#include #include "AP_NavEKF3.h" #include "AP_NavEKF3_core.h" #include #include // minimum GPS horizontal speed required to use GPS ground course for yaw alignment (m/s) #if APM_BUILD_TYPE(APM_BUILD_ArduPlane) #define GPS_VEL_YAW_ALIGN_MIN_SPD 5.0F #else #define GPS_VEL_YAW_ALIGN_MIN_SPD 1.0F #endif /******************************************************** * 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; QuaternionF 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; ftype 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(bool emergency_reset) { // 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 (gpsDataDelayed.vel.xy().length_squared() > sq(GPS_VEL_YAW_ALIGN_MIN_SPD)) { // calculate course yaw angle ftype velYaw = atan2F(stateStruct.velocity.y,stateStruct.velocity.x); // calculate course yaw angle from GPS velocity ftype gpsYaw = atan2F(gpsDataDelayed.vel.y,gpsDataDelayed.vel.x); // Check the yaw angles for consistency ftype 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 // by default fly forward vehicles use ground course for initial yaw unless the GSF is explicitly selected as the yaw source const bool useGSF = !assume_zero_sideslip() || (yaw_source_last == AP_NavEKF_Source::SourceYaw::GSF); if (useGSF && EKFGSF_resetMainFilterYaw(emergency_reset)) { return; } // get yaw variance from GPS speed uncertainty const ftype gpsVelAcc = fmaxF(gpsSpdAccuracy, ftype(frontend->_gpsHorizVelNoise)); const ftype gps_yaw_variance = sq(asinF(constrain_float(gpsVelAcc/gpsDataDelayed.vel.xy().length(), -1.0F, 1.0F))); if (gps_yaw_variance < sq(radians(GPS_VEL_YAW_ALIGN_MAX_ANG_ERR))) { yawAlignGpsValidCount++; } else { yawAlignGpsValidCount = 0; } if (yawAlignGpsValidCount >= GPS_VEL_YAW_ALIGN_COUNT_THRESHOLD) { yawAlignGpsValidCount = 0; // keep roll and pitch and reset yaw rotationOrder order; bestRotationOrder(order); resetQuatStateYawOnly(gpsYaw, gps_yaw_variance, 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; } } } } else { yawAlignGpsValidCount = 0; } } // 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-2)), 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; // 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 or GPS ground course. if ((yaw_source_last == AP_NavEKF_Source::SourceYaw::GSF) || (!use_compass() && yaw_source_last != AP_NavEKF_Source::SourceYaw::GPS && yaw_source_last != AP_NavEKF_Source::SourceYaw::GPS_COMPASS_FALLBACK && yaw_source_last != AP_NavEKF_Source::SourceYaw::EXTNAV)) { if ((!yawAlignComplete || yaw_source_reset) && ((yaw_source_last != AP_NavEKF_Source::SourceYaw::GSF) || (EKFGSF_yaw_valid_count >= GSF_YAW_VALID_HISTORY_THRESHOLD))) { realignYawGPS(false); yaw_source_reset = false; } else { 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 ftype gsfYaw, gsfYawVariance; const bool didUseEKFGSF = yawAlignComplete && (yaw_source_last == AP_NavEKF_Source::SourceYaw::GSF) && 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_last == AP_NavEKF_Source::SourceYaw::GPS || yaw_source_last == 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_last == 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_last == 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_last != 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_last == AP_NavEKF_Source::SourceYaw::COMPASS || yaw_source_last == 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() { // 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 // create aliases for state to make code easier to read: const ftype q0 = stateStruct.quat[0]; const ftype q1 = stateStruct.quat[1]; const ftype q2 = stateStruct.quat[2]; const ftype q3 = stateStruct.quat[3]; const ftype magN = stateStruct.earth_magfield[0]; const ftype magE = stateStruct.earth_magfield[1]; const ftype magD = stateStruct.earth_magfield[2]; const ftype magXbias = stateStruct.body_magfield[0]; const ftype magYbias = stateStruct.body_magfield[1]; const ftype magZbias = stateStruct.body_magfield[2]; // rotate predicted earth components into body axes and calculate // predicted measurements const Matrix3F DCM { q0*q0 + q1*q1 - q2*q2 - q3*q3, 2.0f*(q1*q2 + q0*q3), 2.0f*(q1*q3-q0*q2), 2.0f*(q1*q2 - q0*q3), q0*q0 - q1*q1 + q2*q2 - q3*q3, 2.0f*(q2*q3 + q0*q1), 2.0f*(q1*q3 + q0*q2), 2.0f*(q2*q3 - q0*q1), q0*q0 - q1*q1 - q2*q2 + q3*q3 }; const Vector3F MagPred { DCM[0][0]*magN + DCM[0][1]*magE + DCM[0][2]*magD + magXbias, DCM[1][0]*magN + DCM[1][1]*magE + DCM[1][2]*magD + magYbias, DCM[2][0]*magN + DCM[2][1]*magE + DCM[2][2]*magD + magZbias }; // calculate the measurement innovation for each axis innovMag = MagPred - magDataDelayed.mag; // scale magnetometer observation error with total angular rate to allow for timing errors const ftype R_MAG = sq(constrain_ftype(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 const Vector9 SH_MAG { 2.0f*magD*q3 + 2.0f*magE*q2 + 2.0f*magN*q1, 2.0f*magD*q0 - 2.0f*magE*q1 + 2.0f*magN*q2, 2.0f*magD*q1 + 2.0f*magE*q0 - 2.0f*magN*q3, sq(q3), sq(q2), sq(q1), sq(q0), 2.0f*magN*q0, 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 * (ftype)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; } Vector24 H_MAG; 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 const Vector5 SK_MX { 1.0f / varInnovMag[0], SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6], SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2, 2.0f*q0*q2 - 2.0f*q1*q3, 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 zero_range(&Kfusion[0], 10, 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 zero_range(&Kfusion[0], 13, 15); } // 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 zero_range(&Kfusion[0], 16, 21); } // 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 zero_range(&Kfusion[0], 22, 23); } // 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 const Vector5 SK_MY { 1.0f / varInnovMag[1], SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6], SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2, 2.0f*q0*q3 - 2.0f*q1*q2, 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 zero_range(&Kfusion[0], 10, 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 zero_range(&Kfusion[0], 13, 15); } // 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 zero_range(&Kfusion[0], 16, 21); } // 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 zero_range(&Kfusion[0], 22, 23); } // 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 const Vector5 SK_MZ { 1.0f / varInnovMag[2], SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6], SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2, 2.0f*q0*q1 - 2.0f*q2*q3, 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 zero_range(&Kfusion[0], 10, 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 zero_range(&Kfusion[0], 13, 15); } // 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 zero_range(&Kfusion[0], 16, 21); } // 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 zero_range(&Kfusion[0], 22, 23); } // 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 ftype &q0 = stateStruct.quat[0]; const ftype &q1 = stateStruct.quat[1]; const ftype &q2 = stateStruct.quat[2]; const ftype &q3 = stateStruct.quat[3]; ftype gsfYaw, gsfYawVariance; if (method == yawFusionMethod::GSF) { if (!EKFGSF_getYaw(gsfYaw, gsfYawVariance)) { return false; } } // yaw measurement error variance (rad^2) ftype 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 ftype yawAngPredicted; ftype 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 ftype SA0 = 2*q3; const ftype SA1 = 2*q2; const ftype SA2 = SA0*q0 + SA1*q1; const ftype SA3 = sq(q0) + sq(q1) - sq(q2) - sq(q3); ftype 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 ftype SB0 = 2*q0; const ftype SB1 = 2*q1; const ftype SB2 = SB0*q3 + SB1*q2; const ftype SB4 = sq(q0) + sq(q1) - sq(q2) - sq(q3); ftype 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 ftype SA5 = 1.0F/SA5_inv; const ftype SA6 = 1.0F/SA3; const ftype SA7 = SA2*SA4; const ftype SA8 = 2*SA7; const ftype 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 ftype SB5 = 1.0F/SB5_inv; const ftype SB6 = 1.0F/SB2; const ftype SB7 = SB3*SB4; const ftype SB8 = 2*SB7; const ftype 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 ftype SA0 = 2*q3; const ftype SA1 = 2*q2; const ftype SA2 = SA0*q0 - SA1*q1; const ftype SA3 = sq(q0) - sq(q1) + sq(q2) - sq(q3); ftype 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 ftype SB0 = 2*q0; const ftype SB1 = 2*q1; const ftype SB2 = -SB0*q3 + SB1*q2; const ftype SB4 = -sq(q0) + sq(q1) - sq(q2) + sq(q3); ftype 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 ftype SA5 = 1.0F/SA5_inv; const ftype SA6 = 1.0F/SA3; const ftype SA7 = SA2*SA4; const ftype SA8 = 2*SA7; const ftype 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 ftype SB5 = 1.0F/SB5_inv; const ftype SB6 = 1.0F/SB2; const ftype SB7 = SB3*SB4; const ftype SB8 = 2*SB7; const ftype 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; ftype 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 ftype PH[4]; ftype 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]; } ftype 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 * (ftype)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++) { ftype 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_ftype(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(ftype declErr) { // declination error variance (rad^2) const ftype R_DECL = sq(declErr); // copy required states to local variables ftype magN = stateStruct.earth_magfield.x; ftype 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 ftype t2 = magE*magE; ftype t3 = magN*magN; ftype t4 = t2+t3; // if the horizontal magnetic field is too small, this calculation will be badly conditioned if (t4 < 1e-4f) { return; } ftype t5 = P[16][16]*t2; ftype t6 = P[17][17]*t3; ftype t7 = t2*t2; ftype t8 = R_DECL*t7; ftype t9 = t3*t3; ftype t10 = R_DECL*t9; ftype t11 = R_DECL*t2*t3*2.0f; ftype t14 = P[16][17]*magE*magN; ftype t15 = P[17][16]*magE*magN; ftype t12 = t5+t6+t8+t10+t11-t14-t15; ftype t13; if (fabsF(t12) > 1e-6f) { t13 = 1.0f / t12; } else { return; } ftype t18 = magE*magE; ftype t19 = magN*magN; ftype t20 = t18+t19; ftype 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 ftype 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 zero_range(&Kfusion[0], 10, 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 zero_range(&Kfusion[0], 13, 15); } 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 zero_range(&Kfusion[0], 16, 21); } 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 zero_range(&Kfusion[0], 22, 23); } // get the magnetic declination ftype magDecAng = MagDeclination(); // Calculate the innovation ftype 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 ftype magDecAng = MagDeclination(); // rotate the NE values so that the declination matches the published value Vector3F initMagNED = stateStruct.earth_magfield; ftype magLengthNE = initMagNED.xy().length(); 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 ftype var_16 = P[16][16]; ftype 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 QuaternionF 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 ftype 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(bool emergency_reset) { // Don't do a reset unless permitted by the EK3_GSF_USE_MASK and EK3_GSF_RUN_MASK parameter masks if ((yawEstimator == nullptr) || !(frontend->_gsfUseMask & (1U<= frontend->_gsfResetMaxCount)) { return false; } ftype 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 ((yaw_source_last == 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 if (emergency_reset) { 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(ftype &yaw, ftype &yawVariance) const { // return immediately if no yaw estimator if (yawEstimator == nullptr) { return false; } ftype 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(ftype yaw, ftype yawVariance, rotationOrder order) { QuaternionF 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); ftype deltaYaw = wrap_PI(yaw - eulerAngles.z); // calculate the change in the quaternion state and apply it to the output history buffer QuaternionF quat_delta = stateStruct.quat / quatBeforeReset; StoreQuatRotate(quat_delta); // assume tilt uncertainty split equally between roll and pitch Vector3F angleErrVarVec = Vector3F(0.5 * tiltErrorVariance, 0.5 * 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; }