18][4] = P[18][4] + P[18][1]*SF[1] + P[18][0]*SF[3] + P[18][2]*SPP[0] - P[18][3]*SPP[2] - P[18][13]*SPP[4];
|
|
nextP[18][5] = P[18][5] + P[18][0]*SF[2] + P[18][2]*SF[1] + P[18][3]*SF[3] - P[18][1]*SPP[0] + P[18][13]*SPP[3];
|
|
nextP[18][6] = P[18][6] + P[18][1]*SF[2] + P[18][3]*SF[1] + P[18][0]*SPP[0] - P[18][2]*SPP[1] - P[18][13]*SPP[5];
|
|
nextP[18][7] = P[18][7] + P[18][4]*dt;
|
|
nextP[18][8] = P[18][8] + P[18][5]*dt;
|
|
nextP[18][9] = P[18][9] + P[18][6]*dt;
|
|
nextP[18][10] = P[18][10];
|
|
nextP[18][11] = P[18][11];
|
|
nextP[18][12] = P[18][12];
|
|
nextP[18][13] = P[18][13];
|
|
nextP[18][14] = P[18][14];
|
|
nextP[18][15] = P[18][15];
|
|
nextP[18][16] = P[18][16];
|
|
nextP[18][17] = P[18][17];
|
|
nextP[18][18] = P[18][18];
|
|
nextP[18][19] = P[18][19];
|
|
nextP[18][20] = P[18][20];
|
|
nextP[18][21] = P[18][21];
|
|
nextP[19][0] = P[19][0] + P[19][1]*SF[7] + P[19][2]*SF[9] + P[19][3]*SF[8] + P[19][10]*SF[11] + P[19][11]*SPP[7] + P[19][12]*SPP[6];
|
|
nextP[19][1] = P[19][1] + P[19][0]*SF[6] + P[19][2]*SF[5] + P[19][3]*SF[9] + P[19][11]*SPP[6] - P[19][12]*SPP[7] - (P[19][10]*q0)/2;
|
|
nextP[19][2] = P[19][2] + P[19][0]*SF[4] + P[19][1]*SF[8] + P[19][3]*SF[6] + P[19][12]*SF[11] - P[19][10]*SPP[6] - (P[19][11]*q0)/2;
|
|
nextP[19][3] = P[19][3] + P[19][0]*SF[5] + P[19][1]*SF[4] + P[19][2]*SF[7] - P[19][11]*SF[11] + P[19][10]*SPP[7] - (P[19][12]*q0)/2;
|
|
nextP[19][4] = P[19][4] + P[19][1]*SF[1] + P[19][0]*SF[3] + P[19][2]*SPP[0] - P[19][3]*SPP[2] - P[19][13]*SPP[4];
|
|
nextP[19][5] = P[19][5] + P[19][0]*SF[2] + P[19][2]*SF[1] + P[19][3]*SF[3] - P[19][1]*SPP[0] + P[19][13]*SPP[3];
|
|
nextP[19][6] = P[19][6] + P[19][1]*SF[2] + P[19][3]*SF[1] + P[19][0]*SPP[0] - P[19][2]*SPP[1] - P[19][13]*SPP[5];
|
|
nextP[19][7] = P[19][7] + P[19][4]*dt;
|
|
nextP[19][8] = P[19][8] + P[19][5]*dt;
|
|
nextP[19][9] = P[19][9] + P[19][6]*dt;
|
|
nextP[19][10] = P[19][10];
|
|
nextP[19][11] = P[19][11];
|
|
nextP[19][12] = P[19][12];
|
|
nextP[19][13] = P[19][13];
|
|
nextP[19][14] = P[19][14];
|
|
nextP[19][15] = P[19][15];
|
|
nextP[19][16] = P[19][16];
|
|
nextP[19][17] = P[19][17];
|
|
nextP[19][18] = P[19][18];
|
|
nextP[19][19] = P[19][19];
|
|
nextP[19][20] = P[19][20];
|
|
nextP[19][21] = P[19][21];
|
|
nextP[20][0] = P[20][0] + P[20][1]*SF[7] + P[20][2]*SF[9] + P[20][3]*SF[8] + P[20][10]*SF[11] + P[20][11]*SPP[7] + P[20][12]*SPP[6];
|
|
nextP[20][1] = P[20][1] + P[20][0]*SF[6] + P[20][2]*SF[5] + P[20][3]*SF[9] + P[20][11]*SPP[6] - P[20][12]*SPP[7] - (P[20][10]*q0)/2;
|
|
nextP[20][2] = P[20][2] + P[20][0]*SF[4] + P[20][1]*SF[8] + P[20][3]*SF[6] + P[20][12]*SF[11] - P[20][10]*SPP[6] - (P[20][11]*q0)/2;
|
|
nextP[20][3] = P[20][3] + P[20][0]*SF[5] + P[20][1]*SF[4] + P[20][2]*SF[7] - P[20][11]*SF[11] + P[20][10]*SPP[7] - (P[20][12]*q0)/2;
|
|
nextP[20][4] = P[20][4] + P[20][1]*SF[1] + P[20][0]*SF[3] + P[20][2]*SPP[0] - P[20][3]*SPP[2] - P[20][13]*SPP[4];
|
|
nextP[20][5] = P[20][5] + P[20][0]*SF[2] + P[20][2]*SF[1] + P[20][3]*SF[3] - P[20][1]*SPP[0] + P[20][13]*SPP[3];
|
|
nextP[20][6] = P[20][6] + P[20][1]*SF[2] + P[20][3]*SF[1] + P[20][0]*SPP[0] - P[20][2]*SPP[1] - P[20][13]*SPP[5];
|
|
nextP[20][7] = P[20][7] + P[20][4]*dt;
|
|
nextP[20][8] = P[20][8] + P[20][5]*dt;
|
|
nextP[20][9] = P[20][9] + P[20][6]*dt;
|
|
nextP[20][10] = P[20][10];
|
|
nextP[20][11] = P[20][11];
|
|
nextP[20][12] = P[20][12];
|
|
nextP[20][13] = P[20][13];
|
|
nextP[20][14] = P[20][14];
|
|
nextP[20][15] = P[20][15];
|
|
nextP[20][16] = P[20][16];
|
|
nextP[20][17] = P[20][17];
|
|
nextP[20][18] = P[20][18];
|
|
nextP[20][19] = P[20][19];
|
|
nextP[20][20] = P[20][20];
|
|
nextP[20][21] = P[20][21];
|
|
nextP[21][0] = P[21][0] + P[21][1]*SF[7] + P[21][2]*SF[9] + P[21][3]*SF[8] + P[21][10]*SF[11] + P[21][11]*SPP[7] + P[21][12]*SPP[6];
|
|
nextP[21][1] = P[21][1] + P[21][0]*SF[6] + P[21][2]*SF[5] + P[21][3]*SF[9] + P[21][11]*SPP[6] - P[21][12]*SPP[7] - (P[21][10]*q0)/2;
|
|
nextP[21][2] = P[21][2] + P[21][0]*SF[4] + P[21][1]*SF[8] + P[21][3]*SF[6] + P[21][12]*SF[11] - P[21][10]*SPP[6] - (P[21][11]*q0)/2;
|
|
nextP[21][3] = P[21][3] + P[21][0]*SF[5] + P[21][1]*SF[4] + P[21][2]*SF[7] - P[21][11]*SF[11] + P[21][10]*SPP[7] - (P[21][12]*q0)/2;
|
|
nextP[21][4] = P[21][4] + P[21][1]*SF[1] + P[21][0]*SF[3] + P[21][2]*SPP[0] - P[21][3]*SPP[2] - P[21][13]*SPP[4];
|
|
nextP[21][5] = P[21][5] + P[21][0]*SF[2] + P[21][2]*SF[1] + P[21][3]*SF[3] - P[21][1]*SPP[0] + P[21][13]*SPP[3];
|
|
nextP[21][6] = P[21][6] + P[21][1]*SF[2] + P[21][3]*SF[1] + P[21][0]*SPP[0] - P[21][2]*SPP[1] - P[21][13]*SPP[5];
|
|
nextP[21][7] = P[21][7] + P[21][4]*dt;
|
|
nextP[21][8] = P[21][8] + P[21][5]*dt;
|
|
nextP[21][9] = P[21][9] + P[21][6]*dt;
|
|
nextP[21][10] = P[21][10];
|
|
nextP[21][11] = P[21][11];
|
|
nextP[21][12] = P[21][12];
|
|
nextP[21][13] = P[21][13];
|
|
nextP[21][14] = P[21][14];
|
|
nextP[21][15] = P[21][15];
|
|
nextP[21][16] = P[21][16];
|
|
nextP[21][17] = P[21][17];
|
|
nextP[21][18] = P[21][18];
|
|
nextP[21][19] = P[21][19];
|
|
nextP[21][20] = P[21][20];
|
|
nextP[21][21] = P[21][21];
|
|
|
|
// add the general state process noise variances
|
|
for (uint8_t i=0; i<= 21; i++)
|
|
{
|
|
nextP[i][i] = nextP[i][i] + processNoise[i];
|
|
}
|
|
|
|
// if the total position variance exceeds 1E6 (1000m), then stop covariance
|
|
// growth by setting the predicted to the previous values
|
|
// This prevent an ill conditioned matrix from occurring for long periods
|
|
// without GPS
|
|
if ((P[7][7] + P[8][8]) > 1e6f)
|
|
{
|
|
for (uint8_t i=7; i<=8; i++)
|
|
{
|
|
for (uint8_t j=0; j<=21; j++)
|
|
{
|
|
nextP[i][j] = P[i][j];
|
|
nextP[j][i] = P[j][i];
|
|
}
|
|
}
|
|
}
|
|
|
|
// copy covariances to output and fix numerical errors
|
|
CopyAndFixCovariances();
|
|
|
|
// constrain diagonals to prevent ill-conditioning
|
|
ConstrainVariances();
|
|
|
|
perf_end(_perf_CovariancePrediction);
|
|
}
|
|
|
|
// fuse selected position, velocity and height measurements, checking dat for consistency
|
|
// provide a static mode that allows maintenance of the attitude reference without GPS provided the vehicle is not accelerating
|
|
// check innovation consistency of velocity states calculated using IMU1 and IMU2 and calculate the optimal weighting of accel data
|
|
void NavEKF::FuseVelPosNED()
|
|
{
|
|
// start performance timer
|
|
perf_begin(_perf_FuseVelPosNED);
|
|
|
|
// health is set bad until test passed
|
|
velHealth = false;
|
|
posHealth = false;
|
|
hgtHealth = false;
|
|
|
|
// declare variables used to check measurement errors
|
|
Vector3f velInnov;
|
|
Vector3f velInnov1;
|
|
Vector3f velInnov2;
|
|
Vector2 posInnov;
|
|
float hgtInnov = 0;
|
|
|
|
// declare variables used to control access to arrays
|
|
bool fuseData[6] = {false,false,false,false,false,false};
|
|
uint8_t stateIndex;
|
|
uint8_t obsIndex;
|
|
|
|
// declare variables used by state and covariance update calculations
|
|
float NEvelErr;
|
|
float DvelErr;
|
|
float posErr;
|
|
Vector6 R_OBS;
|
|
Vector6 observation;
|
|
float SK;
|
|
|
|
// perform sequential fusion of GPS measurements. This assumes that the
|
|
// errors in the different velocity and position components are
|
|
// uncorrelated which is not true, however in the absence of covariance
|
|
// data from the GPS receiver it is the only assumption we can make
|
|
// so we might as well take advantage of the computational efficiencies
|
|
// associated with sequential fusion
|
|
if (fuseVelData || fusePosData || fuseHgtData) {
|
|
|
|
// if static mode is active use the current states to calculate the predicted
|
|
// measurement rather than use states from a previous time. We need to do this
|
|
// because there may be no stored states due to lack of real measurements.
|
|
// in static mode, only position and height fusion is used
|
|
if (staticMode) {
|
|
statesAtPosTime = state;
|
|
statesAtHgtTime = state;
|
|
}
|
|
|
|
// set the GPS data timeout depending on whether airspeed data is present
|
|
uint32_t gpsRetryTime;
|
|
if (useAirspeed()) gpsRetryTime = _gpsRetryTimeUseTAS;
|
|
else gpsRetryTime = _gpsRetryTimeNoTAS;
|
|
|
|
// form the observation vector and zero velocity and horizontal position observations if in static mode
|
|
if (!staticMode) {
|
|
for (uint8_t i=0; i<=2; i++) observation[i] = velNED[i];
|
|
observation[3] = gpsPosNE.x + gpsPosGlitchOffsetNE.x;
|
|
observation[4] = gpsPosNE.y + gpsPosGlitchOffsetNE.y;
|
|
} else {
|
|
for (uint8_t i=0; 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] = gpsVarScaler*(sq(constrain_float(_gpsHorizVelNoise, 0.05f, 5.0f)) + sq(NEvelErr));
|
|
R_OBS[1] = R_OBS[0];
|
|
R_OBS[2] = gpsVarScaler*(sq(constrain_float(_gpsVertVelNoise, 0.05f, 5.0f)) + sq(DvelErr));
|
|
R_OBS[3] = gpsVarScaler*(sq(constrain_float(_gpsHorizPosNoise, 0.1f, 10.0f)) + sq(posErr));
|
|
R_OBS[4] = R_OBS[3];
|
|
R_OBS[5] = hgtVarScaler*sq(constrain_float(_baroAltNoise, 0.1f, 10.0f));
|
|
|
|
// if vertical GPS velocity data is being used, check to see if the GPS vertical velocity and barometer
|
|
// innovations have the same sign and are outside limits. If so, then it is likely aliasing is affecting
|
|
// the accelerometers and we should disable the GPS and barometer innovation consistency checks.
|
|
bool badIMUdata = false;
|
|
if (_fusionModeGPS == 0 && fuseVelData && fuseHgtData) {
|
|
// calculate innovations for height and vertical GPS vel measurements
|
|
float hgtErr = statesAtVelTime.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 * accNavMagHoriz);
|
|
float maxPosInnov2 = sq(_gpsPosInnovGate * _gpsHorizPosNoise + 0.005f * accelScale * float(_gpsGlitchAccelMax) * sq(0.001f * float(hal.scheduler->millis() - posFailTime)));
|
|
posTestRatio = (sq(posInnov[0]) + sq(posInnov[1])) / maxPosInnov2;
|
|
posHealth = ((posTestRatio < 1.0f) || badIMUdata);
|
|
// declare a timeout condition if we have been too long without data
|
|
posTimeout = ((hal.scheduler->millis() - posFailTime) > gpsRetryTime);
|
|
// use position data if healthy, timed out, or in static mode
|
|
if (posHealth || posTimeout || staticMode) {
|
|
posHealth = true;
|
|
posFailTime = hal.scheduler->millis();
|
|
// 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) {
|
|
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 singloe IMU velocity states using
|
|
// observation error to normalise
|
|
float R_hgt;
|
|
if (i == 2) {
|
|
R_hgt = sq(constrain_float(_gpsVertVelNoise, 0.05f, 5.0f));
|
|
} else {
|
|
R_hgt = sq(constrain_float(_gpsHorizVelNoise, 0.05f, 5.0f));
|
|
}
|
|
K1 += R_hgt / (R_hgt + sq(velInnov1[i]));
|
|
K2 += R_hgt / (R_hgt + sq(velInnov2[i]));
|
|
// sum the innovation and innovation variances
|
|
innovVelSumSq += sq(velInnov[i]);
|
|
varVelSum += varInnovVelPos[i];
|
|
}
|
|
// calculate weighting used by fuseVelPosNED to do IMU accel data blending
|
|
// this is used to detect and compensate for aliasing errors with the accelerometers
|
|
// provide for a first order lowpass filter to reduce noise on the weighting if required
|
|
IMU1_weighting = 1.0f * (K1 / (K1 + K2)) + 0.0f * IMU1_weighting; // filter currently inactive
|
|
// apply an innovation consistency threshold test, but don't fail if bad IMU data
|
|
// calculate the test ratio
|
|
velTestRatio = innovVelSumSq / (varVelSum * sq(_gpsVelInnovGate));
|
|
// fail if the ratio is greater than 1
|
|
velHealth = ((velTestRatio < 1.0f) || badIMUdata);
|
|
// declare a timeout if we have not fused velocity data for too long
|
|
velTimeout = (hal.scheduler->millis() - velFailTime) > gpsRetryTime;
|
|
// if data is healthy or in static mode we fuse it
|
|
if (velHealth || staticMode) {
|
|
velHealth = true;
|
|
velFailTime = hal.scheduler->millis();
|
|
} else if (velTimeout && !posHealth) {
|
|
// if data is not healthy and timed out and position is unhealthy we reset the velocity, but do not fuse data on this time step
|
|
ResetVelocity();
|
|
StoreStatesReset();
|
|
fuseVelData = false;
|
|
} else {
|
|
// if data is unhealthy and position is healthy, we do not fuse it
|
|
velHealth = false;
|
|
}
|
|
}
|
|
|
|
// test height measurements
|
|
if (fuseHgtData) {
|
|
// set the height data timeout depending on whether vertical velocity data is being used
|
|
uint32_t hgtRetryTime;
|
|
if (_fusionModeGPS == 0) hgtRetryTime = _hgtRetryTimeMode0;
|
|
else hgtRetryTime = _hgtRetryTimeMode12;
|
|
// calculate height innovations
|
|
hgtInnov = statesAtHgtTime.position.z - observation[5];
|
|
varInnovVelPos[5] = P[9][9] + R_OBS[5];
|
|
// calculate the innovation consistency test ratio
|
|
hgtTestRatio = sq(hgtInnov) / (sq(_hgtInnovGate) * varInnovVelPos[5]);
|
|
// fail if the ratio is > 1, but don't fail if bad IMU data
|
|
hgtHealth = ((hgtTestRatio < 1.0f) || badIMUdata);
|
|
hgtTimeout = (hal.scheduler->millis() - hgtFailTime) > hgtRetryTime;
|
|
// Fuse height data if healthy or timed out or in static mode
|
|
if (hgtHealth || hgtTimeout || staticMode) {
|
|
hgtHealth = true;
|
|
hgtFailTime = hal.scheduler->millis();
|
|
// if timed out, reset the height, but do not fuse data on this time step
|
|
if (hgtTimeout) {
|
|
ResetHeight();
|
|
StoreStatesReset();
|
|
fuseHgtData = false;
|
|
}
|
|
}
|
|
else {
|
|
hgtHealth = false;
|
|
}
|
|
}
|
|
|
|
// set range for sequential fusion of velocity and position measurements depending on which data is available and its health
|
|
if (fuseVelData && _fusionModeGPS == 0 && velHealth && !staticMode) {
|
|
fuseData[0] = true;
|
|
fuseData[1] = true;
|
|
fuseData[2] = true;
|
|
}
|
|
if (fuseVelData && _fusionModeGPS == 1 && velHealth && !staticMode) {
|
|
fuseData[0] = true;
|
|
fuseData[1] = true;
|
|
}
|
|
if ((fusePosData && _fusionModeGPS <= 2 && posHealth) || staticMode) {
|
|
fuseData[3] = true;
|
|
fuseData[4] = true;
|
|
}
|
|
if ((fuseHgtData && hgtHealth) || staticMode) {
|
|
fuseData[5] = true;
|
|
}
|
|
|
|
// 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
|
|
if (obsIndex <= 2)
|
|
{
|
|
innovVelPos[obsIndex] = statesAtVelTime.velocity[obsIndex] - observation[obsIndex];
|
|
}
|
|
else if (obsIndex == 3 || obsIndex == 4) {
|
|
innovVelPos[obsIndex] = statesAtPosTime.position[obsIndex-3] - observation[obsIndex];
|
|
} else {
|
|
innovVelPos[obsIndex] = statesAtHgtTime.position[obsIndex-3] - observation[obsIndex];
|
|
}
|
|
|
|
// calculate the Kalman gain and calculate innovation variances
|
|
varInnovVelPos[obsIndex] = P[stateIndex][stateIndex] + R_OBS[obsIndex];
|
|
SK = 1.0f/varInnovVelPos[obsIndex];
|
|
for (uint8_t i= 0; i<=12; i++) {
|
|
Kfusion[i] = P[i][stateIndex]*SK;
|
|
}
|
|
// Only height observations are used to update z accel bias estimate
|
|
// Protect Kalman gain from ill-conditioning
|
|
// Don't update Z accel bias if off-level by greater than 60 degrees to avoid scale factor error effects
|
|
if (obsIndex == 5 && prevTnb.c.z > 0.5f) {
|
|
Kfusion[13] = constrain_float(P[13][stateIndex]*SK,-1.0f,0.0f);
|
|
} else {
|
|
Kfusion[13] = 0.0f;
|
|
}
|
|
// inhibit wind state estimation by setting Kalman gains to zero
|
|
if (!inhibitWindStates) {
|
|
Kfusion[14] = P[14][stateIndex]*SK;
|
|
Kfusion[15] = P[15][stateIndex]*SK;
|
|
} else {
|
|
Kfusion[14] = 0.0f;
|
|
Kfusion[15] = 0.0f;
|
|
}
|
|
// inhibit magnetic field state estimation by setting Kalman gains to zero
|
|
if (!inhibitMagStates) {
|
|
for (uint8_t i = 16; i<=21; i++) {
|
|
Kfusion[i] = P[i][stateIndex]*SK;
|
|
}
|
|
} else {
|
|
for (uint8_t i = 16; i<=21; i++) {
|
|
Kfusion[i] = 0.0f;
|
|
}
|
|
}
|
|
// Set the Kalman gain values for the single IMU states
|
|
Kfusion[22] = Kfusion[13]; // IMU2 Z accel bias
|
|
Kfusion[26] = Kfusion[9]; // IMU1 posD
|
|
Kfusion[30] = Kfusion[9]; // IMU2 posD
|
|
for (uint8_t i = 0; i<=2; i++) {
|
|
Kfusion[i+23] = Kfusion[i+4]; // IMU1 velNED
|
|
Kfusion[i+27] = Kfusion[i+4]; // IMU2 velNED
|
|
}
|
|
|
|
// Correct states that have been predicted using single (not blended) IMU data
|
|
if (obsIndex == 5){
|
|
// Calculate height measurement innovations using single IMU states
|
|
float hgtInnov1 = statesAtHgtTime.posD1 - observation[obsIndex];
|
|
float hgtInnov2 = statesAtHgtTime.posD2 - observation[obsIndex];
|
|
// Correct single IMU prediction states using height measurement, limiting rate of change of bias to 0.02 m/s3
|
|
float correctionLimit = 0.02f * dtIMU *dtVelPos;
|
|
states[13] = states[13] - constrain_float(Kfusion[13] * hgtInnov1, -correctionLimit, correctionLimit); // IMU1 Z accel bias
|
|
states[22] = states[22] - 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 blended IMU data predicted states
|
|
for (uint8_t i = 0; i<=21; i++) {
|
|
states[i] = states[i] - Kfusion[i] * innovVelPos[obsIndex];
|
|
}
|
|
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 me 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()
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{
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// start performance timer
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perf_begin(_perf_FuseMagnetometer);
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// declarations
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ftype &q0 = mag_state.q0;
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ftype &q1 = mag_state.q1;
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ftype &q2 = mag_state.q2;
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ftype &q3 = mag_state.q3;
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ftype &magN = mag_state.magN;
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ftype &magE = mag_state.magE;
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ftype &magD = mag_state.magD;
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ftype &magXbias = mag_state.magXbias;
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ftype &magYbias = mag_state.magYbias;
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ftype &magZbias = mag_state.magZbias;
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uint8_t &obsIndex = mag_state.obsIndex;
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Matrix3f &DCM = mag_state.DCM;
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Vector3f &MagPred = mag_state.MagPred;
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ftype &R_MAG = mag_state.R_MAG;
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ftype *SH_MAG = &mag_state.SH_MAG[0];
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Vector22 H_MAG;
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Vector6 SK_MX;
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Vector6 SK_MY;
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Vector6 SK_MZ;
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// perform sequential fusion of magnetometer measurements.
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// this assumes that the errors in the different components are
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// uncorrelated which is not true, however in the absence of covariance
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// data fit is the only assumption we can make
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// so we might as well take advantage of the computational efficiencies
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// associated with sequential fusion
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if (fuseMagData || obsIndex == 1 || obsIndex == 2)
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{
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// calculate observation jacobians and Kalman gains
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if (fuseMagData)
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{
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// copy required states to local variable names
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q0 = statesAtMagMeasTime.quat[0];
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q1 = statesAtMagMeasTime.quat[1];
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q2 = statesAtMagMeasTime.quat[2];
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q3 = statesAtMagMeasTime.quat[3];
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magN = statesAtMagMeasTime.earth_magfield[0];
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magE = statesAtMagMeasTime.earth_magfield[1];
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magD = statesAtMagMeasTime.earth_magfield[2];
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magXbias = statesAtMagMeasTime.body_magfield[0];
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magYbias = statesAtMagMeasTime.body_magfield[1];
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magZbias = statesAtMagMeasTime.body_magfield[2];
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// rotate predicted earth components into body axes and calculate
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// predicted measurements
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DCM[0][0] = q0*q0 + q1*q1 - q2*q2 - q3*q3;
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DCM[0][1] = 2*(q1*q2 + q0*q3);
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DCM[0][2] = 2*(q1*q3-q0*q2);
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DCM[1][0] = 2*(q1*q2 - q0*q3);
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DCM[1][1] = q0*q0 - q1*q1 + q2*q2 - q3*q3;
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DCM[1][2] = 2*(q2*q3 + q0*q1);
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DCM[2][0] = 2*(q1*q3 + q0*q2);
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DCM[2][1] = 2*(q2*q3 - q0*q1);
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DCM[2][2] = q0*q0 - q1*q1 - q2*q2 + q3*q3;
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MagPred[0] = DCM[0][0]*magN + DCM[0][1]*magE + DCM[0][2]*magD + magXbias;
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MagPred[1] = DCM[1][0]*magN + DCM[1][1]*magE + DCM[1][2]*magD + magYbias;
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MagPred[2] = DCM[2][0]*magN + DCM[2][1]*magE + DCM[2][2]*magD + magZbias;
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// scale magnetometer observation error with total angular rate
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R_MAG = sq(constrain_float(_magNoise, 0.01f, 0.5f)) + sq(_magVarRateScale*dAngIMU.length() / dtIMU);
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// calculate observation jacobians
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SH_MAG[0] = 2*magD*q3 + 2*magE*q2 + 2*magN*q1;
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SH_MAG[1] = 2*magD*q0 - 2*magE*q1 + 2*magN*q2;
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SH_MAG[2] = 2*magD*q1 + 2*magE*q0 - 2*magN*q3;
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SH_MAG[3] = sq(q3);
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SH_MAG[4] = sq(q2);
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SH_MAG[5] = sq(q1);
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SH_MAG[6] = sq(q0);
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SH_MAG[7] = 2*magN*q0;
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SH_MAG[8] = 2*magE*q3;
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for (uint8_t i=0; i<=21; i++) H_MAG[i] = 0;
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H_MAG[0] = SH_MAG[7] + SH_MAG[8] - 2*magD*q2;
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H_MAG[1] = SH_MAG[0];
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H_MAG[2] = 2*magE*q1 - 2*magD*q0 - 2*magN*q2;
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H_MAG[3] = SH_MAG[2];
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H_MAG[16] = SH_MAG[5] - SH_MAG[4] - SH_MAG[3] + SH_MAG[6];
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H_MAG[17] = 2*q0*q3 + 2*q1*q2;
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H_MAG[18] = 2*q1*q3 - 2*q0*q2;
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H_MAG[19] = 1;
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// calculate Kalman gain
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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));
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if (temp >= R_MAG) {
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SK_MX[0] = 1.0f / temp;
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faultStatus.bad_xmag = false;
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} else {
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// the calculation is badly conditioned, so we cannot perform fusion on this step
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// we increase the state variances and try again next time
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P[19][19] += 0.1f*R_MAG;
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obsIndex = 1;
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faultStatus.bad_xmag = true;
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return;
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}
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SK_MX[1] = SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6];
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SK_MX[2] = 2*magD*q0 - 2*magE*q1 + 2*magN*q2;
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SK_MX[3] = SH_MAG[7] + SH_MAG[8] - 2*magD*q2;
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SK_MX[4] = 2*q0*q2 - 2*q1*q3;
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SK_MX[5] = 2*q0*q3 + 2*q1*q2;
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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// this term has been zeroed to improve stability of the Z accel bias
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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]);
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// zero Kalman gains to inhibit wind state estimation
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if (!inhibitWindStates) {
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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]);
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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]);
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} else {
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Kfusion[14] = 0.0;
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Kfusion[15] = 0.0;
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}
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// zero Kalman gains to inhibit magnetic field state estimation
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if (!inhibitMagStates) {
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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} else {
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for (uint8_t i=16; i<=21; i++) {
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Kfusion[i] = 0.0f;
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}
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}
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// calculate the observation innovation variance
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varInnovMag[0] = 1.0f/SK_MX[0];
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// reset the observation index to 0 (we start by fusing the X measurement)
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obsIndex = 0;
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// set flags to indicate to other processes that fusion has been performed and is required on the next frame
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// this can be used by other fusion processes to avoid fusing on the same frame as this expensive step
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magFusePerformed = true;
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magFuseRequired = true;
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}
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else if (obsIndex == 1) // we are now fusing the Y measurement
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{
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// calculate observation jacobians
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for (uint8_t i=0; i<=21; i++) H_MAG[i] = 0;
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H_MAG[0] = SH_MAG[2];
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H_MAG[1] = SH_MAG[1];
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H_MAG[2] = SH_MAG[0];
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H_MAG[3] = 2*magD*q2 - SH_MAG[8] - SH_MAG[7];
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H_MAG[16] = 2*q1*q2 - 2*q0*q3;
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H_MAG[17] = SH_MAG[4] - SH_MAG[3] - SH_MAG[5] + SH_MAG[6];
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H_MAG[18] = 2*q0*q1 + 2*q2*q3;
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H_MAG[20] = 1;
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// calculate Kalman gain
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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));
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if (temp >= R_MAG) {
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SK_MY[0] = 1.0f / temp;
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faultStatus.bad_ymag = false;
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} else {
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// the calculation is badly conditioned, so we cannot perform fusion on this step
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// we increase the state variances and try again next time
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P[20][20] += 0.1f*R_MAG;
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obsIndex = 2;
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faultStatus.bad_ymag = true;
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return;
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}
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SK_MY[1] = SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6];
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SK_MY[2] = SH_MAG[7] + SH_MAG[8] - 2*magD*q2;
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SK_MY[3] = 2*q0*q3 - 2*q1*q2;
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SK_MY[4] = 2*q0*q1 + 2*q2*q3;
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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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]);
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// 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]);
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|
// 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]);
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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]);
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} else {
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|
Kfusion[14] = 0.0;
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|
Kfusion[15] = 0.0;
|
|
}
|
|
// zero Kalman gains to inhibit magnetic field state estimation
|
|
if (!inhibitMagStates) {
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|
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]);
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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]);
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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]);
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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]);
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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]);
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|
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]);
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|
} 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)) {
|
|
// correct the state vector
|
|
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;
|
|
}
|
|
states[j] = states[j] - Kfusion[j] * innovMag[obsIndex];
|
|
}
|
|
// 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);
|
|
}
|
|
|
|
// fuse true airspeed measurements
|
|
void NavEKF::FuseAirspeed()
|
|
{
|
|
// start performance timer
|
|
perf_begin(_perf_FuseAirspeed);
|
|
|
|
// declarations
|
|
float vn;
|
|
float ve;
|
|
float vd;
|
|
float vwn;
|
|
float vwe;
|
|
float EAS2TAS = _ahrs->get_EAS2TAS();
|
|
const float R_TAS = sq(constrain_float(_easNoise, 0.5f, 5.0f) * constrain_float(EAS2TAS, 0.9f, 10.0f));
|
|
Vector3f SH_TAS;
|
|
float SK_TAS;
|
|
Vector22 H_TAS;
|
|
float VtasPred;
|
|
|
|
// copy required states to local variable names
|
|
vn = statesAtVtasMeasTime.velocity.x;
|
|
ve = statesAtVtasMeasTime.velocity.y;
|
|
vd = statesAtVtasMeasTime.velocity.z;
|
|
vwn = statesAtVtasMeasTime.wind_vel.x;
|
|
vwe = statesAtVtasMeasTime.wind_vel.y;
|
|
|
|
// calculate the predicted airspeed
|
|
VtasPred = pythagorous3((ve - vwe) , (vn - vwn) , vd);
|
|
// perform fusion of True Airspeed measurement
|
|
if (VtasPred > 1.0f)
|
|
{
|
|
// calculate observation jacobians
|
|
SH_TAS[0] = 1.0f/VtasPred;
|
|
SH_TAS[1] = (SH_TAS[0]*(2*ve - 2*vwe))/2;
|
|
SH_TAS[2] = (SH_TAS[0]*(2*vn - 2*vwn))/2;
|
|
for (uint8_t i=0; i<=21; i++) H_TAS[i] = 0.0f;
|
|
H_TAS[4] = SH_TAS[2];
|
|
H_TAS[5] = SH_TAS[1];
|
|
H_TAS[6] = vd*SH_TAS[0];
|
|
H_TAS[14] = -SH_TAS[2];
|
|
H_TAS[15] = -SH_TAS[1];
|
|
|
|
// calculate Kalman gains
|
|
float temp = (R_TAS + SH_TAS[2]*(P[4][4]*SH_TAS[2] + P[5][4]*SH_TAS[1] - P[14][4]*SH_TAS[2] - P[15][4]*SH_TAS[1] + P[6][4]*vd*SH_TAS[0]) + SH_TAS[1]*(P[4][5]*SH_TAS[2] + P[5][5]*SH_TAS[1] - P[14][5]*SH_TAS[2] - P[15][5]*SH_TAS[1] + P[6][5]*vd*SH_TAS[0]) - SH_TAS[2]*(P[4][14]*SH_TAS[2] + P[5][14]*SH_TAS[1] - P[14][14]*SH_TAS[2] - P[15][14]*SH_TAS[1] + P[6][14]*vd*SH_TAS[0]) - SH_TAS[1]*(P[4][15]*SH_TAS[2] + P[5][15]*SH_TAS[1] - P[14][15]*SH_TAS[2] - P[15][15]*SH_TAS[1] + P[6][15]*vd*SH_TAS[0]) + vd*SH_TAS[0]*(P[4][6]*SH_TAS[2] + P[5][6]*SH_TAS[1] - P[14][6]*SH_TAS[2] - P[15][6]*SH_TAS[1] + P[6][6]*vd*SH_TAS[0]));
|
|
if (temp >= R_TAS) {
|
|
SK_TAS = 1.0f / temp;
|
|
faultStatus.bad_airspeed = false;
|
|
} else {
|
|
// the calculation is badly conditioned, so we cannot perform fusion on this step
|
|
// we increase the wind state variances and try again next time
|
|
P[14][14] += 0.05f*R_TAS;
|
|
P[15][15] += 0.05f*R_TAS;
|
|
faultStatus.bad_airspeed = true;
|
|
return;
|
|
}
|
|
Kfusion[0] = SK_TAS*(P[0][4]*SH_TAS[2] - P[0][14]*SH_TAS[2] + P[0][5]*SH_TAS[1] - P[0][15]*SH_TAS[1] + P[0][6]*vd*SH_TAS[0]);
|
|
Kfusion[1] = SK_TAS*(P[1][4]*SH_TAS[2] - P[1][14]*SH_TAS[2] + P[1][5]*SH_TAS[1] - P[1][15]*SH_TAS[1] + P[1][6]*vd*SH_TAS[0]);
|
|
Kfusion[2] = SK_TAS*(P[2][4]*SH_TAS[2] - P[2][14]*SH_TAS[2] + P[2][5]*SH_TAS[1] - P[2][15]*SH_TAS[1] + P[2][6]*vd*SH_TAS[0]);
|
|
Kfusion[3] = SK_TAS*(P[3][4]*SH_TAS[2] - P[3][14]*SH_TAS[2] + P[3][5]*SH_TAS[1] - P[3][15]*SH_TAS[1] + P[3][6]*vd*SH_TAS[0]);
|
|
Kfusion[4] = SK_TAS*(P[4][4]*SH_TAS[2] - P[4][14]*SH_TAS[2] + P[4][5]*SH_TAS[1] - P[4][15]*SH_TAS[1] + P[4][6]*vd*SH_TAS[0]);
|
|
Kfusion[5] = SK_TAS*(P[5][4]*SH_TAS[2] - P[5][14]*SH_TAS[2] + P[5][5]*SH_TAS[1] - P[5][15]*SH_TAS[1] + P[5][6]*vd*SH_TAS[0]);
|
|
Kfusion[6] = SK_TAS*(P[6][4]*SH_TAS[2] - P[6][14]*SH_TAS[2] + P[6][5]*SH_TAS[1] - P[6][15]*SH_TAS[1] + P[6][6]*vd*SH_TAS[0]);
|
|
Kfusion[7] = SK_TAS*(P[7][4]*SH_TAS[2] - P[7][14]*SH_TAS[2] + P[7][5]*SH_TAS[1] - P[7][15]*SH_TAS[1] + P[7][6]*vd*SH_TAS[0]);
|
|
Kfusion[8] = SK_TAS*(P[8][4]*SH_TAS[2] - P[8][14]*SH_TAS[2] + P[8][5]*SH_TAS[1] - P[8][15]*SH_TAS[1] + P[8][6]*vd*SH_TAS[0]);
|
|
Kfusion[9] = SK_TAS*(P[9][4]*SH_TAS[2] - P[9][14]*SH_TAS[2] + P[9][5]*SH_TAS[1] - P[9][15]*SH_TAS[1] + P[9][6]*vd*SH_TAS[0]);
|
|
Kfusion[10] = SK_TAS*(P[10][4]*SH_TAS[2] - P[10][14]*SH_TAS[2] + P[10][5]*SH_TAS[1] - P[10][15]*SH_TAS[1] + P[10][6]*vd*SH_TAS[0]);
|
|
Kfusion[11] = SK_TAS*(P[11][4]*SH_TAS[2] - P[11][14]*SH_TAS[2] + P[11][5]*SH_TAS[1] - P[11][15]*SH_TAS[1] + P[11][6]*vd*SH_TAS[0]);
|
|
Kfusion[12] = SK_TAS*(P[12][4]*SH_TAS[2] - P[12][14]*SH_TAS[2] + P[12][5]*SH_TAS[1] - P[12][15]*SH_TAS[1] + P[12][6]*vd*SH_TAS[0]);
|
|
// this term has been zeroed to improve stability of the Z accel bias
|
|
Kfusion[13] = 0.0f;//SK_TAS*(P[13][4]*SH_TAS[2] - P[13][14]*SH_TAS[2] + P[13][5]*SH_TAS[1] - P[13][15]*SH_TAS[1] + P[13][6]*vd*SH_TAS[0]);
|
|
Kfusion[14] = SK_TAS*(P[14][4]*SH_TAS[2] - P[14][14]*SH_TAS[2] + P[14][5]*SH_TAS[1] - P[14][15]*SH_TAS[1] + P[14][6]*vd*SH_TAS[0]);
|
|
Kfusion[15] = SK_TAS*(P[15][4]*SH_TAS[2] - P[15][14]*SH_TAS[2] + P[15][5]*SH_TAS[1] - P[15][15]*SH_TAS[1] + P[15][6]*vd*SH_TAS[0]);
|
|
// zero Kalman gains to inhibit magnetic field state estimation
|
|
if (!inhibitMagStates) {
|
|
Kfusion[16] = SK_TAS*(P[16][4]*SH_TAS[2] - P[16][14]*SH_TAS[2] + P[16][5]*SH_TAS[1] - P[16][15]*SH_TAS[1] + P[16][6]*vd*SH_TAS[0]);
|
|
Kfusion[17] = SK_TAS*(P[17][4]*SH_TAS[2] - P[17][14]*SH_TAS[2] + P[17][5]*SH_TAS[1] - P[17][15]*SH_TAS[1] + P[17][6]*vd*SH_TAS[0]);
|
|
Kfusion[18] = SK_TAS*(P[18][4]*SH_TAS[2] - P[18][14]*SH_TAS[2] + P[18][5]*SH_TAS[1] - P[18][15]*SH_TAS[1] + P[18][6]*vd*SH_TAS[0]);
|
|
Kfusion[19] = SK_TAS*(P[19][4]*SH_TAS[2] - P[19][14]*SH_TAS[2] + P[19][5]*SH_TAS[1] - P[19][15]*SH_TAS[1] + P[19][6]*vd*SH_TAS[0]);
|
|
Kfusion[20] = SK_TAS*(P[20][4]*SH_TAS[2] - P[20][14]*SH_TAS[2] + P[20][5]*SH_TAS[1] - P[20][15]*SH_TAS[1] + P[20][6]*vd*SH_TAS[0]);
|
|
Kfusion[21] = SK_TAS*(P[21][4]*SH_TAS[2] - P[21][14]*SH_TAS[2] + P[21][5]*SH_TAS[1] - P[21][15]*SH_TAS[1] + P[21][6]*vd*SH_TAS[0]);
|
|
} else {
|
|
for (uint8_t i=16; i<=21; i++) {
|
|
Kfusion[i] = 0.0f;
|
|
}
|
|
}
|
|
|
|
// calculate measurement innovation variance
|
|
varInnovVtas = 1.0f/SK_TAS;
|
|
|
|
// calculate measurement innovation
|
|
innovVtas = VtasPred - VtasMeas;
|
|
|
|
// calculate the innovation consistency test ratio
|
|
tasTestRatio = sq(innovVtas) / (sq(_tasInnovGate) * varInnovVtas);
|
|
|
|
// test the ratio before fusing data
|
|
if (tasTestRatio < 1.0f)
|
|
{
|
|
// correct the state vector
|
|
for (uint8_t j=0; j<=21; j++)
|
|
{
|
|
states[j] = states[j] - Kfusion[j] * innovVtas;
|
|
}
|
|
|
|
Quaternion q(states[0], states[1], states[2], states[3]);
|
|
q.normalize();
|
|
for (uint8_t i = 0; i<=3; i++) {
|
|
states[i] = q[i];
|
|
}
|
|
// 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
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void NavEKF::FuseSideslip()
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{
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// start performance timer
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perf_begin(_perf_FuseSideslip);
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// declarations
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float q0;
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float q1;
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float q2;
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float q3;
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float vn;
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float ve;
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float vd;
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float vwn;
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float vwe;
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const float R_BETA = 0.03f; // assume a sideslip angle RMS of ~10 deg
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float SH_BETA[13];
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float SK_BETA[8];
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Vector3f vel_rel_wind;
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Vector22 H_BETA;
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float innovBeta;
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// copy required states to local variable names
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q0 = states[0];
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q1 = states[1];
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q2 = states[2];
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q3 = states[3];
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vn = states[4];
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ve = states[5];
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vd = states[6];
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vwn = states[14];
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vwe = states[15];
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// calculate predicted wind relative velocity in NED
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vel_rel_wind.x = vn - vwn;
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vel_rel_wind.y = ve - vwe;
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vel_rel_wind.z = vd;
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// rotate into body axes
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vel_rel_wind = prevTnb * vel_rel_wind;
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// perform fusion of assumed sideslip = 0
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if (vel_rel_wind.x > 5.0f)
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{
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// Calculate observation jacobians
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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);
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if (fabsf(SH_BETA[0]) <= 1e-9f) {
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faultStatus.bad_sideslip = true;
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return;
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} else {
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faultStatus.bad_sideslip = false;
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}
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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);
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SH_BETA[2] = vn - vwn;
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SH_BETA[3] = ve - vwe;
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SH_BETA[4] = 1/sq(SH_BETA[0]);
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SH_BETA[5] = 1/SH_BETA[0];
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SH_BETA[6] = SH_BETA[5]*(sq(q0) - sq(q1) + sq(q2) - sq(q3));
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SH_BETA[7] = sq(q0) + sq(q1) - sq(q2) - sq(q3);
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SH_BETA[8] = 2*q0*SH_BETA[3] - 2*q3*SH_BETA[2] + 2*q1*vd;
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SH_BETA[9] = 2*q0*SH_BETA[2] + 2*q3*SH_BETA[3] - 2*q2*vd;
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SH_BETA[10] = 2*q2*SH_BETA[2] - 2*q1*SH_BETA[3] + 2*q0*vd;
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SH_BETA[11] = 2*q1*SH_BETA[2] + 2*q2*SH_BETA[3] + 2*q3*vd;
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SH_BETA[12] = 2*q0*q3;
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for (uint8_t i=0; i<=21; i++) {
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H_BETA[i] = 0.0f;
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}
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H_BETA[0] = SH_BETA[5]*SH_BETA[8] - SH_BETA[1]*SH_BETA[4]*SH_BETA[9];
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H_BETA[1] = SH_BETA[5]*SH_BETA[10] - SH_BETA[1]*SH_BETA[4]*SH_BETA[11];
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H_BETA[2] = SH_BETA[5]*SH_BETA[11] + SH_BETA[1]*SH_BETA[4]*SH_BETA[10];
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H_BETA[3] = - SH_BETA[5]*SH_BETA[9] - SH_BETA[1]*SH_BETA[4]*SH_BETA[8];
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H_BETA[4] = - SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) - SH_BETA[1]*SH_BETA[4]*SH_BETA[7];
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H_BETA[5] = SH_BETA[6] - SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2);
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H_BETA[6] = SH_BETA[5]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[4]*(2*q0*q2 - 2*q1*q3);
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H_BETA[14] = SH_BETA[5]*(SH_BETA[12] - 2*q1*q2) + SH_BETA[1]*SH_BETA[4]*SH_BETA[7];
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H_BETA[15] = SH_BETA[1]*SH_BETA[4]*(SH_BETA[12] + 2*q1*q2) - SH_BETA[6];
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// Calculate Kalman gains
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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]);
|
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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]);
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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;
|
|
}
|
|
|
|
Quaternion q(states[0], states[1], states[2], states[3]);
|
|
q.normalize();
|
|
for (uint8_t i = 0; i<=3; i++) {
|
|
states[i] = q[i];
|
|
}
|
|
// 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 (hal.scheduler->millis() - lastStateStoreTime_ms >= 10) {
|
|
lastStateStoreTime_ms = hal.scheduler->millis();
|
|
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] = hal.scheduler->millis();
|
|
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;
|
|
}
|
|
}
|
|
|
|
// 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
|
|
{
|
|
Quaternion q(states[0], states[1], states[2], states[3]);
|
|
q.to_euler(&euler.x, &euler.y, &euler.z);
|
|
euler = euler - _ahrs->get_trim();
|
|
}
|
|
|
|
// return NED velocity in m/s
|
|
void NavEKF::getVelNED(Vector3f &vel) const
|
|
{
|
|
vel.x = states[4];
|
|
vel.y = states[5];
|
|
vel.z = states[6];
|
|
}
|
|
|
|
// return the last calculated NED position relative to the reference point (m).
|
|
// return false if no position is available
|
|
bool NavEKF::getPosNED(Vector3f &pos) const
|
|
{
|
|
pos.x = states[7];
|
|
pos.y = states[8];
|
|
pos.z = states[9];
|
|
return true;
|
|
}
|
|
|
|
// return body axis gyro bias estimates in rad/sec
|
|
void NavEKF::getGyroBias(Vector3f &gyroBias) const
|
|
{
|
|
if (dtIMU == 0) {
|
|
gyroBias.zero();
|
|
return;
|
|
}
|
|
gyroBias.x = states[10] / dtIMU;
|
|
gyroBias.y = states[11] / dtIMU;
|
|
gyroBias.z = states[12] / dtIMU;
|
|
}
|
|
|
|
// return weighting of first IMU in blending function and the individual Z-accel bias estimates in m/s^2
|
|
void NavEKF::getAccelBias(Vector3f &accelBias) const
|
|
{
|
|
accelBias.x = IMU1_weighting;
|
|
if (dtIMU == 0) {
|
|
accelBias.y = 0;
|
|
accelBias.z = 0;
|
|
} else {
|
|
accelBias.y = states[22] / dtIMU;
|
|
accelBias.z = states[13] / dtIMU;
|
|
}
|
|
}
|
|
|
|
// 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 = states[14];
|
|
wind.y = states[15];
|
|
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.x = states[16]*1000.0f;
|
|
magNED.y = states[17]*1000.0f;
|
|
magNED.z = states[18]*1000.0f;
|
|
}
|
|
|
|
// return body magnetic field estimates in measurement units / 1000
|
|
void NavEKF::getMagXYZ(Vector3f &magXYZ) const
|
|
{
|
|
magXYZ.x = states[19]*1000.0f;
|
|
magXYZ.y = states[20]*1000.0f;
|
|
magXYZ.z = states[21]*1000.0f;
|
|
}
|
|
|
|
// return the last calculated latitude, longitude and height
|
|
bool NavEKF::getLLH(struct Location &loc) const
|
|
{
|
|
loc.lat = _ahrs->get_home().lat;
|
|
loc.lng = _ahrs->get_home().lng;
|
|
loc.alt = _ahrs->get_home().alt - states[9]*100;
|
|
location_offset(loc, states[7], states[8]);
|
|
return true;
|
|
}
|
|
|
|
// calculate whether the flight vehicle is on the ground or flying from height, airspeed and GPS speed
|
|
void NavEKF::SetFlightAndFusionModes()
|
|
{
|
|
const AP_Airspeed *airspeed = _ahrs->get_airspeed();
|
|
uint8_t highAirSpd = (airspeed && airspeed->use() && airspeed->get_airspeed() * airspeed->get_EAS2TAS() > 8.0f);
|
|
float gndSpdSq = sq(velNED[0]) + sq(velNED[1]);
|
|
uint8_t highGndSpdStage1 = (uint8_t)(gndSpdSq > 9.0f);
|
|
uint8_t highGndSpdStage2 = (uint8_t)(gndSpdSq > 36.0f);
|
|
uint8_t highGndSpdStage3 = (uint8_t)(gndSpdSq > 81.0f);
|
|
uint8_t largeHgt = (uint8_t)(fabsf(hgtMea) > 15.0f);
|
|
uint8_t inAirSum = highAirSpd + highGndSpdStage1 + highGndSpdStage2 + highGndSpdStage3 + largeHgt;
|
|
// if magnetometer calibration mode 1 is selected, use a manoeuvre threshold test
|
|
// otherwise use a height and velocity test
|
|
if ((_magCal == 1) && (accNavMagHoriz > 0.5f) && !static_mode_demanded() && use_compass()) {
|
|
onGround = false;
|
|
} else {
|
|
// detect on-ground to in-air transition
|
|
// if we are already on the ground then 3 or more out of 5 criteria are required
|
|
// if we are in the air then only 2 or more are required
|
|
// this prevents rapid tansitions
|
|
if ((onGround && (inAirSum >= 3)) || (!onGround && (inAirSum >= 2))) {
|
|
onGround = false;
|
|
} else {
|
|
onGround = true;
|
|
}
|
|
// force a yaw alignment if exiting onGround without a compass or if compass is timed out and we are a fly forward vehicle
|
|
if (!onGround && prevOnGround && (!use_compass() || (magTimeout && assume_zero_sideslip()))) {
|
|
alignYawGPS();
|
|
}
|
|
// If we are flying a fly-forward type vehicle without an airspeed sensor and exiting onGround
|
|
// we set the wind velocity to the reciprocal of the velocity vector and scale states so that the
|
|
// wind speed is equal to the 6m/s. This prevents 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
|
|
if (!onGround && prevOnGround && !useAirspeed() && assume_zero_sideslip()) {
|
|
setWindVelStates();
|
|
}
|
|
}
|
|
// store current on-ground status for next time
|
|
prevOnGround = onGround;
|
|
// If we are on ground, or in static mode, or don't have the right vehicle and sensing to estimate wind, inhibit wind states
|
|
inhibitWindStates = ((!useAirspeed() && !assume_zero_sideslip()) || onGround || staticMode);
|
|
// If magnetometer calibration mode is turned off by the user or we are on ground or in static mode, then inhibit magnetometer states
|
|
inhibitMagStates = ((_magCal == 2) || !use_compass() || onGround || staticMode);
|
|
}
|
|
|
|
// 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(0.1f * 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];
|
|
}
|
|
|
|
// 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++)
|
|
{
|
|
if (fabsf(P[i][j]) > EKF_COVARIENCE_MAX ||
|
|
fabsf(P[j][i]) > EKF_COVARIENCE_MAX) {
|
|
// set the filter status as diverged and re-initialise the filter
|
|
filterDiverged = true;
|
|
faultStatus.diverged = true;
|
|
lastDivergeTime_ms = hal.scheduler->millis();
|
|
InitialiseFilterDynamic();
|
|
return;
|
|
}
|
|
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)
|
|
|
|
// get the time the IMU data was read
|
|
IMUmsec = 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 accels 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, (IMUmsec - constrain_int16(_msecVelDelay, 0, 500)));
|
|
RecallStates(statesAtPosTime, (IMUmsec - constrain_int16(_msecPosDelay, 0, 500)));
|
|
|
|
// read the NED velocity from the GPS
|
|
velNED = _ahrs->get_gps().velocity();
|
|
|
|
// Check if GPS can output vertical velocity and set GPS fusion mode accordingly
|
|
if (!_ahrs->get_gps().have_vertical_velocity()) {
|
|
// vertical velocity should not be fused
|
|
if (_fusionModeGPS == 0) {
|
|
_fusionModeGPS = 1;
|
|
}
|
|
}
|
|
|
|
// read latitutde and longitude from GPS and convert to NE position
|
|
const struct Location &gpsloc = _ahrs->get_gps().location();
|
|
gpsPosNE = location_diff(_ahrs->get_home(), gpsloc);
|
|
// decay and limit the position offset which is applied to NE position wherever it is used throughout code to allow GPS position jumps to be accommodated gradually
|
|
decayGpsOffset();
|
|
}
|
|
}
|
|
|
|
// check for new altitude measurement data and update stored measurement if available
|
|
void NavEKF::readHgtData()
|
|
{
|
|
// check to see if baro measurement has changed so we know if a new measurement has arrived
|
|
if (_baro.get_last_update() != lastHgtMeasTime) {
|
|
// time stamp used to check for new measurement
|
|
lastHgtMeasTime = _baro.get_last_update();
|
|
|
|
// time stamp used to check for timeout
|
|
lastHgtTime_ms = hal.scheduler->millis();
|
|
|
|
// 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, (IMUmsec - _msecHgtDelay));
|
|
} else {
|
|
newDataHgt = false;
|
|
}
|
|
}
|
|
|
|
// check for new magnetometer data and update store measurements if available
|
|
void NavEKF::readMagData()
|
|
{
|
|
if (use_compass() && _ahrs->get_compass()->last_update != lastMagUpdate) {
|
|
// store time of last measurement update
|
|
lastMagUpdate = _ahrs->get_compass()->last_update;
|
|
|
|
// read compass data and assign to bias and uncorrected measurement
|
|
// body fixed magnetic bias is opposite sign to APM compass offsets
|
|
// we scale compass data to improve numerical conditioning
|
|
magBias = -_ahrs->get_compass()->get_offsets() * 0.001f;
|
|
magData = _ahrs->get_compass()->get_field() * 0.001f + magBias;
|
|
|
|
// get states stored at time closest to measurement time after allowance for measurement delay
|
|
RecallStates(statesAtMagMeasTime, (IMUmsec - _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, (IMUmsec - _msecTasDelay));
|
|
} else {
|
|
newDataTas = 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 amgentic 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 - magBias);
|
|
|
|
// 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
|
|
initQuat.from_euler(roll, pitch, yaw);
|
|
|
|
// calculate initial Tbn matrix and rotate Mag measurements into NED
|
|
// to set initial NED magnetic field states
|
|
initQuat.rotation_matrix(Tbn);
|
|
initMagNED = Tbn * (magData - magBias);
|
|
|
|
// write to earth magnetic field state vector
|
|
state.earth_magfield = initMagNED;
|
|
} 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 aligwith the horizontal velocity
|
|
// vector from GPS. It is used to align the yaw angle after launch or takeoff without a magnetometer.
|
|
void NavEKF::alignYawGPS()
|
|
{
|
|
if ((sq(velNED[0]) + sq(velNED[1])) > 16.0f) {
|
|
float roll;
|
|
float pitch;
|
|
float oldYaw;
|
|
float newYaw;
|
|
float yawErr;
|
|
// get quaternion from existing filter states and calculate roll, pitch and yaw angles
|
|
Quaternion initQuat;
|
|
Quaternion newQuat;
|
|
for (uint8_t i=0; i<=3; i++) initQuat[i] = states[i];
|
|
initQuat.to_euler(&roll, &pitch, &oldYaw);
|
|
// calculate yaw angle from GPS velocity
|
|
newYaw = atan2f(velNED[1],velNED[0]);
|
|
// modify yaw angle using GPS ground course if more than 45 degrees away or if not previously aligned
|
|
yawErr = fabsf(newYaw - oldYaw);
|
|
if (((yawErr > 0.7854f) && (yawErr < 5.4978f)) || !yawAligned) {
|
|
// calculate new filter quaternion states from Euler angles
|
|
newQuat.from_euler(roll, pitch, newYaw);
|
|
for (uint8_t i=0; i<=3; i++) states[i] = newQuat[i];
|
|
// the yaw angle is now aligned so update its status
|
|
yawAligned = true;
|
|
// set the velocity states
|
|
if (_fusionModeGPS < 2) {
|
|
states[4] = velNED[0];
|
|
states[5] = velNED[1];
|
|
}
|
|
// reinitialise the quaternion, velocity and position covariances
|
|
// zero the matrix entries
|
|
zeroRows(P,0,9);
|
|
zeroCols(P,0,9);
|
|
// quaternions - TODO maths that sets them based on different roll, yaw and pitch uncertainties
|
|
P[0][0] = 1.0e-9f;
|
|
P[1][1] = 0.25f*sq(radians(1.0f));
|
|
P[2][2] = 0.25f*sq(radians(1.0f));
|
|
P[3][3] = 0.25f*sq(radians(1.0f));
|
|
// velocities - we could have a big error coming out of static mode due to GPS lag
|
|
P[4][4] = 400.0f;
|
|
P[5][5] = P[4][4];
|
|
P[6][6] = sq(0.7f);
|
|
// positions - we could have a big error coming out of static mode due to GPS lag
|
|
P[7][7] = 400.0f;
|
|
P[8][8] = P[7][7];
|
|
P[9][9] = sq(5.0f);
|
|
}
|
|
}
|
|
}
|
|
|
|
// 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 = sqrtf(sq(states[4]) + sq(states[5]));
|
|
if (gndSpd > 4.0f) {
|
|
// set the wind states to be the reciprocal of the velocity and scale
|
|
float scaleFactor = STARTUP_WIND_SPEED / gndSpd;
|
|
states[14] = - states[4] * scaleFactor;
|
|
states[15] = - states[5] * 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();
|
|
Quaternion q(states[0], states[1], states[2], states[3]);
|
|
q.rotation_matrix(mat);
|
|
mat.rotateXYinv(trim);
|
|
}
|
|
|
|
// return the innovations for the NED Pos, NED Vel, XYZ Mag and Vtas measurements
|
|
void NavEKF::getInnovations(Vector3f &velInnov, Vector3f &posInnov, Vector3f &magInnov, float &tasInnov) const
|
|
{
|
|
velInnov.x = innovVelPos[0];
|
|
velInnov.y = innovVelPos[1];
|
|
velInnov.z = innovVelPos[2];
|
|
posInnov.x = innovVelPos[3];
|
|
posInnov.y = innovVelPos[4];
|
|
posInnov.z = innovVelPos[5];
|
|
magInnov.x = 1e3f*innovMag[0]; // Convert back to sensor units
|
|
magInnov.y = 1e3f*innovMag[1]; // Convert back to sensor units
|
|
magInnov.z = 1e3f*innovMag[2]; // Convert back to sensor units
|
|
tasInnov = innovVtas;
|
|
}
|
|
|
|
// return the innovation consistency test ratios for the velocity, position, magnetometer and true airspeed measurements
|
|
// this indicates the amount of margin available when tuning the various error traps
|
|
// also return the current offsets applied to the GPS position measurements
|
|
void NavEKF::getVariances(float &velVar, float &posVar, float &hgtVar, Vector3f &magVar, float &tasVar, Vector2f &offset) const
|
|
{
|
|
velVar = sqrtf(velTestRatio);
|
|
posVar = sqrtf(posTestRatio);
|
|
hgtVar = sqrtf(hgtTestRatio);
|
|
magVar.x = sqrtf(magTestRatio.x);
|
|
magVar.y = sqrtf(magTestRatio.y);
|
|
magVar.z = sqrtf(magTestRatio.z);
|
|
tasVar = sqrtf(tasTestRatio);
|
|
offset = gpsPosGlitchOffsetNE;
|
|
}
|
|
|
|
// zero stored variables - this needs to be called before a full filter initialisation
|
|
void NavEKF::ZeroVariables()
|
|
{
|
|
velTimeout = false;
|
|
posTimeout = false;
|
|
hgtTimeout = false;
|
|
filterDiverged = false;
|
|
lastStateStoreTime_ms = 0;
|
|
lastFixTime_ms = 0;
|
|
secondLastFixTime_ms = 0;
|
|
lastMagUpdate = 0;
|
|
lastAirspeedUpdate = 0;
|
|
velFailTime = 0;
|
|
posFailTime = 0;
|
|
hgtFailTime = 0;
|
|
storeIndex = 0;
|
|
TASmsecPrev = 0;
|
|
BETAmsecPrev = 0;
|
|
MAGmsecPrev = 0;
|
|
HGTmsecPrev = 0;
|
|
lastMagUpdate = 0;
|
|
lastAirspeedUpdate = 0;
|
|
lastHgtMeasTime = 0;
|
|
dtIMU = 0;
|
|
dt = 0;
|
|
hgtMea = 0;
|
|
storeIndex = 0;
|
|
lastGyroBias.zero();
|
|
prevDelAng.zero();
|
|
lastAngRate.zero();
|
|
lastAccel1.zero();
|
|
lastAccel2.zero();
|
|
velDotNEDfilt.zero();
|
|
summedDelAng.zero();
|
|
summedDelVel.zero();
|
|
velNED.zero();
|
|
gpsPosGlitchOffsetNE.zero();
|
|
gpsPosNE.zero();
|
|
prevTnb.zero();
|
|
memset(&P[0][0], 0, sizeof(P));
|
|
memset(&nextP[0][0], 0, sizeof(nextP));
|
|
memset(&processNoise[0], 0, sizeof(processNoise));
|
|
memset(&storedStates[0], 0, sizeof(storedStates));
|
|
memset(&statetimeStamp[0], 0, sizeof(statetimeStamp));
|
|
}
|
|
|
|
// return true if we should use the airspeed sensor
|
|
bool NavEKF::useAirspeed(void) const
|
|
{
|
|
if (_ahrs->get_airspeed() == NULL) {
|
|
return false;
|
|
}
|
|
return _ahrs->get_airspeed()->use();
|
|
}
|
|
|
|
// return true if the vehicle code has requested use of static mode
|
|
// in static mode, position and height are constrained to zero, allowing an attitude
|
|
// reference to be initialised and maintained when on the ground and without GPS lock
|
|
bool NavEKF::static_mode_demanded(void) const
|
|
{
|
|
return !_ahrs->get_armed() || !_ahrs->get_correct_centrifugal();
|
|
}
|
|
|
|
// return true if we should use the compass
|
|
bool NavEKF::use_compass(void) const
|
|
{
|
|
return _ahrs->get_compass() && _ahrs->get_compass()->use_for_yaw();
|
|
}
|
|
|
|
// decay GPS horizontal position offset to close to zero at a rate of 1 m/s
|
|
// limit radius to a maximum of 100m
|
|
// apply glitch offset to GPS measurements
|
|
void NavEKF::decayGpsOffset()
|
|
{
|
|
float lapsedTime = 0.001f*float(hal.scheduler->millis() - lastDecayTime_ms);
|
|
lastDecayTime_ms = hal.scheduler->millis();
|
|
float offsetRadius = pythagorous2(gpsPosGlitchOffsetNE.x, gpsPosGlitchOffsetNE.y);
|
|
// decay radius if larger than velocity of 1.0 multiplied by lapsed time (plus a margin to prevent divide by zero)
|
|
if (offsetRadius > (lapsedTime + 0.1f)) {
|
|
// calculate scale factor to be applied to both offset components
|
|
float scaleFactor = constrain_float((offsetRadius - lapsedTime), 0.0f, 100.0f) / offsetRadius;
|
|
gpsPosGlitchOffsetNE.x *= scaleFactor;
|
|
gpsPosGlitchOffsetNE.y *= scaleFactor;
|
|
}
|
|
}
|
|
|
|
/*
|
|
should we assume zero sideslip?
|
|
*/
|
|
bool NavEKF::assume_zero_sideslip(void) const
|
|
{
|
|
// we don't assume zero sideslip for ground vehicles as EKF could
|
|
// be quite sensitive to a rapid spin of the ground vehicle if
|
|
// traction is lost
|
|
return _ahrs->get_fly_forward() && _ahrs->get_vehicle_class() != AHRS_VEHICLE_GROUND;
|
|
}
|
|
|
|
// Check for filter divergence
|
|
void NavEKF::checkDivergence()
|
|
{
|
|
// If filter is diverging, then fail for 10 seconds
|
|
// delay checking to allow bias estimate to settle after reset
|
|
// filter divergence is detected by looking for rapid changes in gyro bias
|
|
Vector3f tempVec = state.gyro_bias - lastGyroBias;
|
|
float tempLength = tempVec.length();
|
|
if (tempLength != 0.0f) {
|
|
float temp = constrain_float((P[10][10] + P[11][11] + P[12][12]),1e-12f,1e-8f);
|
|
scaledDeltaGyrBiasLgth = (5e-7f / temp) * tempVec.length() / dtIMU;
|
|
}
|
|
bool divergenceDetected = (scaledDeltaGyrBiasLgth > 1.0f);
|
|
lastGyroBias = state.gyro_bias;
|
|
if (hal.scheduler->millis() - lastDivergeTime_ms > 10000) {
|
|
if (divergenceDetected) {
|
|
filterDiverged = true;
|
|
faultStatus.diverged = true;
|
|
lastDivergeTime_ms = hal.scheduler->millis();
|
|
} else {
|
|
filterDiverged = false;
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
/*
|
|
return the filter fault status as a bitmasked integer
|
|
0 = filter divergence detected via gyro bias growth
|
|
1 = filter divergence detected by large covariances
|
|
2 = badly conditioned X magnetometer fusion
|
|
3 = badly conditioned Y magnetometer fusion
|
|
4 = badly conditioned Z magnetometer fusion
|
|
5 = badly conditioned airspeed fusion
|
|
6 = badly conditioned synthetic sideslip fusion
|
|
7 = unassigned
|
|
return normalised delta gyro bias length used for divergence test
|
|
*/
|
|
void NavEKF::getFilterFaults(uint8_t &faults, float &deltaGyroBias) const
|
|
{
|
|
faults = (faultStatus.diverged<<0 |
|
|
faultStatus.large_covarience<<1 |
|
|
faultStatus.bad_xmag<<2 |
|
|
faultStatus.bad_ymag<<3 |
|
|
faultStatus.bad_zmag<<4 |
|
|
faultStatus.bad_airspeed<<5 |
|
|
faultStatus.bad_sideslip<<6);
|
|
deltaGyroBias = scaledDeltaGyrBiasLgth;
|
|
}
|
|
|
|
|
|
#endif // HAL_CPU_CLASS
|