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ardupilot/libraries/AP_NavEKF3/AP_NavEKF3_MagFusion.cpp

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#include <AP_HAL/AP_HAL.h>
#include "AP_NavEKF3.h"
#include "AP_NavEKF3_core.h"
#include <GCS_MAVLink/GCS.h>
#include <AP_DAL/AP_DAL.h>
/********************************************************
* RESET FUNCTIONS *
********************************************************/
// Control reset of yaw and magnetic field states
void NavEKF3_core::controlMagYawReset()
{
// Vehicles that can use a zero sideslip assumption (Planes) are a special case
// They can use the GPS velocity to recover from bad initial compass data
// This allows recovery for heading alignment errors due to compass faults
if (assume_zero_sideslip() && (!finalInflightYawInit || !yawAlignComplete) && inFlight) {
gpsYawResetRequest = true;
return;
} else {
gpsYawResetRequest = false;
}
// Quaternion and delta rotation vector that are re-used for different calculations
Vector3f deltaRotVecTemp;
Quaternion deltaQuatTemp;
bool flightResetAllowed = false;
bool initialResetAllowed = false;
if (!finalInflightYawInit) {
// Use a quaternion division to calculate the delta quaternion between the rotation at the current and last time
deltaQuatTemp = stateStruct.quat / prevQuatMagReset;
prevQuatMagReset = stateStruct.quat;
// convert the quaternion to a rotation vector and find its length
deltaQuatTemp.to_axis_angle(deltaRotVecTemp);
// check if the spin rate is OK - high spin rates can cause angular alignment errors
bool angRateOK = deltaRotVecTemp.length() < 0.1745f;
initialResetAllowed = angRateOK && tiltAlignComplete;
flightResetAllowed = angRateOK && !onGround;
}
// reset the limit on the number of magnetic anomaly resets for each takeoff
if (onGround) {
magYawAnomallyCount = 0;
}
// Check if conditions for a interim or final yaw/mag reset are met
bool finalResetRequest = false;
bool interimResetRequest = false;
if (flightResetAllowed && !assume_zero_sideslip()) {
// check that we have reached a height where ground magnetic interference effects are insignificant
// and can perform a final reset of the yaw and field states
finalResetRequest = (stateStruct.position.z - posDownAtTakeoff) < -EKF3_MAG_FINAL_RESET_ALT;
// check for increasing height
bool hgtIncreasing = (posDownAtLastMagReset-stateStruct.position.z) > 0.5f;
float yawInnovIncrease = fabsf(innovYaw) - fabsf(yawInnovAtLastMagReset);
// check for increasing yaw innovations
bool yawInnovIncreasing = yawInnovIncrease > 0.25f;
// check that the yaw innovations haven't been caused by a large change in attitude
deltaQuatTemp = quatAtLastMagReset / stateStruct.quat;
deltaQuatTemp.to_axis_angle(deltaRotVecTemp);
bool largeAngleChange = deltaRotVecTemp.length() > yawInnovIncrease;
// if yaw innovations and height have increased and we haven't rotated much
// then we are climbing away from a ground based magnetic anomaly and need to reset
interimResetRequest = !finalInflightYawInit
&& !finalResetRequest
&& (magYawAnomallyCount < MAG_ANOMALY_RESET_MAX)
&& hgtIncreasing
&& yawInnovIncreasing
&& !largeAngleChange;
}
// an initial reset is required if we have not yet aligned the yaw angle
bool initialResetRequest = initialResetAllowed && !yawAlignComplete;
// a combined yaw angle and magnetic field reset can be initiated by:
magYawResetRequest = magYawResetRequest || // an external request
initialResetRequest || // an initial alignment performed by all vehicle types using magnetometer
interimResetRequest || // an interim alignment required to recover from ground based magnetic anomaly
finalResetRequest; // the final reset when we have achieved enough height to be in stable magnetic field environment
// Perform a reset of magnetic field states and reset yaw to corrected magnetic heading
if (magYawResetRequest && use_compass()) {
// send initial alignment status to console
if (!yawAlignComplete) {
GCS_SEND_TEXT(MAV_SEVERITY_INFO, "EKF3 IMU%u MAG%u initial yaw alignment complete",(unsigned)imu_index, (unsigned)magSelectIndex);
}
// set yaw from a single mag sample
setYawFromMag();
// send in-flight yaw alignment status to console
if (finalResetRequest) {
GCS_SEND_TEXT(MAV_SEVERITY_INFO, "EKF3 IMU%u MAG%u in-flight yaw alignment complete",(unsigned)imu_index, (unsigned)magSelectIndex);
} else if (interimResetRequest) {
magYawAnomallyCount++;
GCS_SEND_TEXT(MAV_SEVERITY_WARNING, "EKF3 IMU%u MAG%u ground mag anomaly, yaw re-aligned",(unsigned)imu_index, (unsigned)magSelectIndex);
}
// clear the complete flags if an interim reset has been performed to allow subsequent
// and final reset to occur
if (interimResetRequest) {
finalInflightYawInit = false;
finalInflightMagInit = false;
}
// mag states
if (!magFieldLearned) {
resetMagFieldStates();
}
}
if (magStateResetRequest) {
resetMagFieldStates();
}
}
// this function is used to do a forced re-alignment of the yaw angle to align with the horizontal velocity
// vector from GPS. It is used to align the yaw angle after launch or takeoff.
void NavEKF3_core::realignYawGPS()
{
// get quaternion from existing filter states and calculate roll, pitch and yaw angles
Vector3f eulerAngles;
stateStruct.quat.to_euler(eulerAngles.x, eulerAngles.y, eulerAngles.z);
if ((sq(gpsDataDelayed.vel.x) + sq(gpsDataDelayed.vel.y)) > 25.0f) {
// calculate course yaw angle
float velYaw = atan2f(stateStruct.velocity.y,stateStruct.velocity.x);
// calculate course yaw angle from GPS velocity
float gpsYaw = atan2f(gpsDataDelayed.vel.y,gpsDataDelayed.vel.x);
// Check the yaw angles for consistency
float yawErr = MAX(fabsf(wrap_PI(gpsYaw - velYaw)),fabsf(wrap_PI(gpsYaw - eulerAngles.z)));
// If the angles disagree by more than 45 degrees and GPS innovations are large or no previous yaw alignment, we declare the magnetic yaw as bad
bool badMagYaw = ((yawErr > 0.7854f) && (velTestRatio > 1.0f) && (PV_AidingMode == AID_ABSOLUTE)) || !yawAlignComplete;
// correct yaw angle using GPS ground course if compass yaw bad
if (badMagYaw) {
// attempt to use EKF-GSF estimate if available as it is more robust to GPS glitches
if (EKFGSF_resetMainFilterYaw()) {
return;
}
// keep roll and pitch and reset yaw
rotationOrder order;
bestRotationOrder(order);
resetQuatStateYawOnly(gpsYaw, sq(radians(45.0f)), order);
// reset the velocity and position states as they will be inaccurate due to bad yaw
ResetVelocity(resetDataSource::GPS);
ResetPosition(resetDataSource::GPS);
// send yaw alignment information to console
GCS_SEND_TEXT(MAV_SEVERITY_INFO, "EKF3 IMU%u yaw aligned to GPS velocity",(unsigned)imu_index);
if (use_compass()) {
// request a mag field reset which may enable us to use the magnetometer if the previous fault was due to bad initialisation
magStateResetRequest = true;
// clear the all sensors failed status so that the magnetometers sensors get a second chance now that we are flying
allMagSensorsFailed = false;
}
}
}
}
// align the yaw angle for the quaternion states to the given yaw angle which should be at the fusion horizon
void NavEKF3_core::alignYawAngle(const yaw_elements &yawAngData)
{
// update quaternion states and covariances
resetQuatStateYawOnly(yawAngData.yawAng, sq(MAX(yawAngData.yawAngErr, 1.0e-2f)), yawAngData.order);
// send yaw alignment information to console
GCS_SEND_TEXT(MAV_SEVERITY_INFO, "EKF3 IMU%u yaw aligned",(unsigned)imu_index);
}
/********************************************************
* FUSE MEASURED_DATA *
********************************************************/
// select fusion of magnetometer data
void NavEKF3_core::SelectMagFusion()
{
// clear the flag that lets other processes know that the expensive magnetometer fusion operation has been performed on that time step
// used for load levelling
magFusePerformed = false;
// get default yaw source
const AP_NavEKF_Source::SourceYaw yaw_source = frontend->sources.getYawSource();
if (yaw_source != yaw_source_last) {
yaw_source_last = yaw_source;
yaw_source_reset = true;
}
// Store yaw angle when moving for use as a static reference when not moving
if (!onGroundNotMoving) {
if (fabsf(prevTnb[0][2]) < fabsf(prevTnb[1][2])) {
// A 321 rotation order is best conditioned because the X axis is closer to horizontal than the Y axis
yawAngDataStatic.order = rotationOrder::TAIT_BRYAN_321;
yawAngDataStatic.yawAng = atan2f(prevTnb[0][1], prevTnb[0][0]);
} else {
// A 312 rotation order is best conditioned because the Y axis is closer to horizontal than the X axis
yawAngDataStatic.order = rotationOrder::TAIT_BRYAN_312;
yawAngDataStatic.yawAng = atan2f(-prevTnb[1][0], prevTnb[1][1]);
}
yawAngDataStatic.yawAngErr = MAX(frontend->_yawNoise, 0.05f);
yawAngDataStatic.time_ms = imuDataDelayed.time_ms;
}
// Handle case where we are not using a yaw sensor of any type and attempt to reset the yaw in
// flight using the output from the GSF yaw estimator.
if ((yaw_source == AP_NavEKF_Source::SourceYaw::GSF) ||
(!use_compass() &&
yaw_source != AP_NavEKF_Source::SourceYaw::GPS &&
yaw_source != AP_NavEKF_Source::SourceYaw::GPS_COMPASS_FALLBACK &&
yaw_source != AP_NavEKF_Source::SourceYaw::EXTNAV)) {
// because this type of reset event is not as time critical, require a continuous history of valid estimates
if ((!yawAlignComplete || yaw_source_reset) && EKFGSF_yaw_valid_count >= GSF_YAW_VALID_HISTORY_THRESHOLD) {
yawAlignComplete = EKFGSF_resetMainFilterYaw();
yaw_source_reset = false;
}
if (imuSampleTime_ms - lastSynthYawTime_ms > 140) {
// use the EKF-GSF yaw estimator output as this is more robust than the EKF can achieve without a yaw measurement
// for non fixed wing platform types
float gsfYaw, gsfYawVariance;
const bool didUseEKFGSF = yawAlignComplete && EKFGSF_getYaw(gsfYaw, gsfYawVariance) && !assume_zero_sideslip() && fuseEulerYaw(yawFusionMethod::GSF);
// fallback methods
if (!didUseEKFGSF) {
if (onGroundNotMoving) {
// fuse last known good yaw angle before we stopped moving to allow yaw bias learning when on ground before flight
fuseEulerYaw(yawFusionMethod::STATIC);
} else if (onGround || PV_AidingMode == AID_NONE || (P[0][0]+P[1][1]+P[2][2]+P[3][3] > 0.01f)) {
// prevent uncontrolled yaw variance growth that can destabilise the covariance matrix
// by fusing a zero innovation
fuseEulerYaw(yawFusionMethod::PREDICTED);
}
}
magTestRatio.zero();
yawTestRatio = 0.0f;
lastSynthYawTime_ms = imuSampleTime_ms;
}
return;
}
// Handle case where we are using GPS yaw sensor instead of a magnetomer
if (yaw_source == AP_NavEKF_Source::SourceYaw::GPS || yaw_source == AP_NavEKF_Source::SourceYaw::GPS_COMPASS_FALLBACK) {
bool have_fused_gps_yaw = false;
if (storedYawAng.recall(yawAngDataDelayed,imuDataDelayed.time_ms)) {
if (tiltAlignComplete && (!yawAlignComplete || yaw_source_reset)) {
alignYawAngle(yawAngDataDelayed);
yaw_source_reset = false;
have_fused_gps_yaw = true;
lastSynthYawTime_ms = imuSampleTime_ms;
last_gps_yaw_fuse_ms = imuSampleTime_ms;
} else if (tiltAlignComplete && yawAlignComplete) {
have_fused_gps_yaw = fuseEulerYaw(yawFusionMethod::GPS);
if (have_fused_gps_yaw) {
last_gps_yaw_fuse_ms = imuSampleTime_ms;
}
}
last_gps_yaw_ms = imuSampleTime_ms;
} else if (tiltAlignComplete && !yawAlignComplete) {
// External yaw sources can take significant time to start providing yaw data so
// wuile waiting, fuse a 'fake' yaw observation at 7Hz to keeop the filter stable
if(imuSampleTime_ms - lastSynthYawTime_ms > 140) {
yawAngDataDelayed.yawAngErr = MAX(frontend->_yawNoise, 0.05f);
// update the yaw angle using the last estimate which will be used as a static yaw reference when movement stops
if (!onGroundNotMoving) {
// prevent uncontrolled yaw variance growth by fusing a zero innovation
fuseEulerYaw(yawFusionMethod::PREDICTED);
} else {
// fuse last known good yaw angle before we stopped moving to allow yaw bias learning when on ground before flight
fuseEulerYaw(yawFusionMethod::STATIC);
}
lastSynthYawTime_ms = imuSampleTime_ms;
}
} else if (tiltAlignComplete && yawAlignComplete && onGround && imuSampleTime_ms - last_gps_yaw_fuse_ms > 10000) {
// handle scenario where we were using GPS yaw previously, but the yaw fusion has timed out.
yaw_source_reset = true;
}
if (yaw_source == AP_NavEKF_Source::SourceYaw::GPS) {
// no fallback
return;
}
// get new mag data into delay buffer
readMagData();
if (have_fused_gps_yaw) {
if (gps_yaw_mag_fallback_active) {
gps_yaw_mag_fallback_active = false;
GCS_SEND_TEXT(MAV_SEVERITY_INFO, "EKF3 IMU%u yaw external",(unsigned)imu_index);
}
// update mag bias from GPS yaw
gps_yaw_mag_fallback_ok = learnMagBiasFromGPS();
return;
}
// we don't have GPS yaw data and are configured for
// fallback. If we've only just lost GPS yaw
if (imuSampleTime_ms - last_gps_yaw_ms < 10000) {
// don't fallback to magnetometer fusion for 10s
return;
}
if (!gps_yaw_mag_fallback_ok) {
// mag was not consistent enough with GPS to use it as
// fallback
return;
}
if (!inFlight) {
// don't fall back if not flying but reset to GPS yaw if it becomes available
return;
}
if (!gps_yaw_mag_fallback_active) {
gps_yaw_mag_fallback_active = true;
GCS_SEND_TEXT(MAV_SEVERITY_INFO, "EKF3 IMU%u yaw fallback active",(unsigned)imu_index);
}
// fall through to magnetometer fusion
}
#if EK3_FEATURE_EXTERNAL_NAV
// Handle case where we are using an external nav for yaw
const bool extNavYawDataToFuse = storedExtNavYawAng.recall(extNavYawAngDataDelayed, imuDataDelayed.time_ms);
if (yaw_source == AP_NavEKF_Source::SourceYaw::EXTNAV) {
if (extNavYawDataToFuse) {
if (tiltAlignComplete && (!yawAlignComplete || yaw_source_reset)) {
alignYawAngle(extNavYawAngDataDelayed);
yaw_source_reset = false;
} else if (tiltAlignComplete && yawAlignComplete) {
fuseEulerYaw(yawFusionMethod::EXTNAV);
}
last_extnav_yaw_fusion_ms = imuSampleTime_ms;
} else if (tiltAlignComplete && !yawAlignComplete) {
// External yaw sources can take significant time to start providing yaw data so
// while waiting, fuse a 'fake' yaw observation at 7Hz to keep the filter stable
if (imuSampleTime_ms - lastSynthYawTime_ms > 140) {
// update the yaw angle using the last estimate which will be used as a static yaw reference when movement stops
if (!onGroundNotMoving) {
// prevent uncontrolled yaw variance growth by fusing a zero innovation
fuseEulerYaw(yawFusionMethod::PREDICTED);
} else {
// fuse last known good yaw angle before we stopped moving to allow yaw bias learning when on ground before flight
fuseEulerYaw(yawFusionMethod::STATIC);
}
lastSynthYawTime_ms = imuSampleTime_ms;
}
}
}
#endif // EK3_FEATURE_EXTERNAL_NAV
// If we are using the compass and the magnetometer has been unhealthy for too long we declare a timeout
if (magHealth) {
magTimeout = false;
lastHealthyMagTime_ms = imuSampleTime_ms;
} else if ((imuSampleTime_ms - lastHealthyMagTime_ms) > frontend->magFailTimeLimit_ms && use_compass()) {
magTimeout = true;
}
if (yaw_source != AP_NavEKF_Source::SourceYaw::GPS_COMPASS_FALLBACK) {
// check for and read new magnetometer measurements. We don't
// read for GPS_COMPASS_FALLBACK as it has already been read
// above
readMagData();
}
// check for availability of magnetometer or other yaw data to fuse
magDataToFuse = storedMag.recall(magDataDelayed,imuDataDelayed.time_ms);
// Control reset of yaw and magnetic field states if we are using compass data
if (magDataToFuse) {
if (yaw_source_reset && (yaw_source == AP_NavEKF_Source::SourceYaw::COMPASS ||
yaw_source == AP_NavEKF_Source::SourceYaw::GPS_COMPASS_FALLBACK)) {
magYawResetRequest = true;
yaw_source_reset = false;
}
controlMagYawReset();
}
// determine if conditions are right to start a new fusion cycle
// wait until the EKF time horizon catches up with the measurement
bool dataReady = (magDataToFuse && statesInitialised && use_compass() && yawAlignComplete);
if (dataReady) {
// use the simple method of declination to maintain heading if we cannot use the magnetic field states
if(inhibitMagStates || magStateResetRequest || !magStateInitComplete) {
fuseEulerYaw(yawFusionMethod::MAGNETOMETER);
// zero the test ratio output from the inactive 3-axis magnetometer fusion
magTestRatio.zero();
} else {
// if we are not doing aiding with earth relative observations (eg GPS) then the declination is
// maintained by fusing declination as a synthesised observation
// We also fuse declination if we are using the WMM tables
if (PV_AidingMode != AID_ABSOLUTE ||
(frontend->_mag_ef_limit > 0 && have_table_earth_field)) {
FuseDeclination(0.34f);
}
// fuse the three magnetometer componenents using sequential fusion for each axis
FuseMagnetometer();
// zero the test ratio output from the inactive simple magnetometer yaw fusion
yawTestRatio = 0.0f;
}
}
// If the final yaw reset has been performed and the state variances are sufficiently low
// record that the earth field has been learned.
if (!magFieldLearned && finalInflightMagInit) {
magFieldLearned = (P[16][16] < sq(0.01f)) && (P[17][17] < sq(0.01f)) && (P[18][18] < sq(0.01f));
}
// record the last learned field variances
if (magFieldLearned && !inhibitMagStates) {
earthMagFieldVar.x = P[16][16];
earthMagFieldVar.y = P[17][17];
earthMagFieldVar.z = P[18][18];
bodyMagFieldVar.x = P[19][19];
bodyMagFieldVar.y = P[20][20];
bodyMagFieldVar.z = P[21][21];
}
}
/*
* Fuse magnetometer measurements using explicit algebraic equations generated with Matlab symbolic toolbox.
* The script file used to generate these and other equations in this filter can be found here:
* https://github.com/PX4/ecl/blob/master/matlab/scripts/Inertial%20Nav%20EKF/GenerateNavFilterEquations.m
*/
void NavEKF3_core::FuseMagnetometer()
{
// declarations
ftype &q0 = mag_state.q0;
ftype &q1 = mag_state.q1;
ftype &q2 = mag_state.q2;
ftype &q3 = mag_state.q3;
ftype &magN = mag_state.magN;
ftype &magE = mag_state.magE;
ftype &magD = mag_state.magD;
ftype &magXbias = mag_state.magXbias;
ftype &magYbias = mag_state.magYbias;
ftype &magZbias = mag_state.magZbias;
Matrix3f &DCM = mag_state.DCM;
Vector3f &MagPred = mag_state.MagPred;
ftype &R_MAG = mag_state.R_MAG;
ftype *SH_MAG = &mag_state.SH_MAG[0];
Vector24 H_MAG;
Vector5 SK_MX;
Vector5 SK_MY;
Vector5 SK_MZ;
// perform sequential fusion of magnetometer measurements.
// this assumes that the errors in the different components are
// uncorrelated which is not true, however in the absence of covariance
// data fit is the only assumption we can make
// so we might as well take advantage of the computational efficiencies
// associated with sequential fusion
// calculate observation jacobians and Kalman gains
// copy required states to local variable names
q0 = stateStruct.quat[0];
q1 = stateStruct.quat[1];
q2 = stateStruct.quat[2];
q3 = stateStruct.quat[3];
magN = stateStruct.earth_magfield[0];
magE = stateStruct.earth_magfield[1];
magD = stateStruct.earth_magfield[2];
magXbias = stateStruct.body_magfield[0];
magYbias = stateStruct.body_magfield[1];
magZbias = stateStruct.body_magfield[2];
// rotate predicted earth components into body axes and calculate
// predicted measurements
DCM[0][0] = q0*q0 + q1*q1 - q2*q2 - q3*q3;
DCM[0][1] = 2.0f*(q1*q2 + q0*q3);
DCM[0][2] = 2.0f*(q1*q3-q0*q2);
DCM[1][0] = 2.0f*(q1*q2 - q0*q3);
DCM[1][1] = q0*q0 - q1*q1 + q2*q2 - q3*q3;
DCM[1][2] = 2.0f*(q2*q3 + q0*q1);
DCM[2][0] = 2.0f*(q1*q3 + q0*q2);
DCM[2][1] = 2.0f*(q2*q3 - q0*q1);
DCM[2][2] = q0*q0 - q1*q1 - q2*q2 + q3*q3;
MagPred[0] = DCM[0][0]*magN + DCM[0][1]*magE + DCM[0][2]*magD + magXbias;
MagPred[1] = DCM[1][0]*magN + DCM[1][1]*magE + DCM[1][2]*magD + magYbias;
MagPred[2] = DCM[2][0]*magN + DCM[2][1]*magE + DCM[2][2]*magD + magZbias;
// calculate the measurement innovation for each axis
for (uint8_t i = 0; i<=2; i++) {
innovMag[i] = MagPred[i] - magDataDelayed.mag[i];
}
// scale magnetometer observation error with total angular rate to allow for timing errors
R_MAG = sq(constrain_float(frontend->_magNoise, 0.01f, 0.5f)) + sq(frontend->magVarRateScale*imuDataDelayed.delAng.length() / imuDataDelayed.delAngDT);
// calculate common expressions used to calculate observation jacobians an innovation variance for each component
SH_MAG[0] = 2.0f*magD*q3 + 2.0f*magE*q2 + 2.0f*magN*q1;
SH_MAG[1] = 2.0f*magD*q0 - 2.0f*magE*q1 + 2.0f*magN*q2;
SH_MAG[2] = 2.0f*magD*q1 + 2.0f*magE*q0 - 2.0f*magN*q3;
SH_MAG[3] = sq(q3);
SH_MAG[4] = sq(q2);
SH_MAG[5] = sq(q1);
SH_MAG[6] = sq(q0);
SH_MAG[7] = 2.0f*magN*q0;
SH_MAG[8] = 2.0f*magE*q3;
// Calculate the innovation variance for each axis
// X axis
varInnovMag[0] = (P[19][19] + R_MAG + P[1][19]*SH_MAG[0] - P[2][19]*SH_MAG[1] + P[3][19]*SH_MAG[2] - P[16][19]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + (2.0f*q0*q3 + 2.0f*q1*q2)*(P[19][17] + P[1][17]*SH_MAG[0] - P[2][17]*SH_MAG[1] + P[3][17]*SH_MAG[2] - P[16][17]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[17][17]*(2.0f*q0*q3 + 2.0f*q1*q2) - P[18][17]*(2.0f*q0*q2 - 2.0f*q1*q3) + P[0][17]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - (2.0f*q0*q2 - 2.0f*q1*q3)*(P[19][18] + P[1][18]*SH_MAG[0] - P[2][18]*SH_MAG[1] + P[3][18]*SH_MAG[2] - P[16][18]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[17][18]*(2.0f*q0*q3 + 2.0f*q1*q2) - P[18][18]*(2.0f*q0*q2 - 2.0f*q1*q3) + P[0][18]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + (SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)*(P[19][0] + P[1][0]*SH_MAG[0] - P[2][0]*SH_MAG[1] + P[3][0]*SH_MAG[2] - P[16][0]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[17][0]*(2.0f*q0*q3 + 2.0f*q1*q2) - P[18][0]*(2.0f*q0*q2 - 2.0f*q1*q3) + P[0][0]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + P[17][19]*(2.0f*q0*q3 + 2.0f*q1*q2) - P[18][19]*(2.0f*q0*q2 - 2.0f*q1*q3) + SH_MAG[0]*(P[19][1] + P[1][1]*SH_MAG[0] - P[2][1]*SH_MAG[1] + P[3][1]*SH_MAG[2] - P[16][1]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[17][1]*(2.0f*q0*q3 + 2.0f*q1*q2) - P[18][1]*(2.0f*q0*q2 - 2.0f*q1*q3) + P[0][1]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - SH_MAG[1]*(P[19][2] + P[1][2]*SH_MAG[0] - P[2][2]*SH_MAG[1] + P[3][2]*SH_MAG[2] - P[16][2]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[17][2]*(2.0f*q0*q3 + 2.0f*q1*q2) - P[18][2]*(2.0f*q0*q2 - 2.0f*q1*q3) + P[0][2]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + SH_MAG[2]*(P[19][3] + P[1][3]*SH_MAG[0] - P[2][3]*SH_MAG[1] + P[3][3]*SH_MAG[2] - P[16][3]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[17][3]*(2.0f*q0*q3 + 2.0f*q1*q2) - P[18][3]*(2.0f*q0*q2 - 2.0f*q1*q3) + P[0][3]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - (SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6])*(P[19][16] + P[1][16]*SH_MAG[0] - P[2][16]*SH_MAG[1] + P[3][16]*SH_MAG[2] - P[16][16]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[17][16]*(2.0f*q0*q3 + 2.0f*q1*q2) - P[18][16]*(2.0f*q0*q2 - 2.0f*q1*q3) + P[0][16]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + P[0][19]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2));
if (varInnovMag[0] >= R_MAG) {
faultStatus.bad_xmag = false;
} else {
// the calculation is badly conditioned, so we cannot perform fusion on this step
// we reset the covariance matrix and try again next measurement
CovarianceInit();
faultStatus.bad_xmag = true;
return;
}
// Y axis
varInnovMag[1] = (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]) - (2.0f*q0*q3 - 2.0f*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]*(2.0f*q0*q3 - 2.0f*q1*q2) + P[18][16]*(2.0f*q0*q1 + 2.0f*q2*q3) - P[3][16]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + (2.0f*q0*q1 + 2.0f*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]*(2.0f*q0*q3 - 2.0f*q1*q2) + P[18][18]*(2.0f*q0*q1 + 2.0f*q2*q3) - P[3][18]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - (SH_MAG[7] + SH_MAG[8] - 2.0f*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]*(2.0f*q0*q3 - 2.0f*q1*q2) + P[18][3]*(2.0f*q0*q1 + 2.0f*q2*q3) - P[3][3]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - P[16][20]*(2.0f*q0*q3 - 2.0f*q1*q2) + P[18][20]*(2.0f*q0*q1 + 2.0f*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]*(2.0f*q0*q3 - 2.0f*q1*q2) + P[18][0]*(2.0f*q0*q1 + 2.0f*q2*q3) - P[3][0]*(SH_MAG[7] + SH_MAG[8] - 2.0f*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]*(2.0f*q0*q3 - 2.0f*q1*q2) + P[18][1]*(2.0f*q0*q1 + 2.0f*q2*q3) - P[3][1]*(SH_MAG[7] + SH_MAG[8] - 2.0f*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]*(2.0f*q0*q3 - 2.0f*q1*q2) + P[18][2]*(2.0f*q0*q1 + 2.0f*q2*q3) - P[3][2]*(SH_MAG[7] + SH_MAG[8] - 2.0f*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]*(2.0f*q0*q3 - 2.0f*q1*q2) + P[18][17]*(2.0f*q0*q1 + 2.0f*q2*q3) - P[3][17]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - P[3][20]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2));
if (varInnovMag[1] >= R_MAG) {
faultStatus.bad_ymag = false;
} else {
// the calculation is badly conditioned, so we cannot perform fusion on this step
// we reset the covariance matrix and try again next measurement
CovarianceInit();
faultStatus.bad_ymag = true;
return;
}
// Z axis
varInnovMag[2] = (P[21][21] + R_MAG + P[0][21]*SH_MAG[1] - P[1][21]*SH_MAG[2] + P[3][21]*SH_MAG[0] + P[18][21]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + (2.0f*q0*q2 + 2.0f*q1*q3)*(P[21][16] + P[0][16]*SH_MAG[1] - P[1][16]*SH_MAG[2] + P[3][16]*SH_MAG[0] + P[18][16]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P[16][16]*(2.0f*q0*q2 + 2.0f*q1*q3) - P[17][16]*(2.0f*q0*q1 - 2.0f*q2*q3) + P[2][16]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - (2.0f*q0*q1 - 2.0f*q2*q3)*(P[21][17] + P[0][17]*SH_MAG[1] - P[1][17]*SH_MAG[2] + P[3][17]*SH_MAG[0] + P[18][17]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P[16][17]*(2.0f*q0*q2 + 2.0f*q1*q3) - P[17][17]*(2.0f*q0*q1 - 2.0f*q2*q3) + P[2][17]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + (SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)*(P[21][2] + P[0][2]*SH_MAG[1] - P[1][2]*SH_MAG[2] + P[3][2]*SH_MAG[0] + P[18][2]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P[16][2]*(2.0f*q0*q2 + 2.0f*q1*q3) - P[17][2]*(2.0f*q0*q1 - 2.0f*q2*q3) + P[2][2]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + P[16][21]*(2.0f*q0*q2 + 2.0f*q1*q3) - P[17][21]*(2.0f*q0*q1 - 2.0f*q2*q3) + SH_MAG[1]*(P[21][0] + P[0][0]*SH_MAG[1] - P[1][0]*SH_MAG[2] + P[3][0]*SH_MAG[0] + P[18][0]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P[16][0]*(2.0f*q0*q2 + 2.0f*q1*q3) - P[17][0]*(2.0f*q0*q1 - 2.0f*q2*q3) + P[2][0]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - SH_MAG[2]*(P[21][1] + P[0][1]*SH_MAG[1] - P[1][1]*SH_MAG[2] + P[3][1]*SH_MAG[0] + P[18][1]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P[16][1]*(2.0f*q0*q2 + 2.0f*q1*q3) - P[17][1]*(2.0f*q0*q1 - 2.0f*q2*q3) + P[2][1]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + SH_MAG[0]*(P[21][3] + P[0][3]*SH_MAG[1] - P[1][3]*SH_MAG[2] + P[3][3]*SH_MAG[0] + P[18][3]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P[16][3]*(2.0f*q0*q2 + 2.0f*q1*q3) - P[17][3]*(2.0f*q0*q1 - 2.0f*q2*q3) + P[2][3]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + (SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6])*(P[21][18] + P[0][18]*SH_MAG[1] - P[1][18]*SH_MAG[2] + P[3][18]*SH_MAG[0] + P[18][18]*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P[16][18]*(2.0f*q0*q2 + 2.0f*q1*q3) - P[17][18]*(2.0f*q0*q1 - 2.0f*q2*q3) + P[2][18]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + P[2][21]*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2));
if (varInnovMag[2] >= R_MAG) {
faultStatus.bad_zmag = false;
} else {
// the calculation is badly conditioned, so we cannot perform fusion on this step
// we reset the covariance matrix and try again next measurement
CovarianceInit();
faultStatus.bad_zmag = true;
return;
}
// calculate the innovation test ratios
for (uint8_t i = 0; i<=2; i++) {
magTestRatio[i] = sq(innovMag[i]) / (sq(MAX(0.01f * (float)frontend->_magInnovGate, 1.0f)) * varInnovMag[i]);
}
// 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);
// if the magnetometer is unhealthy, do not proceed further
if (!magHealth) {
return;
}
for (uint8_t obsIndex = 0; obsIndex <= 2; obsIndex++) {
if (obsIndex == 0) {
for (uint8_t i = 0; i<=stateIndexLim; i++) H_MAG[i] = 0.0f;
H_MAG[0] = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
H_MAG[1] = SH_MAG[0];
H_MAG[2] = -SH_MAG[1];
H_MAG[3] = SH_MAG[2];
H_MAG[16] = SH_MAG[5] - SH_MAG[4] - SH_MAG[3] + SH_MAG[6];
H_MAG[17] = 2.0f*q0*q3 + 2.0f*q1*q2;
H_MAG[18] = 2.0f*q1*q3 - 2.0f*q0*q2;
H_MAG[19] = 1.0f;
H_MAG[20] = 0.0f;
H_MAG[21] = 0.0f;
// calculate Kalman gain
SK_MX[0] = 1.0f / varInnovMag[0];
SK_MX[1] = SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6];
SK_MX[2] = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
SK_MX[3] = 2.0f*q0*q2 - 2.0f*q1*q3;
SK_MX[4] = 2.0f*q0*q3 + 2.0f*q1*q2;
Kfusion[0] = SK_MX[0]*(P[0][19] + P[0][1]*SH_MAG[0] - P[0][2]*SH_MAG[1] + P[0][3]*SH_MAG[2] + P[0][0]*SK_MX[2] - P[0][16]*SK_MX[1] + P[0][17]*SK_MX[4] - P[0][18]*SK_MX[3]);
Kfusion[1] = SK_MX[0]*(P[1][19] + P[1][1]*SH_MAG[0] - P[1][2]*SH_MAG[1] + P[1][3]*SH_MAG[2] + P[1][0]*SK_MX[2] - P[1][16]*SK_MX[1] + P[1][17]*SK_MX[4] - P[1][18]*SK_MX[3]);
Kfusion[2] = SK_MX[0]*(P[2][19] + P[2][1]*SH_MAG[0] - P[2][2]*SH_MAG[1] + P[2][3]*SH_MAG[2] + P[2][0]*SK_MX[2] - P[2][16]*SK_MX[1] + P[2][17]*SK_MX[4] - P[2][18]*SK_MX[3]);
Kfusion[3] = SK_MX[0]*(P[3][19] + P[3][1]*SH_MAG[0] - P[3][2]*SH_MAG[1] + P[3][3]*SH_MAG[2] + P[3][0]*SK_MX[2] - P[3][16]*SK_MX[1] + P[3][17]*SK_MX[4] - P[3][18]*SK_MX[3]);
Kfusion[4] = SK_MX[0]*(P[4][19] + P[4][1]*SH_MAG[0] - P[4][2]*SH_MAG[1] + P[4][3]*SH_MAG[2] + P[4][0]*SK_MX[2] - P[4][16]*SK_MX[1] + P[4][17]*SK_MX[4] - P[4][18]*SK_MX[3]);
Kfusion[5] = SK_MX[0]*(P[5][19] + P[5][1]*SH_MAG[0] - P[5][2]*SH_MAG[1] + P[5][3]*SH_MAG[2] + P[5][0]*SK_MX[2] - P[5][16]*SK_MX[1] + P[5][17]*SK_MX[4] - P[5][18]*SK_MX[3]);
Kfusion[6] = SK_MX[0]*(P[6][19] + P[6][1]*SH_MAG[0] - P[6][2]*SH_MAG[1] + P[6][3]*SH_MAG[2] + P[6][0]*SK_MX[2] - P[6][16]*SK_MX[1] + P[6][17]*SK_MX[4] - P[6][18]*SK_MX[3]);
Kfusion[7] = SK_MX[0]*(P[7][19] + P[7][1]*SH_MAG[0] - P[7][2]*SH_MAG[1] + P[7][3]*SH_MAG[2] + P[7][0]*SK_MX[2] - P[7][16]*SK_MX[1] + P[7][17]*SK_MX[4] - P[7][18]*SK_MX[3]);
Kfusion[8] = SK_MX[0]*(P[8][19] + P[8][1]*SH_MAG[0] - P[8][2]*SH_MAG[1] + P[8][3]*SH_MAG[2] + P[8][0]*SK_MX[2] - P[8][16]*SK_MX[1] + P[8][17]*SK_MX[4] - P[8][18]*SK_MX[3]);
Kfusion[9] = SK_MX[0]*(P[9][19] + P[9][1]*SH_MAG[0] - P[9][2]*SH_MAG[1] + P[9][3]*SH_MAG[2] + P[9][0]*SK_MX[2] - P[9][16]*SK_MX[1] + P[9][17]*SK_MX[4] - P[9][18]*SK_MX[3]);
if (!inhibitDelAngBiasStates) {
Kfusion[10] = SK_MX[0]*(P[10][19] + P[10][1]*SH_MAG[0] - P[10][2]*SH_MAG[1] + P[10][3]*SH_MAG[2] + P[10][0]*SK_MX[2] - P[10][16]*SK_MX[1] + P[10][17]*SK_MX[4] - P[10][18]*SK_MX[3]);
Kfusion[11] = SK_MX[0]*(P[11][19] + P[11][1]*SH_MAG[0] - P[11][2]*SH_MAG[1] + P[11][3]*SH_MAG[2] + P[11][0]*SK_MX[2] - P[11][16]*SK_MX[1] + P[11][17]*SK_MX[4] - P[11][18]*SK_MX[3]);
Kfusion[12] = SK_MX[0]*(P[12][19] + P[12][1]*SH_MAG[0] - P[12][2]*SH_MAG[1] + P[12][3]*SH_MAG[2] + P[12][0]*SK_MX[2] - P[12][16]*SK_MX[1] + P[12][17]*SK_MX[4] - P[12][18]*SK_MX[3]);
} else {
// zero indexes 10 to 12 = 3*4 bytes
memset(&Kfusion[10], 0, 12);
}
if (!inhibitDelVelBiasStates) {
for (uint8_t index = 0; index < 3; index++) {
const uint8_t stateIndex = index + 13;
if (!dvelBiasAxisInhibit[index]) {
Kfusion[stateIndex] = SK_MX[0]*(P[stateIndex][19] + P[stateIndex][1]*SH_MAG[0] - P[stateIndex][2]*SH_MAG[1] + P[stateIndex][3]*SH_MAG[2] + P[stateIndex][0]*SK_MX[2] - P[stateIndex][16]*SK_MX[1] + P[stateIndex][17]*SK_MX[4] - P[stateIndex][18]*SK_MX[3]);
} else {
Kfusion[stateIndex] = 0.0f;
}
}
} else {
// zero indexes 13 to 15 = 3*4 bytes
memset(&Kfusion[13], 0, 12);
}
// zero Kalman gains to inhibit magnetic field state estimation
if (!inhibitMagStates) {
Kfusion[16] = SK_MX[0]*(P[16][19] + P[16][1]*SH_MAG[0] - P[16][2]*SH_MAG[1] + P[16][3]*SH_MAG[2] + P[16][0]*SK_MX[2] - P[16][16]*SK_MX[1] + P[16][17]*SK_MX[4] - P[16][18]*SK_MX[3]);
Kfusion[17] = SK_MX[0]*(P[17][19] + P[17][1]*SH_MAG[0] - P[17][2]*SH_MAG[1] + P[17][3]*SH_MAG[2] + P[17][0]*SK_MX[2] - P[17][16]*SK_MX[1] + P[17][17]*SK_MX[4] - P[17][18]*SK_MX[3]);
Kfusion[18] = SK_MX[0]*(P[18][19] + P[18][1]*SH_MAG[0] - P[18][2]*SH_MAG[1] + P[18][3]*SH_MAG[2] + P[18][0]*SK_MX[2] - P[18][16]*SK_MX[1] + P[18][17]*SK_MX[4] - P[18][18]*SK_MX[3]);
Kfusion[19] = SK_MX[0]*(P[19][19] + P[19][1]*SH_MAG[0] - P[19][2]*SH_MAG[1] + P[19][3]*SH_MAG[2] + P[19][0]*SK_MX[2] - P[19][16]*SK_MX[1] + P[19][17]*SK_MX[4] - P[19][18]*SK_MX[3]);
Kfusion[20] = SK_MX[0]*(P[20][19] + P[20][1]*SH_MAG[0] - P[20][2]*SH_MAG[1] + P[20][3]*SH_MAG[2] + P[20][0]*SK_MX[2] - P[20][16]*SK_MX[1] + P[20][17]*SK_MX[4] - P[20][18]*SK_MX[3]);
Kfusion[21] = SK_MX[0]*(P[21][19] + P[21][1]*SH_MAG[0] - P[21][2]*SH_MAG[1] + P[21][3]*SH_MAG[2] + P[21][0]*SK_MX[2] - P[21][16]*SK_MX[1] + P[21][17]*SK_MX[4] - P[21][18]*SK_MX[3]);
} else {
// zero indexes 16 to 21 = 6*4 bytes
memset(&Kfusion[16], 0, 24);
}
// zero Kalman gains to inhibit wind state estimation
if (!inhibitWindStates) {
Kfusion[22] = SK_MX[0]*(P[22][19] + P[22][1]*SH_MAG[0] - P[22][2]*SH_MAG[1] + P[22][3]*SH_MAG[2] + P[22][0]*SK_MX[2] - P[22][16]*SK_MX[1] + P[22][17]*SK_MX[4] - P[22][18]*SK_MX[3]);
Kfusion[23] = SK_MX[0]*(P[23][19] + P[23][1]*SH_MAG[0] - P[23][2]*SH_MAG[1] + P[23][3]*SH_MAG[2] + P[23][0]*SK_MX[2] - P[23][16]*SK_MX[1] + P[23][17]*SK_MX[4] - P[23][18]*SK_MX[3]);
} else {
// zero indexes 22 to 23 = 2*4 bytes
memset(&Kfusion[22], 0, 8);
}
// set flags to indicate to other processes that fusion has been performed and is required on the next frame
// this can be used by other fusion processes to avoid fusing on the same frame as this expensive step
magFusePerformed = true;
} else if (obsIndex == 1) { // Fuse Y axis
// calculate observation jacobians
for (uint8_t i = 0; i<=stateIndexLim; i++) H_MAG[i] = 0.0f;
H_MAG[0] = SH_MAG[2];
H_MAG[1] = SH_MAG[1];
H_MAG[2] = SH_MAG[0];
H_MAG[3] = 2.0f*magD*q2 - SH_MAG[8] - SH_MAG[7];
H_MAG[16] = 2.0f*q1*q2 - 2.0f*q0*q3;
H_MAG[17] = SH_MAG[4] - SH_MAG[3] - SH_MAG[5] + SH_MAG[6];
H_MAG[18] = 2.0f*q0*q1 + 2.0f*q2*q3;
H_MAG[19] = 0.0f;
H_MAG[20] = 1.0f;
H_MAG[21] = 0.0f;
// calculate Kalman gain
SK_MY[0] = 1.0f / varInnovMag[1];
SK_MY[1] = SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6];
SK_MY[2] = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
SK_MY[3] = 2.0f*q0*q3 - 2.0f*q1*q2;
SK_MY[4] = 2.0f*q0*q1 + 2.0f*q2*q3;
Kfusion[0] = SK_MY[0]*(P[0][20] + P[0][0]*SH_MAG[2] + P[0][1]*SH_MAG[1] + P[0][2]*SH_MAG[0] - P[0][3]*SK_MY[2] - P[0][17]*SK_MY[1] - P[0][16]*SK_MY[3] + P[0][18]*SK_MY[4]);
Kfusion[1] = SK_MY[0]*(P[1][20] + P[1][0]*SH_MAG[2] + P[1][1]*SH_MAG[1] + P[1][2]*SH_MAG[0] - P[1][3]*SK_MY[2] - P[1][17]*SK_MY[1] - P[1][16]*SK_MY[3] + P[1][18]*SK_MY[4]);
Kfusion[2] = SK_MY[0]*(P[2][20] + P[2][0]*SH_MAG[2] + P[2][1]*SH_MAG[1] + P[2][2]*SH_MAG[0] - P[2][3]*SK_MY[2] - P[2][17]*SK_MY[1] - P[2][16]*SK_MY[3] + P[2][18]*SK_MY[4]);
Kfusion[3] = SK_MY[0]*(P[3][20] + P[3][0]*SH_MAG[2] + P[3][1]*SH_MAG[1] + P[3][2]*SH_MAG[0] - P[3][3]*SK_MY[2] - P[3][17]*SK_MY[1] - P[3][16]*SK_MY[3] + P[3][18]*SK_MY[4]);
Kfusion[4] = SK_MY[0]*(P[4][20] + P[4][0]*SH_MAG[2] + P[4][1]*SH_MAG[1] + P[4][2]*SH_MAG[0] - P[4][3]*SK_MY[2] - P[4][17]*SK_MY[1] - P[4][16]*SK_MY[3] + P[4][18]*SK_MY[4]);
Kfusion[5] = SK_MY[0]*(P[5][20] + P[5][0]*SH_MAG[2] + P[5][1]*SH_MAG[1] + P[5][2]*SH_MAG[0] - P[5][3]*SK_MY[2] - P[5][17]*SK_MY[1] - P[5][16]*SK_MY[3] + P[5][18]*SK_MY[4]);
Kfusion[6] = SK_MY[0]*(P[6][20] + P[6][0]*SH_MAG[2] + P[6][1]*SH_MAG[1] + P[6][2]*SH_MAG[0] - P[6][3]*SK_MY[2] - P[6][17]*SK_MY[1] - P[6][16]*SK_MY[3] + P[6][18]*SK_MY[4]);
Kfusion[7] = SK_MY[0]*(P[7][20] + P[7][0]*SH_MAG[2] + P[7][1]*SH_MAG[1] + P[7][2]*SH_MAG[0] - P[7][3]*SK_MY[2] - P[7][17]*SK_MY[1] - P[7][16]*SK_MY[3] + P[7][18]*SK_MY[4]);
Kfusion[8] = SK_MY[0]*(P[8][20] + P[8][0]*SH_MAG[2] + P[8][1]*SH_MAG[1] + P[8][2]*SH_MAG[0] - P[8][3]*SK_MY[2] - P[8][17]*SK_MY[1] - P[8][16]*SK_MY[3] + P[8][18]*SK_MY[4]);
Kfusion[9] = SK_MY[0]*(P[9][20] + P[9][0]*SH_MAG[2] + P[9][1]*SH_MAG[1] + P[9][2]*SH_MAG[0] - P[9][3]*SK_MY[2] - P[9][17]*SK_MY[1] - P[9][16]*SK_MY[3] + P[9][18]*SK_MY[4]);
if (!inhibitDelAngBiasStates) {
Kfusion[10] = SK_MY[0]*(P[10][20] + P[10][0]*SH_MAG[2] + P[10][1]*SH_MAG[1] + P[10][2]*SH_MAG[0] - P[10][3]*SK_MY[2] - P[10][17]*SK_MY[1] - P[10][16]*SK_MY[3] + P[10][18]*SK_MY[4]);
Kfusion[11] = SK_MY[0]*(P[11][20] + P[11][0]*SH_MAG[2] + P[11][1]*SH_MAG[1] + P[11][2]*SH_MAG[0] - P[11][3]*SK_MY[2] - P[11][17]*SK_MY[1] - P[11][16]*SK_MY[3] + P[11][18]*SK_MY[4]);
Kfusion[12] = SK_MY[0]*(P[12][20] + P[12][0]*SH_MAG[2] + P[12][1]*SH_MAG[1] + P[12][2]*SH_MAG[0] - P[12][3]*SK_MY[2] - P[12][17]*SK_MY[1] - P[12][16]*SK_MY[3] + P[12][18]*SK_MY[4]);
} else {
// zero indexes 10 to 12 = 3*4 bytes
memset(&Kfusion[10], 0, 12);
}
if (!inhibitDelVelBiasStates) {
for (uint8_t index = 0; index < 3; index++) {
const uint8_t stateIndex = index + 13;
if (!dvelBiasAxisInhibit[index]) {
Kfusion[stateIndex] = SK_MY[0]*(P[stateIndex][20] + P[stateIndex][0]*SH_MAG[2] + P[stateIndex][1]*SH_MAG[1] + P[stateIndex][2]*SH_MAG[0] - P[stateIndex][3]*SK_MY[2] - P[stateIndex][17]*SK_MY[1] - P[stateIndex][16]*SK_MY[3] + P[stateIndex][18]*SK_MY[4]);
} else {
Kfusion[stateIndex] = 0.0f;
}
}
} else {
// zero indexes 13 to 15 = 3*4 bytes
memset(&Kfusion[13], 0, 12);
}
// zero Kalman gains to inhibit magnetic field state estimation
if (!inhibitMagStates) {
Kfusion[16] = SK_MY[0]*(P[16][20] + P[16][0]*SH_MAG[2] + P[16][1]*SH_MAG[1] + P[16][2]*SH_MAG[0] - P[16][3]*SK_MY[2] - P[16][17]*SK_MY[1] - P[16][16]*SK_MY[3] + P[16][18]*SK_MY[4]);
Kfusion[17] = SK_MY[0]*(P[17][20] + P[17][0]*SH_MAG[2] + P[17][1]*SH_MAG[1] + P[17][2]*SH_MAG[0] - P[17][3]*SK_MY[2] - P[17][17]*SK_MY[1] - P[17][16]*SK_MY[3] + P[17][18]*SK_MY[4]);
Kfusion[18] = SK_MY[0]*(P[18][20] + P[18][0]*SH_MAG[2] + P[18][1]*SH_MAG[1] + P[18][2]*SH_MAG[0] - P[18][3]*SK_MY[2] - P[18][17]*SK_MY[1] - P[18][16]*SK_MY[3] + P[18][18]*SK_MY[4]);
Kfusion[19] = SK_MY[0]*(P[19][20] + P[19][0]*SH_MAG[2] + P[19][1]*SH_MAG[1] + P[19][2]*SH_MAG[0] - P[19][3]*SK_MY[2] - P[19][17]*SK_MY[1] - P[19][16]*SK_MY[3] + P[19][18]*SK_MY[4]);
Kfusion[20] = SK_MY[0]*(P[20][20] + P[20][0]*SH_MAG[2] + P[20][1]*SH_MAG[1] + P[20][2]*SH_MAG[0] - P[20][3]*SK_MY[2] - P[20][17]*SK_MY[1] - P[20][16]*SK_MY[3] + P[20][18]*SK_MY[4]);
Kfusion[21] = SK_MY[0]*(P[21][20] + P[21][0]*SH_MAG[2] + P[21][1]*SH_MAG[1] + P[21][2]*SH_MAG[0] - P[21][3]*SK_MY[2] - P[21][17]*SK_MY[1] - P[21][16]*SK_MY[3] + P[21][18]*SK_MY[4]);
} else {
// zero indexes 16 to 21 = 6*4 bytes
memset(&Kfusion[16], 0, 24);
}
// zero Kalman gains to inhibit wind state estimation
if (!inhibitWindStates) {
Kfusion[22] = SK_MY[0]*(P[22][20] + P[22][0]*SH_MAG[2] + P[22][1]*SH_MAG[1] + P[22][2]*SH_MAG[0] - P[22][3]*SK_MY[2] - P[22][17]*SK_MY[1] - P[22][16]*SK_MY[3] + P[22][18]*SK_MY[4]);
Kfusion[23] = SK_MY[0]*(P[23][20] + P[23][0]*SH_MAG[2] + P[23][1]*SH_MAG[1] + P[23][2]*SH_MAG[0] - P[23][3]*SK_MY[2] - P[23][17]*SK_MY[1] - P[23][16]*SK_MY[3] + P[23][18]*SK_MY[4]);
} else {
// zero indexes 22 to 23 = 2*4 bytes
memset(&Kfusion[22], 0, 8);
}
// set flags to indicate to other processes that fusion has been performed and is required on the next frame
// this can be used by other fusion processes to avoid fusing on the same frame as this expensive step
magFusePerformed = true;
}
else if (obsIndex == 2) // we are now fusing the Z measurement
{
// calculate observation jacobians
for (uint8_t i = 0; i<=stateIndexLim; i++) H_MAG[i] = 0.0f;
H_MAG[0] = SH_MAG[1];
H_MAG[1] = -SH_MAG[2];
H_MAG[2] = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
H_MAG[3] = SH_MAG[0];
H_MAG[16] = 2.0f*q0*q2 + 2.0f*q1*q3;
H_MAG[17] = 2.0f*q2*q3 - 2.0f*q0*q1;
H_MAG[18] = SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6];
H_MAG[19] = 0.0f;
H_MAG[20] = 0.0f;
H_MAG[21] = 1.0f;
// calculate Kalman gain
SK_MZ[0] = 1.0f / varInnovMag[2];
SK_MZ[1] = SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6];
SK_MZ[2] = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
SK_MZ[3] = 2.0f*q0*q1 - 2.0f*q2*q3;
SK_MZ[4] = 2.0f*q0*q2 + 2.0f*q1*q3;
Kfusion[0] = SK_MZ[0]*(P[0][21] + P[0][0]*SH_MAG[1] - P[0][1]*SH_MAG[2] + P[0][3]*SH_MAG[0] + P[0][2]*SK_MZ[2] + P[0][18]*SK_MZ[1] + P[0][16]*SK_MZ[4] - P[0][17]*SK_MZ[3]);
Kfusion[1] = SK_MZ[0]*(P[1][21] + P[1][0]*SH_MAG[1] - P[1][1]*SH_MAG[2] + P[1][3]*SH_MAG[0] + P[1][2]*SK_MZ[2] + P[1][18]*SK_MZ[1] + P[1][16]*SK_MZ[4] - P[1][17]*SK_MZ[3]);
Kfusion[2] = SK_MZ[0]*(P[2][21] + P[2][0]*SH_MAG[1] - P[2][1]*SH_MAG[2] + P[2][3]*SH_MAG[0] + P[2][2]*SK_MZ[2] + P[2][18]*SK_MZ[1] + P[2][16]*SK_MZ[4] - P[2][17]*SK_MZ[3]);
Kfusion[3] = SK_MZ[0]*(P[3][21] + P[3][0]*SH_MAG[1] - P[3][1]*SH_MAG[2] + P[3][3]*SH_MAG[0] + P[3][2]*SK_MZ[2] + P[3][18]*SK_MZ[1] + P[3][16]*SK_MZ[4] - P[3][17]*SK_MZ[3]);
Kfusion[4] = SK_MZ[0]*(P[4][21] + P[4][0]*SH_MAG[1] - P[4][1]*SH_MAG[2] + P[4][3]*SH_MAG[0] + P[4][2]*SK_MZ[2] + P[4][18]*SK_MZ[1] + P[4][16]*SK_MZ[4] - P[4][17]*SK_MZ[3]);
Kfusion[5] = SK_MZ[0]*(P[5][21] + P[5][0]*SH_MAG[1] - P[5][1]*SH_MAG[2] + P[5][3]*SH_MAG[0] + P[5][2]*SK_MZ[2] + P[5][18]*SK_MZ[1] + P[5][16]*SK_MZ[4] - P[5][17]*SK_MZ[3]);
Kfusion[6] = SK_MZ[0]*(P[6][21] + P[6][0]*SH_MAG[1] - P[6][1]*SH_MAG[2] + P[6][3]*SH_MAG[0] + P[6][2]*SK_MZ[2] + P[6][18]*SK_MZ[1] + P[6][16]*SK_MZ[4] - P[6][17]*SK_MZ[3]);
Kfusion[7] = SK_MZ[0]*(P[7][21] + P[7][0]*SH_MAG[1] - P[7][1]*SH_MAG[2] + P[7][3]*SH_MAG[0] + P[7][2]*SK_MZ[2] + P[7][18]*SK_MZ[1] + P[7][16]*SK_MZ[4] - P[7][17]*SK_MZ[3]);
Kfusion[8] = SK_MZ[0]*(P[8][21] + P[8][0]*SH_MAG[1] - P[8][1]*SH_MAG[2] + P[8][3]*SH_MAG[0] + P[8][2]*SK_MZ[2] + P[8][18]*SK_MZ[1] + P[8][16]*SK_MZ[4] - P[8][17]*SK_MZ[3]);
Kfusion[9] = SK_MZ[0]*(P[9][21] + P[9][0]*SH_MAG[1] - P[9][1]*SH_MAG[2] + P[9][3]*SH_MAG[0] + P[9][2]*SK_MZ[2] + P[9][18]*SK_MZ[1] + P[9][16]*SK_MZ[4] - P[9][17]*SK_MZ[3]);
if (!inhibitDelAngBiasStates) {
Kfusion[10] = SK_MZ[0]*(P[10][21] + P[10][0]*SH_MAG[1] - P[10][1]*SH_MAG[2] + P[10][3]*SH_MAG[0] + P[10][2]*SK_MZ[2] + P[10][18]*SK_MZ[1] + P[10][16]*SK_MZ[4] - P[10][17]*SK_MZ[3]);
Kfusion[11] = SK_MZ[0]*(P[11][21] + P[11][0]*SH_MAG[1] - P[11][1]*SH_MAG[2] + P[11][3]*SH_MAG[0] + P[11][2]*SK_MZ[2] + P[11][18]*SK_MZ[1] + P[11][16]*SK_MZ[4] - P[11][17]*SK_MZ[3]);
Kfusion[12] = SK_MZ[0]*(P[12][21] + P[12][0]*SH_MAG[1] - P[12][1]*SH_MAG[2] + P[12][3]*SH_MAG[0] + P[12][2]*SK_MZ[2] + P[12][18]*SK_MZ[1] + P[12][16]*SK_MZ[4] - P[12][17]*SK_MZ[3]);
} else {
// zero indexes 10 to 12 = 3*4 bytes
memset(&Kfusion[10], 0, 12);
}
if (!inhibitDelVelBiasStates) {
for (uint8_t index = 0; index < 3; index++) {
const uint8_t stateIndex = index + 13;
if (!dvelBiasAxisInhibit[index]) {
Kfusion[stateIndex] = SK_MZ[0]*(P[stateIndex][21] + P[stateIndex][0]*SH_MAG[1] - P[stateIndex][1]*SH_MAG[2] + P[stateIndex][3]*SH_MAG[0] + P[stateIndex][2]*SK_MZ[2] + P[stateIndex][18]*SK_MZ[1] + P[stateIndex][16]*SK_MZ[4] - P[stateIndex][17]*SK_MZ[3]);
} else {
Kfusion[stateIndex] = 0.0f;
}
}
} else {
// zero indexes 13 to 15 = 3*4 bytes
memset(&Kfusion[13], 0, 12);
}
// 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][1]*SH_MAG[2] + P[16][3]*SH_MAG[0] + P[16][2]*SK_MZ[2] + P[16][18]*SK_MZ[1] + P[16][16]*SK_MZ[4] - P[16][17]*SK_MZ[3]);
Kfusion[17] = SK_MZ[0]*(P[17][21] + P[17][0]*SH_MAG[1] - P[17][1]*SH_MAG[2] + P[17][3]*SH_MAG[0] + P[17][2]*SK_MZ[2] + P[17][18]*SK_MZ[1] + P[17][16]*SK_MZ[4] - P[17][17]*SK_MZ[3]);
Kfusion[18] = SK_MZ[0]*(P[18][21] + P[18][0]*SH_MAG[1] - P[18][1]*SH_MAG[2] + P[18][3]*SH_MAG[0] + P[18][2]*SK_MZ[2] + P[18][18]*SK_MZ[1] + P[18][16]*SK_MZ[4] - P[18][17]*SK_MZ[3]);
Kfusion[19] = SK_MZ[0]*(P[19][21] + P[19][0]*SH_MAG[1] - P[19][1]*SH_MAG[2] + P[19][3]*SH_MAG[0] + P[19][2]*SK_MZ[2] + P[19][18]*SK_MZ[1] + P[19][16]*SK_MZ[4] - P[19][17]*SK_MZ[3]);
Kfusion[20] = SK_MZ[0]*(P[20][21] + P[20][0]*SH_MAG[1] - P[20][1]*SH_MAG[2] + P[20][3]*SH_MAG[0] + P[20][2]*SK_MZ[2] + P[20][18]*SK_MZ[1] + P[20][16]*SK_MZ[4] - P[20][17]*SK_MZ[3]);
Kfusion[21] = SK_MZ[0]*(P[21][21] + P[21][0]*SH_MAG[1] - P[21][1]*SH_MAG[2] + P[21][3]*SH_MAG[0] + P[21][2]*SK_MZ[2] + P[21][18]*SK_MZ[1] + P[21][16]*SK_MZ[4] - P[21][17]*SK_MZ[3]);
} else {
// zero indexes 16 to 21 = 6*4 bytes
memset(&Kfusion[16], 0, 24);
}
// zero Kalman gains to inhibit wind state estimation
if (!inhibitWindStates) {
Kfusion[22] = SK_MZ[0]*(P[22][21] + P[22][0]*SH_MAG[1] - P[22][1]*SH_MAG[2] + P[22][3]*SH_MAG[0] + P[22][2]*SK_MZ[2] + P[22][18]*SK_MZ[1] + P[22][16]*SK_MZ[4] - P[22][17]*SK_MZ[3]);
Kfusion[23] = SK_MZ[0]*(P[23][21] + P[23][0]*SH_MAG[1] - P[23][1]*SH_MAG[2] + P[23][3]*SH_MAG[0] + P[23][2]*SK_MZ[2] + P[23][18]*SK_MZ[1] + P[23][16]*SK_MZ[4] - P[23][17]*SK_MZ[3]);
} else {
// zero indexes 22 to 23 = 2*4 bytes
memset(&Kfusion[22], 0, 8);
}
// set flags to indicate to other processes that fusion has been performed and is required on the next frame
// this can be used by other fusion processes to avoid fusing on the same frame as this expensive step
magFusePerformed = true;
}
// correct the covariance P = (I - K*H)*P
// take advantage of the empty columns in KH to reduce the
// number of operations
for (unsigned i = 0; i<=stateIndexLim; i++) {
for (unsigned j = 0; j<=3; j++) {
KH[i][j] = Kfusion[i] * H_MAG[j];
}
for (unsigned j = 4; j<=15; j++) {
KH[i][j] = 0.0f;
}
for (unsigned j = 16; j<=21; j++) {
KH[i][j] = Kfusion[i] * H_MAG[j];
}
for (unsigned j = 22; j<=23; j++) {
KH[i][j] = 0.0f;
}
}
for (unsigned j = 0; j<=stateIndexLim; j++) {
for (unsigned i = 0; i<=stateIndexLim; i++) {
ftype res = 0;
res += KH[i][0] * P[0][j];
res += KH[i][1] * P[1][j];
res += KH[i][2] * P[2][j];
res += KH[i][3] * P[3][j];
res += KH[i][16] * P[16][j];
res += KH[i][17] * P[17][j];
res += KH[i][18] * P[18][j];
res += KH[i][19] * P[19][j];
res += KH[i][20] * P[20][j];
res += KH[i][21] * P[21][j];
KHP[i][j] = res;
}
}
// Check that we are not going to drive any variances negative and skip the update if so
bool healthyFusion = true;
for (uint8_t i= 0; i<=stateIndexLim; i++) {
if (KHP[i][i] > P[i][i]) {
healthyFusion = false;
}
}
if (healthyFusion) {
// update the covariance matrix
for (uint8_t i= 0; i<=stateIndexLim; i++) {
for (uint8_t j= 0; j<=stateIndexLim; j++) {
P[i][j] = P[i][j] - KHP[i][j];
}
}
// force the covariance matrix to be symmetrical and limit the variances to prevent ill-conditioning.
ForceSymmetry();
ConstrainVariances();
// correct the state vector
for (uint8_t j= 0; j<=stateIndexLim; j++) {
statesArray[j] = statesArray[j] - Kfusion[j] * innovMag[obsIndex];
}
// add table constraint here for faster convergence
if (have_table_earth_field && frontend->_mag_ef_limit > 0) {
MagTableConstrain();
}
stateStruct.quat.normalize();
} else {
// record bad axis
if (obsIndex == 0) {
faultStatus.bad_xmag = true;
} else if (obsIndex == 1) {
faultStatus.bad_ymag = true;
} else if (obsIndex == 2) {
faultStatus.bad_zmag = true;
}
CovarianceInit();
return;
}
}
}
/*
* Fuse direct yaw measurements using explicit algebraic equations auto-generated from
* /AP_NavEKF3/derivation/main.py with output recorded in /AP_NavEKF3/derivation/generated/yaw_generated.cpp
* Returns true if the fusion was successful
*/
bool NavEKF3_core::fuseEulerYaw(yawFusionMethod method)
{
const float &q0 = stateStruct.quat[0];
const float &q1 = stateStruct.quat[1];
const float &q2 = stateStruct.quat[2];
const float &q3 = stateStruct.quat[3];
float gsfYaw, gsfYawVariance;
if (method == yawFusionMethod::GSF) {
if (!EKFGSF_getYaw(gsfYaw, gsfYawVariance)) {
return false;
}
}
// yaw measurement error variance (rad^2)
float R_YAW;
switch (method) {
case yawFusionMethod::GPS:
R_YAW = sq(yawAngDataDelayed.yawAngErr);
break;
case yawFusionMethod::GSF:
R_YAW = gsfYawVariance;
break;
case yawFusionMethod::STATIC:
R_YAW = sq(yawAngDataStatic.yawAngErr);
break;
case yawFusionMethod::MAGNETOMETER:
case yawFusionMethod::PREDICTED:
default:
R_YAW = sq(frontend->_yawNoise);
break;
#if EK3_FEATURE_EXTERNAL_NAV
case yawFusionMethod::EXTNAV:
R_YAW = sq(MAX(extNavYawAngDataDelayed.yawAngErr, 0.05f));
break;
#endif
}
// determine if a 321 or 312 Euler sequence is best
rotationOrder order;
switch (method) {
case yawFusionMethod::GPS:
order = yawAngDataDelayed.order;
break;
case yawFusionMethod::STATIC:
order = yawAngDataStatic.order;
break;
case yawFusionMethod::MAGNETOMETER:
case yawFusionMethod::GSF:
case yawFusionMethod::PREDICTED:
default:
// determined automatically
order = (fabsf(prevTnb[0][2]) < fabsf(prevTnb[1][2])) ? rotationOrder::TAIT_BRYAN_321 : rotationOrder::TAIT_BRYAN_312;
break;
#if EK3_FEATURE_EXTERNAL_NAV
case yawFusionMethod::EXTNAV:
order = extNavYawAngDataDelayed.order;
break;
#endif
}
// calculate observation jacobian, predicted yaw and zero yaw body to earth rotation matrix
float yawAngPredicted;
float H_YAW[4];
Matrix3f Tbn_zeroYaw;
if (order == rotationOrder::TAIT_BRYAN_321) {
// calculate 321 yaw observation matrix - option A or B to avoid singularity in derivation at +-90 degrees yaw
bool canUseA = false;
const float SA0 = 2*q3;
const float SA1 = 2*q2;
const float SA2 = SA0*q0 + SA1*q1;
const float SA3 = sq(q0) + sq(q1) - sq(q2) - sq(q3);
float SA4, SA5_inv;
if (is_positive(sq(SA3))) {
SA4 = 1.0F/sq(SA3);
SA5_inv = sq(SA2)*SA4 + 1;
canUseA = is_positive(fabsf(SA5_inv));
}
bool canUseB = false;
const float SB0 = 2*q0;
const float SB1 = 2*q1;
const float SB2 = SB0*q3 + SB1*q2;
const float SB4 = sq(q0) + sq(q1) - sq(q2) - sq(q3);
float SB3, SB5_inv;
if (is_positive(sq(SB2))) {
SB3 = 1.0F/sq(SB2);
SB5_inv = SB3*sq(SB4) + 1;
canUseB = is_positive(fabsf(SB5_inv));
}
if (canUseA && (!canUseB || fabsf(SA5_inv) >= fabsf(SB5_inv))) {
const float SA5 = 1.0F/SA5_inv;
const float SA6 = 1.0F/SA3;
const float SA7 = SA2*SA4;
const float SA8 = 2*SA7;
const float SA9 = 2*SA6;
H_YAW[0] = SA5*(SA0*SA6 - SA8*q0);
H_YAW[1] = SA5*(SA1*SA6 - SA8*q1);
H_YAW[2] = SA5*(SA1*SA7 + SA9*q1);
H_YAW[3] = SA5*(SA0*SA7 + SA9*q0);
} else if (canUseB && (!canUseA || fabsf(SB5_inv) > fabsf(SA5_inv))) {
const float SB5 = 1.0F/SB5_inv;
const float SB6 = 1.0F/SB2;
const float SB7 = SB3*SB4;
const float SB8 = 2*SB7;
const float SB9 = 2*SB6;
H_YAW[0] = -SB5*(SB0*SB6 - SB8*q3);
H_YAW[1] = -SB5*(SB1*SB6 - SB8*q2);
H_YAW[2] = -SB5*(-SB1*SB7 - SB9*q2);
H_YAW[3] = -SB5*(-SB0*SB7 - SB9*q3);
} else {
return false;
}
// Get the 321 euler angles
Vector3f euler321;
stateStruct.quat.to_euler(euler321.x, euler321.y, euler321.z);
yawAngPredicted = euler321.z;
// set the yaw to zero and calculate the zero yaw rotation from body to earth frame
Tbn_zeroYaw.from_euler(euler321.x, euler321.y, 0.0f);
} else if (order == rotationOrder::TAIT_BRYAN_312) {
// calculate 312 yaw observation matrix - option A or B to avoid singularity in derivation at +-90 degrees yaw
bool canUseA = false;
const float SA0 = 2*q3;
const float SA1 = 2*q2;
const float SA2 = SA0*q0 - SA1*q1;
const float SA3 = sq(q0) - sq(q1) + sq(q2) - sq(q3);
float SA4, SA5_inv;
if (is_positive(sq(SA3))) {
SA4 = 1.0F/sq(SA3);
SA5_inv = sq(SA2)*SA4 + 1;
canUseA = is_positive(fabsf(SA5_inv));
}
bool canUseB = false;
const float SB0 = 2*q0;
const float SB1 = 2*q1;
const float SB2 = -SB0*q3 + SB1*q2;
const float SB4 = -sq(q0) + sq(q1) - sq(q2) + sq(q3);
float SB3, SB5_inv;
if (is_positive(sq(SB2))) {
SB3 = 1.0F/sq(SB2);
SB5_inv = SB3*sq(SB4) + 1;
canUseB = is_positive(fabsf(SB5_inv));
}
if (canUseA && (!canUseB || fabsf(SA5_inv) >= fabsf(SB5_inv))) {
const float SA5 = 1.0F/SA5_inv;
const float SA6 = 1.0F/SA3;
const float SA7 = SA2*SA4;
const float SA8 = 2*SA7;
const float SA9 = 2*SA6;
H_YAW[0] = SA5*(SA0*SA6 - SA8*q0);
H_YAW[1] = SA5*(-SA1*SA6 + SA8*q1);
H_YAW[2] = SA5*(-SA1*SA7 - SA9*q1);
H_YAW[3] = SA5*(SA0*SA7 + SA9*q0);
} else if (canUseB && (!canUseA || fabsf(SB5_inv) > fabsf(SA5_inv))) {
const float SB5 = 1.0F/SB5_inv;
const float SB6 = 1.0F/SB2;
const float SB7 = SB3*SB4;
const float SB8 = 2*SB7;
const float SB9 = 2*SB6;
H_YAW[0] = -SB5*(-SB0*SB6 + SB8*q3);
H_YAW[1] = -SB5*(SB1*SB6 - SB8*q2);
H_YAW[2] = -SB5*(-SB1*SB7 - SB9*q2);
H_YAW[3] = -SB5*(SB0*SB7 + SB9*q3);
} else {
return false;
}
// Get the 312 Tait Bryan rotation angles
Vector3f euler312 = stateStruct.quat.to_vector312();
yawAngPredicted = euler312.z;
// set the yaw to zero and calculate the zero yaw rotation from body to earth frame
Tbn_zeroYaw.from_euler312(euler312.x, euler312.y, 0.0f);
} else {
// order not supported
return false;
}
// Calculate the innovation
switch (method) {
case yawFusionMethod::MAGNETOMETER:
{
// Use the difference between the horizontal projection and declination to give the measured yaw
// rotate measured mag components into earth frame
Vector3f magMeasNED = Tbn_zeroYaw*magDataDelayed.mag;
float yawAngMeasured = wrap_PI(-atan2f(magMeasNED.y, magMeasNED.x) + MagDeclination());
innovYaw = wrap_PI(yawAngPredicted - yawAngMeasured);
break;
}
case yawFusionMethod::GPS:
innovYaw = wrap_PI(yawAngPredicted - yawAngDataDelayed.yawAng);
break;
case yawFusionMethod::STATIC:
innovYaw = wrap_PI(yawAngPredicted - yawAngDataStatic.yawAng);
break;
case yawFusionMethod::GSF:
innovYaw = wrap_PI(yawAngPredicted - gsfYaw);
break;
case yawFusionMethod::PREDICTED:
default:
innovYaw = 0.0f;
break;
#if EK3_FEATURE_EXTERNAL_NAV
case yawFusionMethod::EXTNAV:
innovYaw = wrap_PI(yawAngPredicted - extNavYawAngDataDelayed.yawAng);
break;
#endif
}
// Calculate innovation variance and Kalman gains, taking advantage of the fact that only the first 4 elements in H are non zero
float PH[4];
float varInnov = R_YAW;
for (uint8_t rowIndex=0; rowIndex<=3; rowIndex++) {
PH[rowIndex] = 0.0f;
for (uint8_t colIndex=0; colIndex<=3; colIndex++) {
PH[rowIndex] += P[rowIndex][colIndex]*H_YAW[colIndex];
}
varInnov += H_YAW[rowIndex]*PH[rowIndex];
}
float varInnovInv;
if (varInnov >= R_YAW) {
varInnovInv = 1.0f / varInnov;
// output numerical health status
faultStatus.bad_yaw = false;
} else {
// the calculation is badly conditioned, so we cannot perform fusion on this step
// we reset the covariance matrix and try again next measurement
CovarianceInit();
// output numerical health status
faultStatus.bad_yaw = true;
return false;
}
// calculate Kalman gain
for (uint8_t rowIndex=0; rowIndex<=stateIndexLim; rowIndex++) {
Kfusion[rowIndex] = 0.0f;
for (uint8_t colIndex=0; colIndex<=3; colIndex++) {
Kfusion[rowIndex] += P[rowIndex][colIndex]*H_YAW[colIndex];
}
Kfusion[rowIndex] *= varInnovInv;
}
// calculate the innovation test ratio
yawTestRatio = sq(innovYaw) / (sq(MAX(0.01f * (float)frontend->_yawInnovGate, 1.0f)) * varInnov);
// Declare the magnetometer unhealthy if the innovation test fails
if (yawTestRatio > 1.0f) {
magHealth = false;
// On the ground a large innovation could be due to large initial gyro bias or magnetic interference from nearby objects
// If we are flying, then it is more likely due to a magnetometer fault and we should not fuse the data
if (inFlight) {
return false;
}
} else {
magHealth = true;
}
// correct the covariance using P = P - K*H*P taking advantage of the fact that only the first 3 elements in H are non zero
// calculate K*H*P
for (uint8_t row = 0; row <= stateIndexLim; row++) {
for (uint8_t column = 0; column <= 3; column++) {
KH[row][column] = Kfusion[row] * H_YAW[column];
}
}
for (uint8_t row = 0; row <= stateIndexLim; row++) {
for (uint8_t column = 0; column <= stateIndexLim; column++) {
float tmp = KH[row][0] * P[0][column];
tmp += KH[row][1] * P[1][column];
tmp += KH[row][2] * P[2][column];
tmp += KH[row][3] * P[3][column];
KHP[row][column] = tmp;
}
}
// Check that we are not going to drive any variances negative and skip the update if so
bool healthyFusion = true;
for (uint8_t i= 0; i<=stateIndexLim; i++) {
if (KHP[i][i] > P[i][i]) {
healthyFusion = false;
}
}
if (healthyFusion) {
// update the covariance matrix
for (uint8_t i= 0; i<=stateIndexLim; i++) {
for (uint8_t j= 0; j<=stateIndexLim; j++) {
P[i][j] = P[i][j] - KHP[i][j];
}
}
// force the covariance matrix to be symmetrical and limit the variances to prevent ill-conditioning.
ForceSymmetry();
ConstrainVariances();
// correct the state vector
for (uint8_t i=0; i<=stateIndexLim; i++) {
statesArray[i] -= Kfusion[i] * constrain_float(innovYaw, -0.5f, 0.5f);
}
stateStruct.quat.normalize();
// record fusion numerical health status
faultStatus.bad_yaw = false;
} else {
// record fusion numerical health status
faultStatus.bad_yaw = true;
}
return true;
}
/*
* Fuse declination angle using explicit algebraic equations generated with Matlab symbolic toolbox.
* The script file used to generate these and other equations in this filter can be found here:
* https://github.com/PX4/ecl/blob/master/matlab/scripts/Inertial%20Nav%20EKF/GenerateNavFilterEquations.m
* This is used to prevent the declination of the EKF earth field states from drifting during operation without GPS
* or some other absolute position or velocity reference
*/
void NavEKF3_core::FuseDeclination(float declErr)
{
// declination error variance (rad^2)
const float R_DECL = sq(declErr);
// copy required states to local variables
float magN = stateStruct.earth_magfield.x;
float magE = stateStruct.earth_magfield.y;
// prevent bad earth field states from causing numerical errors or exceptions
if (magN < 1e-3f) {
return;
}
// Calculate observation Jacobian and Kalman gains
// Calculate intermediate variables
float t2 = magE*magE;
float t3 = magN*magN;
float t4 = t2+t3;
// if the horizontal magnetic field is too small, this calculation will be badly conditioned
if (t4 < 1e-4f) {
return;
}
float t5 = P[16][16]*t2;
float t6 = P[17][17]*t3;
float t7 = t2*t2;
float t8 = R_DECL*t7;
float t9 = t3*t3;
float t10 = R_DECL*t9;
float t11 = R_DECL*t2*t3*2.0f;
float t14 = P[16][17]*magE*magN;
float t15 = P[17][16]*magE*magN;
float t12 = t5+t6+t8+t10+t11-t14-t15;
float t13;
if (fabsf(t12) > 1e-6f) {
t13 = 1.0f / t12;
} else {
return;
}
float t18 = magE*magE;
float t19 = magN*magN;
float t20 = t18+t19;
float t21;
if (fabsf(t20) > 1e-6f) {
t21 = 1.0f/t20;
} else {
return;
}
// Calculate the observation Jacobian
// Note only 2 terms are non-zero which can be used in matrix operations for calculation of Kalman gains and covariance update to significantly reduce cost
float H_DECL[24] = {};
H_DECL[16] = -magE*t21;
H_DECL[17] = magN*t21;
Kfusion[0] = -t4*t13*(P[0][16]*magE-P[0][17]*magN);
Kfusion[1] = -t4*t13*(P[1][16]*magE-P[1][17]*magN);
Kfusion[2] = -t4*t13*(P[2][16]*magE-P[2][17]*magN);
Kfusion[3] = -t4*t13*(P[3][16]*magE-P[3][17]*magN);
Kfusion[4] = -t4*t13*(P[4][16]*magE-P[4][17]*magN);
Kfusion[5] = -t4*t13*(P[5][16]*magE-P[5][17]*magN);
Kfusion[6] = -t4*t13*(P[6][16]*magE-P[6][17]*magN);
Kfusion[7] = -t4*t13*(P[7][16]*magE-P[7][17]*magN);
Kfusion[8] = -t4*t13*(P[8][16]*magE-P[8][17]*magN);
Kfusion[9] = -t4*t13*(P[9][16]*magE-P[9][17]*magN);
if (!inhibitDelAngBiasStates) {
Kfusion[10] = -t4*t13*(P[10][16]*magE-P[10][17]*magN);
Kfusion[11] = -t4*t13*(P[11][16]*magE-P[11][17]*magN);
Kfusion[12] = -t4*t13*(P[12][16]*magE-P[12][17]*magN);
} else {
// zero indexes 10 to 12 = 3*4 bytes
memset(&Kfusion[10], 0, 12);
}
if (!inhibitDelVelBiasStates) {
for (uint8_t index = 0; index < 3; index++) {
const uint8_t stateIndex = index + 13;
if (!dvelBiasAxisInhibit[index]) {
Kfusion[stateIndex] = -t4*t13*(P[stateIndex][16]*magE-P[stateIndex][17]*magN);
} else {
Kfusion[stateIndex] = 0.0f;
}
}
} else {
// zero indexes 13 to 15 = 3*4 bytes
memset(&Kfusion[13], 0, 12);
}
if (!inhibitMagStates) {
Kfusion[16] = -t4*t13*(P[16][16]*magE-P[16][17]*magN);
Kfusion[17] = -t4*t13*(P[17][16]*magE-P[17][17]*magN);
Kfusion[18] = -t4*t13*(P[18][16]*magE-P[18][17]*magN);
Kfusion[19] = -t4*t13*(P[19][16]*magE-P[19][17]*magN);
Kfusion[20] = -t4*t13*(P[20][16]*magE-P[20][17]*magN);
Kfusion[21] = -t4*t13*(P[21][16]*magE-P[21][17]*magN);
} else {
// zero indexes 16 to 21 = 6*4 bytes
memset(&Kfusion[16], 0, 24);
}
if (!inhibitWindStates) {
Kfusion[22] = -t4*t13*(P[22][16]*magE-P[22][17]*magN);
Kfusion[23] = -t4*t13*(P[23][16]*magE-P[23][17]*magN);
} else {
// zero indexes 22 to 23 = 2*4 bytes
memset(&Kfusion[22], 0, 8);
}
// get the magnetic declination
float magDecAng = MagDeclination();
// Calculate the innovation
float innovation = atan2f(magE , magN) - magDecAng;
// limit the innovation to protect against data errors
if (innovation > 0.5f) {
innovation = 0.5f;
} else if (innovation < -0.5f) {
innovation = -0.5f;
}
// correct the covariance P = (I - K*H)*P
// take advantage of the empty columns in KH to reduce the
// number of operations
for (unsigned i = 0; i<=stateIndexLim; i++) {
for (unsigned j = 0; j<=15; j++) {
KH[i][j] = 0.0f;
}
KH[i][16] = Kfusion[i] * H_DECL[16];
KH[i][17] = Kfusion[i] * H_DECL[17];
for (unsigned j = 18; j<=23; j++) {
KH[i][j] = 0.0f;
}
}
for (unsigned j = 0; j<=stateIndexLim; j++) {
for (unsigned i = 0; i<=stateIndexLim; i++) {
KHP[i][j] = KH[i][16] * P[16][j] + KH[i][17] * P[17][j];
}
}
// Check that we are not going to drive any variances negative and skip the update if so
bool healthyFusion = true;
for (uint8_t i= 0; i<=stateIndexLim; i++) {
if (KHP[i][i] > P[i][i]) {
healthyFusion = false;
}
}
if (healthyFusion) {
// update the covariance matrix
for (uint8_t i= 0; i<=stateIndexLim; i++) {
for (uint8_t j= 0; j<=stateIndexLim; j++) {
P[i][j] = P[i][j] - KHP[i][j];
}
}
// force the covariance matrix to be symmetrical and limit the variances to prevent ill-conditioning.
ForceSymmetry();
ConstrainVariances();
// correct the state vector
for (uint8_t j= 0; j<=stateIndexLim; j++) {
statesArray[j] = statesArray[j] - Kfusion[j] * innovation;
}
stateStruct.quat.normalize();
// record fusion health status
faultStatus.bad_decl = false;
} else {
// record fusion health status
faultStatus.bad_decl = true;
}
}
/********************************************************
* MISC FUNCTIONS *
********************************************************/
// align the NE earth magnetic field states with the published declination
void NavEKF3_core::alignMagStateDeclination()
{
// don't do this if we already have a learned magnetic field
if (magFieldLearned) {
return;
}
// get the magnetic declination
float magDecAng = MagDeclination();
// rotate the NE values so that the declination matches the published value
Vector3f initMagNED = stateStruct.earth_magfield;
float magLengthNE = norm(initMagNED.x,initMagNED.y);
stateStruct.earth_magfield.x = magLengthNE * cosf(magDecAng);
stateStruct.earth_magfield.y = magLengthNE * sinf(magDecAng);
if (!inhibitMagStates) {
// zero the corresponding state covariances if magnetic field state learning is active
float var_16 = P[16][16];
float var_17 = P[17][17];
zeroRows(P,16,17);
zeroCols(P,16,17);
P[16][16] = var_16;
P[17][17] = var_17;
// fuse the declination angle to establish covariances and prevent large swings in declination
// during initial fusion
FuseDeclination(0.1f);
}
}
// record a magnetic field state reset event
void NavEKF3_core::recordMagReset()
{
magStateResetRequest = false;
magStateInitComplete = true;
if (inFlight) {
finalInflightMagInit = true;
}
// take a snap-shot of the vertical position, quaternion and yaw innovation to use as a reference
// for post alignment checks
posDownAtLastMagReset = stateStruct.position.z;
quatAtLastMagReset = stateStruct.quat;
yawInnovAtLastMagReset = innovYaw;
}
/*
learn magnetometer biases from GPS yaw. Return true if the
resulting mag vector is close enough to the one predicted by GPS
yaw to use it for fallback
*/
bool NavEKF3_core::learnMagBiasFromGPS(void)
{
if (!have_table_earth_field) {
// we need the earth field from WMM
return false;
}
if (!inFlight) {
// don't start learning till we've started flying
return false;
}
mag_elements mag_data;
if (!storedMag.recall(mag_data, imuDataDelayed.time_ms)) {
// no mag data to correct
return false;
}
// combine yaw with current quaternion to get yaw corrected quaternion
Quaternion quat = stateStruct.quat;
if (yawAngDataDelayed.order == rotationOrder::TAIT_BRYAN_321) {
Vector3f euler321;
quat.to_euler(euler321.x, euler321.y, euler321.z);
quat.from_euler(euler321.x, euler321.y, yawAngDataDelayed.yawAng);
} else if (yawAngDataDelayed.order == rotationOrder::TAIT_BRYAN_312) {
Vector3f euler312 = quat.to_vector312();
quat.from_vector312(euler312.x, euler312.y, yawAngDataDelayed.yawAng);
} else {
// rotation order not supported
return false;
}
// build the expected body field from orientation and table earth field
Matrix3f dcm;
quat.rotation_matrix(dcm);
Vector3f expected_body_field = dcm.transposed() * table_earth_field_ga;
// calculate error in field
Vector3f err = (expected_body_field - mag_data.mag) + stateStruct.body_magfield;
// learn body frame mag biases
stateStruct.body_magfield -= err * EK3_GPS_MAG_LEARN_RATE;
// check if error is below threshold. If it is then we can
// fallback to magnetometer on failure of external yaw
float err_length = err.length();
// we allow for yaw backback to compass if we have had 50 samples
// in a row below the threshold. This corresponds to 10 seconds
// for a 5Hz GPS
const uint8_t fallback_count_threshold = 50;
if (err_length > EK3_GPS_MAG_LEARN_LIMIT) {
gps_yaw_fallback_good_counter = 0;
} else if (gps_yaw_fallback_good_counter < fallback_count_threshold) {
gps_yaw_fallback_good_counter++;
}
bool ok = gps_yaw_fallback_good_counter >= fallback_count_threshold;
if (ok) {
// mark mag healthy to prevent a magTimeout when we start using it
lastHealthyMagTime_ms = imuSampleTime_ms;
}
return ok;
}
// Reset states using yaw from EKF-GSF and velocity and position from GPS
bool NavEKF3_core::EKFGSF_resetMainFilterYaw()
{
// Don't do a reset unless permitted by the EK3_GSF_USE and EK3_GSF_RUN parameter masks
if ((yawEstimator == nullptr)
|| !(frontend->_gsfUseMask & (1U<<core_index))
|| EKFGSF_yaw_reset_count >= frontend->_gsfResetMaxCount) {
return false;
};
float yawEKFGSF, yawVarianceEKFGSF;
if (EKFGSF_getYaw(yawEKFGSF, yawVarianceEKFGSF)) {
// keep roll and pitch and reset yaw
rotationOrder order;
bestRotationOrder(order);
resetQuatStateYawOnly(yawEKFGSF, yawVarianceEKFGSF, order);
// record the emergency reset event
EKFGSF_yaw_reset_request_ms = 0;
EKFGSF_yaw_reset_ms = imuSampleTime_ms;
EKFGSF_yaw_reset_count++;
if ((frontend->sources.getYawSource() == AP_NavEKF_Source::SourceYaw::GSF) ||
!use_compass() || (dal.compass().get_num_enabled() == 0)) {
GCS_SEND_TEXT(MAV_SEVERITY_INFO, "EKF3 IMU%u yaw aligned using GPS",(unsigned)imu_index);
} else {
GCS_SEND_TEXT(MAV_SEVERITY_WARNING, "EKF3 IMU%u emergency yaw reset",(unsigned)imu_index);
}
// Fail the magnetomer so it doesn't get used and pull the yaw away from the correct value
allMagSensorsFailed = true;
// record the yaw reset event
recordYawReset();
// reset velocity and position states to GPS - if yaw is fixed then the filter should start to operate correctly
ResetVelocity(resetDataSource::DEFAULT);
ResetPosition(resetDataSource::DEFAULT);
// reset test ratios that are reported to prevent a race condition with the external state machine requesting the reset
velTestRatio = 0.0f;
posTestRatio = 0.0f;
return true;
}
return false;
}
// returns true on success and populates yaw (in radians) and yawVariance (rad^2)
bool NavEKF3_core::EKFGSF_getYaw(float &yaw, float &yawVariance) const
{
// return immediately if no yaw estimator
if (yawEstimator == nullptr) {
return false;
}
float velInnovLength;
if (yawEstimator->getYawData(yaw, yawVariance) &&
is_positive(yawVariance) &&
yawVariance < sq(radians(GSF_YAW_ACCURACY_THRESHOLD_DEG)) &&
(assume_zero_sideslip() || (yawEstimator->getVelInnovLength(velInnovLength) && velInnovLength < frontend->maxYawEstVelInnov))) {
return true;
}
return false;
}
void NavEKF3_core::resetQuatStateYawOnly(float yaw, float yawVariance, rotationOrder order)
{
Quaternion quatBeforeReset = stateStruct.quat;
// check if we should use a 321 or 312 Rotation order and update the quaternion
// states using the preferred yaw definition
stateStruct.quat.inverse().rotation_matrix(prevTnb);
Vector3f eulerAngles;
if (order == rotationOrder::TAIT_BRYAN_321) {
// rolled more than pitched so use 321 rotation order
stateStruct.quat.to_euler(eulerAngles.x, eulerAngles.y, eulerAngles.z);
stateStruct.quat.from_euler(eulerAngles.x, eulerAngles.y, yaw);
} else if (order == rotationOrder::TAIT_BRYAN_312) {
// pitched more than rolled so use 312 rotation order
eulerAngles = stateStruct.quat.to_vector312();
stateStruct.quat.from_vector312(eulerAngles.x, eulerAngles.y, yaw);
} else {
// rotation order not supported
return;
}
// Update the rotation matrix
stateStruct.quat.inverse().rotation_matrix(prevTnb);
float deltaYaw = wrap_PI(yaw - eulerAngles.z);
// calculate the change in the quaternion state and apply it to the output history buffer
Quaternion quat_delta = stateStruct.quat / quatBeforeReset;
StoreQuatRotate(quat_delta);
// assume tilt uncertainty split equally between roll and pitch
Vector3f angleErrVarVec = Vector3f(0.5f * tiltErrorVariance, 0.5f * tiltErrorVariance, yawVariance);
CovariancePrediction(&angleErrVarVec);
// record the yaw reset event
yawResetAngle += deltaYaw;
lastYawReset_ms = imuSampleTime_ms;
// record the yaw reset event
recordYawReset();
// clear all pending yaw reset requests
gpsYawResetRequest = false;
magYawResetRequest = false;
}
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