ardupilot/libraries/AP_NavEKF3/AP_NavEKF3_MagFusion.cpp

#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>

// 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()) {
#if APM_BUILD_TYPE(APM_BUILD_ArduSub)
        // for sub, we'd like to be far enough away from metal structures like docks and vessels
        // diving 0.5m is reasonable for both open water and pools
        finalResetRequest = (stateStruct.position.z  - posDownAtTakeoff) > EKF3_MAG_FINAL_RESET_ALT_SUB;
#else
        // 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;
#endif

        // 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;

        // 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;
        }

        // 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;
            }

            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 if (yawAlignGpsValidCount >= GPS_VEL_YAW_ALIGN_COUNT_THRESHOLD) {
                // There is no need to do a yaw reset
                yawAlignGpsValidCount = 0;
                recordYawResetsCompleted();
        }
    } 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) {
            magFusionSel = MagFuseSel::FUSE_YAW;
            fuseEulerYaw(yawFusionMethod::MAGNETOMETER);

            // zero the test ratio output from the inactive 3-axis magnetometer fusion
            magTestRatio.zero();

        } else {
            magFusionSel = MagFuseSel::FUSE_MAG;
            // 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 && !treatWindStatesAsTruth) {
                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 && !treatWindStatesAsTruth) {
                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 && !treatWindStatesAsTruth) {
                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 && !treatWindStatesAsTruth) {
        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<<core_index))) {
        return false;
    };

    // limit the number of emergency resets
    if (emergency_reset && (EKFGSF_yaw_reset_count >= 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
        recordYawResetsCompleted();

        // 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
    recordYawResetsCompleted();
}