/// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: nil -*- #include #if HAL_CPU_CLASS >= HAL_CPU_CLASS_150 /* optionally turn down optimisation for debugging */ // #pragma GCC optimize("O0") #include "AP_NavEKF2.h" #include "AP_NavEKF2_core.h" #include #include #include extern const AP_HAL::HAL& hal; /******************************************************** * RESET FUNCTIONS * ********************************************************/ // Control reset of yaw and magnetic field states void NavEKF2_core::controlMagYawReset() { // Monitor the gain in height and reset the magnetic field states and heading when initial altitude has been gained // This is done to prevent magnetic field distoration from steel roofs and adjacent structures causing bad earth field and initial yaw values if (inFlight && !firstMagYawInit && (stateStruct.position.z - posDownAtTakeoff) < -1.5f) { // Do the first in-air yaw and earth mag field initialisation when the vehicle has gained 1.5m of altitude after commencement of flight Vector3f eulerAngles; getEulerAngles(eulerAngles); stateStruct.quat = calcQuatAndFieldStates(eulerAngles.x, eulerAngles.y); StoreQuatReset(); firstMagYawInit = true; } else if (inFlight && !secondMagYawInit && (stateStruct.position.z - posDownAtTakeoff) < -5.0f) { // Do the second and final yaw and earth mag field initialisation when the vehicle has gained 5.0m of altitude after commencement of flight // This second and final correction is needed for flight from large metal structures where the magnetic field distortion can extend up to 5m Vector3f eulerAngles; getEulerAngles(eulerAngles); stateStruct.quat = calcQuatAndFieldStates(eulerAngles.x, eulerAngles.y); StoreQuatReset(); secondMagYawInit = true; } // perform a yaw alignment check against GPS if exiting on-ground mode for fly forward type vehicle (plane) // this is done to protect against unrecoverable heading alignment errors due to compass faults if (!onGround && prevOnGround && assume_zero_sideslip()) { alignYawGPS(); } } // this function is used to do a forced alignment of the yaw angle to align with the horizontal velocity // vector from GPS. It is used to align the yaw angle after launch or takeoff. void NavEKF2_core::alignYawGPS() { if ((sq(gpsDataDelayed.vel.x) + sq(gpsDataDelayed.vel.y)) > 25.0f) { float roll; float pitch; float oldYaw; float newYaw; float yawErr; // get quaternion from existing filter states and calculate roll, pitch and yaw angles stateStruct.quat.to_euler(roll, pitch, oldYaw); // calculate course yaw angle oldYaw = atan2f(stateStruct.velocity.y,stateStruct.velocity.x); // calculate yaw angle from GPS velocity newYaw = atan2f(gpsDataNew.vel.y,gpsDataNew.vel.x); // estimate the yaw error yawErr = wrap_PI(newYaw - oldYaw); // If the inertial course angle disagrees with the GPS by more than 45 degrees, we declare the compass as bad badMag = (fabsf(yawErr) > 0.7854f); // correct yaw angle using GPS ground course compass failed or if not previously aligned if (badMag || !yawAligned) { // correct the yaw angle newYaw = oldYaw + yawErr; // calculate new filter quaternion states from Euler angles stateStruct.quat.from_euler(roll, pitch, newYaw); // the yaw angle is now aligned so update its status yawAligned = true; // reset the position and velocity states ResetPosition(); ResetVelocity(); // reset the covariance for the quaternion, velocity and position states // zero the matrix entries zeroRows(P,0,9); zeroCols(P,0,9); // velocities - we could have a big error coming out of constant position mode due to GPS lag P[3][3] = 400.0f; P[4][4] = P[3][3]; P[5][5] = sq(0.7f); // positions - we could have a big error coming out of constant position mode due to GPS lag P[6][6] = 400.0f; P[7][7] = P[6][6]; P[8][8] = sq(5.0f); } // Update magnetic field states if the magnetometer is bad if (badMag) { Vector3f eulerAngles; getEulerAngles(eulerAngles); calcQuatAndFieldStates(eulerAngles.x, eulerAngles.y); } } } /******************************************************** * FUSE MEASURED_DATA * ********************************************************/ // select fusion of magnetometer data void NavEKF2_core::SelectMagFusion() { // start performance timer perf_begin(_perf_FuseMagnetometer); // clear the flag that lets other processes know that the expensive magnetometer fusion operation has been perfomred on that time step // used for load levelling magFusePerformed = false; // check for and read new magnetometer measurements readMagData(); // If we are using the compass and the magnetometer has been unhealthy for too long we declare a timeout if (magHealth) { magTimeout = false; lastHealthyMagTime_ms = imuSampleTime_ms; } else if ((imuSampleTime_ms - lastHealthyMagTime_ms) > frontend.magFailTimeLimit_ms && use_compass()) { magTimeout = true; } bool temp = RecallMag(); // determine if conditions are right to start a new fusion cycle // wait until the EKF time horizon catches up with the measurement bool dataReady = (temp && statesInitialised && use_compass() && yawAlignComplete); if (dataReady) { // ensure that the covariance prediction is up to date before fusing data if (!covPredStep) CovariancePrediction(); // If we haven't performed the first airborne magnetic field update or have inhibited magnetic field learning, then we use the simple method of declination to maintain heading if(inhibitMagStates) { fuseCompass(); magHealth = true; magTimeout = false; } 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 if (PV_AidingMode != AID_ABSOLUTE) { FuseDeclination(); } // fuse the three magnetometer componenents sequentially for (mag_state.obsIndex = 0; mag_state.obsIndex <= 2; mag_state.obsIndex++) FuseMagnetometer(); } } // stop performance timer perf_end(_perf_FuseMagnetometer); } /* * 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/priseborough/InertialNav/blob/master/derivations/RotationVectorAttitudeParameterisation/GenerateNavFilterEquations.m */ void NavEKF2_core::FuseMagnetometer() { // declarations ftype &q0 = mag_state.q0; ftype &q1 = mag_state.q1; ftype &q2 = mag_state.q2; ftype &q3 = mag_state.q3; ftype &magN = mag_state.magN; ftype &magE = mag_state.magE; ftype &magD = mag_state.magD; ftype &magXbias = mag_state.magXbias; ftype &magYbias = mag_state.magYbias; ftype &magZbias = mag_state.magZbias; uint8_t &obsIndex = mag_state.obsIndex; Matrix3f &DCM = mag_state.DCM; Vector3f &MagPred = mag_state.MagPred; ftype &R_MAG = mag_state.R_MAG; ftype *SH_MAG = &mag_state.SH_MAG[0]; Vector24 H_MAG; Vector6 SK_MX; Vector6 SK_MY; Vector6 SK_MZ; // perform sequential fusion of magnetometer measurements. // this assumes that the errors in the different components are // uncorrelated which is not true, however in the absence of covariance // data fit is the only assumption we can make // so we might as well take advantage of the computational efficiencies // associated with sequential fusion // calculate observation jacobians and Kalman gains if (obsIndex == 0) { // copy required states to local variable names q0 = stateStruct.quat[0]; q1 = stateStruct.quat[1]; q2 = stateStruct.quat[2]; q3 = stateStruct.quat[3]; magN = stateStruct.earth_magfield[0]; magE = stateStruct.earth_magfield[1]; magD = stateStruct.earth_magfield[2]; magXbias = stateStruct.body_magfield[0]; magYbias = stateStruct.body_magfield[1]; magZbias = stateStruct.body_magfield[2]; // rotate predicted earth components into body axes and calculate // predicted measurements DCM[0][0] = q0*q0 + q1*q1 - q2*q2 - q3*q3; DCM[0][1] = 2*(q1*q2 + q0*q3); DCM[0][2] = 2*(q1*q3-q0*q2); DCM[1][0] = 2*(q1*q2 - q0*q3); DCM[1][1] = q0*q0 - q1*q1 + q2*q2 - q3*q3; DCM[1][2] = 2*(q2*q3 + q0*q1); DCM[2][0] = 2*(q1*q3 + q0*q2); DCM[2][1] = 2*(q2*q3 - q0*q1); DCM[2][2] = q0*q0 - q1*q1 - q2*q2 + q3*q3; MagPred[0] = DCM[0][0]*magN + DCM[0][1]*magE + DCM[0][2]*magD + magXbias; MagPred[1] = DCM[1][0]*magN + DCM[1][1]*magE + DCM[1][2]*magD + magYbias; MagPred[2] = DCM[2][0]*magN + DCM[2][1]*magE + DCM[2][2]*magD + magZbias; // scale magnetometer observation error with total angular rate R_MAG = sq(constrain_float(frontend._magNoise, 0.01f, 0.5f)) + sq(frontend.magVarRateScale*imuDataDelayed.delAng.length() / dtIMUavg); // calculate observation jacobians SH_MAG[0] = sq(q0) - sq(q1) + sq(q2) - sq(q3); SH_MAG[1] = sq(q0) + sq(q1) - sq(q2) - sq(q3); SH_MAG[2] = sq(q0) - sq(q1) - sq(q2) + sq(q3); SH_MAG[3] = 2*q0*q1 + 2*q2*q3; SH_MAG[4] = 2*q0*q3 + 2*q1*q2; SH_MAG[5] = 2*q0*q2 + 2*q1*q3; SH_MAG[6] = magE*(2*q0*q1 - 2*q2*q3); SH_MAG[7] = 2*q1*q3 - 2*q0*q2; SH_MAG[8] = 2*q0*q3; for (uint8_t i = 0; i<=stateIndexLim; i++) H_MAG[i] = 0.0f; H_MAG[1] = SH_MAG[6] - magD*SH_MAG[2] - magN*SH_MAG[5]; H_MAG[2] = magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2); H_MAG[16] = SH_MAG[1]; H_MAG[17] = SH_MAG[4]; H_MAG[18] = SH_MAG[7]; H_MAG[19] = 1; // calculate Kalman gain varInnovMag[0] = (P[19][19] + R_MAG - P[1][19]*(magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]) + P[16][19]*SH_MAG[1] + P[17][19]*SH_MAG[4] + P[18][19]*SH_MAG[7] + P[2][19]*(magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2)) - (magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5])*(P[19][1] - P[1][1]*(magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]) + P[16][1]*SH_MAG[1] + P[17][1]*SH_MAG[4] + P[18][1]*SH_MAG[7] + P[2][1]*(magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2))) + SH_MAG[1]*(P[19][16] - P[1][16]*(magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]) + P[16][16]*SH_MAG[1] + P[17][16]*SH_MAG[4] + P[18][16]*SH_MAG[7] + P[2][16]*(magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2))) + SH_MAG[4]*(P[19][17] - P[1][17]*(magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]) + P[16][17]*SH_MAG[1] + P[17][17]*SH_MAG[4] + P[18][17]*SH_MAG[7] + P[2][17]*(magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2))) + SH_MAG[7]*(P[19][18] - P[1][18]*(magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]) + P[16][18]*SH_MAG[1] + P[17][18]*SH_MAG[4] + P[18][18]*SH_MAG[7] + P[2][18]*(magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2))) + (magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2))*(P[19][2] - P[1][2]*(magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]) + P[16][2]*SH_MAG[1] + P[17][2]*SH_MAG[4] + P[18][2]*SH_MAG[7] + P[2][2]*(magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2)))); if (varInnovMag[0] >= R_MAG) { SK_MX[0] = 1.0f / varInnovMag[0]; 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(); obsIndex = 1; faultStatus.bad_xmag = true; return; } SK_MX[1] = magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2); SK_MX[2] = magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]; SK_MX[3] = SH_MAG[7]; Kfusion[0] = SK_MX[0]*(P[0][19] + P[0][16]*SH_MAG[1] + P[0][17]*SH_MAG[4] - P[0][1]*SK_MX[2] + P[0][2]*SK_MX[1] + P[0][18]*SK_MX[3]); Kfusion[1] = SK_MX[0]*(P[1][19] + P[1][16]*SH_MAG[1] + P[1][17]*SH_MAG[4] - P[1][1]*SK_MX[2] + P[1][2]*SK_MX[1] + P[1][18]*SK_MX[3]); Kfusion[2] = SK_MX[0]*(P[2][19] + P[2][16]*SH_MAG[1] + P[2][17]*SH_MAG[4] - P[2][1]*SK_MX[2] + P[2][2]*SK_MX[1] + P[2][18]*SK_MX[3]); Kfusion[3] = SK_MX[0]*(P[3][19] + P[3][16]*SH_MAG[1] + P[3][17]*SH_MAG[4] - P[3][1]*SK_MX[2] + P[3][2]*SK_MX[1] + P[3][18]*SK_MX[3]); Kfusion[4] = SK_MX[0]*(P[4][19] + P[4][16]*SH_MAG[1] + P[4][17]*SH_MAG[4] - P[4][1]*SK_MX[2] + P[4][2]*SK_MX[1] + P[4][18]*SK_MX[3]); Kfusion[5] = SK_MX[0]*(P[5][19] + P[5][16]*SH_MAG[1] + P[5][17]*SH_MAG[4] - P[5][1]*SK_MX[2] + P[5][2]*SK_MX[1] + P[5][18]*SK_MX[3]); Kfusion[6] = SK_MX[0]*(P[6][19] + P[6][16]*SH_MAG[1] + P[6][17]*SH_MAG[4] - P[6][1]*SK_MX[2] + P[6][2]*SK_MX[1] + P[6][18]*SK_MX[3]); Kfusion[7] = SK_MX[0]*(P[7][19] + P[7][16]*SH_MAG[1] + P[7][17]*SH_MAG[4] - P[7][1]*SK_MX[2] + P[7][2]*SK_MX[1] + P[7][18]*SK_MX[3]); Kfusion[8] = SK_MX[0]*(P[8][19] + P[8][16]*SH_MAG[1] + P[8][17]*SH_MAG[4] - P[8][1]*SK_MX[2] + P[8][2]*SK_MX[1] + P[8][18]*SK_MX[3]); Kfusion[9] = SK_MX[0]*(P[9][19] + P[9][16]*SH_MAG[1] + P[9][17]*SH_MAG[4] - P[9][1]*SK_MX[2] + P[9][2]*SK_MX[1] + P[9][18]*SK_MX[3]); Kfusion[10] = SK_MX[0]*(P[10][19] + P[10][16]*SH_MAG[1] + P[10][17]*SH_MAG[4] - P[10][1]*SK_MX[2] + P[10][2]*SK_MX[1] + P[10][18]*SK_MX[3]); Kfusion[11] = SK_MX[0]*(P[11][19] + P[11][16]*SH_MAG[1] + P[11][17]*SH_MAG[4] - P[11][1]*SK_MX[2] + P[11][2]*SK_MX[1] + P[11][18]*SK_MX[3]); Kfusion[12] = SK_MX[0]*(P[12][19] + P[12][16]*SH_MAG[1] + P[12][17]*SH_MAG[4] - P[12][1]*SK_MX[2] + P[12][2]*SK_MX[1] + P[12][18]*SK_MX[3]); Kfusion[13] = SK_MX[0]*(P[13][19] + P[13][16]*SH_MAG[1] + P[13][17]*SH_MAG[4] - P[13][1]*SK_MX[2] + P[13][2]*SK_MX[1] + P[13][18]*SK_MX[3]); Kfusion[14] = SK_MX[0]*(P[14][19] + P[14][16]*SH_MAG[1] + P[14][17]*SH_MAG[4] - P[14][1]*SK_MX[2] + P[14][2]*SK_MX[1] + P[14][18]*SK_MX[3]); Kfusion[15] = SK_MX[0]*(P[15][19] + P[15][16]*SH_MAG[1] + P[15][17]*SH_MAG[4] - P[15][1]*SK_MX[2] + P[15][2]*SK_MX[1] + P[15][18]*SK_MX[3]); // zero Kalman gains to inhibit wind state estimation if (!inhibitWindStates) { Kfusion[22] = SK_MX[0]*(P[22][19] + P[22][16]*SH_MAG[1] + P[22][17]*SH_MAG[4] - P[22][1]*SK_MX[2] + P[22][2]*SK_MX[1] + P[22][18]*SK_MX[3]); Kfusion[23] = SK_MX[0]*(P[23][19] + P[23][16]*SH_MAG[1] + P[23][17]*SH_MAG[4] - P[23][1]*SK_MX[2] + P[23][2]*SK_MX[1] + P[23][18]*SK_MX[3]); } else { Kfusion[22] = 0.0f; Kfusion[23] = 0.0f; } // zero Kalman gains to inhibit magnetic field state estimation if (!inhibitMagStates) { Kfusion[16] = SK_MX[0]*(P[16][19] + P[16][16]*SH_MAG[1] + P[16][17]*SH_MAG[4] - P[16][1]*SK_MX[2] + P[16][2]*SK_MX[1] + P[16][18]*SK_MX[3]); Kfusion[17] = SK_MX[0]*(P[17][19] + P[17][16]*SH_MAG[1] + P[17][17]*SH_MAG[4] - P[17][1]*SK_MX[2] + P[17][2]*SK_MX[1] + P[17][18]*SK_MX[3]); Kfusion[18] = SK_MX[0]*(P[18][19] + P[18][16]*SH_MAG[1] + P[18][17]*SH_MAG[4] - P[18][1]*SK_MX[2] + P[18][2]*SK_MX[1] + P[18][18]*SK_MX[3]); Kfusion[19] = SK_MX[0]*(P[19][19] + P[19][16]*SH_MAG[1] + P[19][17]*SH_MAG[4] - P[19][1]*SK_MX[2] + P[19][2]*SK_MX[1] + P[19][18]*SK_MX[3]); Kfusion[20] = SK_MX[0]*(P[20][19] + P[20][16]*SH_MAG[1] + P[20][17]*SH_MAG[4] - P[20][1]*SK_MX[2] + P[20][2]*SK_MX[1] + P[20][18]*SK_MX[3]); Kfusion[21] = SK_MX[0]*(P[21][19] + P[21][16]*SH_MAG[1] + P[21][17]*SH_MAG[4] - P[21][1]*SK_MX[2] + P[21][2]*SK_MX[1] + P[21][18]*SK_MX[3]); } else { for (uint8_t i=16; i<=21; i++) { Kfusion[i] = 0.0f; } } // reset the observation index to 0 (we start by fusing the X measurement) obsIndex = 0; // set flags to indicate to other processes that fusion has been performed and is required on the next frame // this can be used by other fusion processes to avoid fusing on the same frame as this expensive step magFusePerformed = true; magFuseRequired = true; } else if (obsIndex == 1) // we are now fusing the Y measurement { // calculate observation jacobians for (uint8_t i = 0; i<=stateIndexLim; i++) H_MAG[i] = 0.0f; H_MAG[0] = magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]; H_MAG[2] = - magE*SH_MAG[4] - magD*SH_MAG[7] - magN*SH_MAG[1]; H_MAG[16] = 2*q1*q2 - SH_MAG[8]; H_MAG[17] = SH_MAG[0]; H_MAG[18] = SH_MAG[3]; H_MAG[20] = 1; // calculate Kalman gain varInnovMag[1] = (P[20][20] + R_MAG + P[0][20]*(magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]) + P[17][20]*SH_MAG[0] + P[18][20]*SH_MAG[3] - (SH_MAG[8] - 2*q1*q2)*(P[20][16] + P[0][16]*(magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]) + P[17][16]*SH_MAG[0] + P[18][16]*SH_MAG[3] - P[2][16]*(magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]) - P[16][16]*(SH_MAG[8] - 2*q1*q2)) - P[2][20]*(magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]) + (magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5])*(P[20][0] + P[0][0]*(magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]) + P[17][0]*SH_MAG[0] + P[18][0]*SH_MAG[3] - P[2][0]*(magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]) - P[16][0]*(SH_MAG[8] - 2*q1*q2)) + SH_MAG[0]*(P[20][17] + P[0][17]*(magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]) + P[17][17]*SH_MAG[0] + P[18][17]*SH_MAG[3] - P[2][17]*(magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]) - P[16][17]*(SH_MAG[8] - 2*q1*q2)) + SH_MAG[3]*(P[20][18] + P[0][18]*(magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]) + P[17][18]*SH_MAG[0] + P[18][18]*SH_MAG[3] - P[2][18]*(magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]) - P[16][18]*(SH_MAG[8] - 2*q1*q2)) - P[16][20]*(SH_MAG[8] - 2*q1*q2) - (magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1])*(P[20][2] + P[0][2]*(magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]) + P[17][2]*SH_MAG[0] + P[18][2]*SH_MAG[3] - P[2][2]*(magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]) - P[16][2]*(SH_MAG[8] - 2*q1*q2))); if (varInnovMag[1] >= R_MAG) { SK_MY[0] = 1.0f / varInnovMag[1]; 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(); obsIndex = 2; faultStatus.bad_ymag = true; return; } SK_MY[1] = magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]; SK_MY[2] = magD*SH_MAG[2] - SH_MAG[6] + magN*SH_MAG[5]; SK_MY[3] = SH_MAG[8] - 2*q1*q2; Kfusion[0] = SK_MY[0]*(P[0][20] + P[0][17]*SH_MAG[0] + P[0][18]*SH_MAG[3] + P[0][0]*SK_MY[2] - P[0][2]*SK_MY[1] - P[0][16]*SK_MY[3]); Kfusion[1] = SK_MY[0]*(P[1][20] + P[1][17]*SH_MAG[0] + P[1][18]*SH_MAG[3] + P[1][0]*SK_MY[2] - P[1][2]*SK_MY[1] - P[1][16]*SK_MY[3]); Kfusion[2] = SK_MY[0]*(P[2][20] + P[2][17]*SH_MAG[0] + P[2][18]*SH_MAG[3] + P[2][0]*SK_MY[2] - P[2][2]*SK_MY[1] - P[2][16]*SK_MY[3]); Kfusion[3] = SK_MY[0]*(P[3][20] + P[3][17]*SH_MAG[0] + P[3][18]*SH_MAG[3] + P[3][0]*SK_MY[2] - P[3][2]*SK_MY[1] - P[3][16]*SK_MY[3]); Kfusion[4] = SK_MY[0]*(P[4][20] + P[4][17]*SH_MAG[0] + P[4][18]*SH_MAG[3] + P[4][0]*SK_MY[2] - P[4][2]*SK_MY[1] - P[4][16]*SK_MY[3]); Kfusion[5] = SK_MY[0]*(P[5][20] + P[5][17]*SH_MAG[0] + P[5][18]*SH_MAG[3] + P[5][0]*SK_MY[2] - P[5][2]*SK_MY[1] - P[5][16]*SK_MY[3]); Kfusion[6] = SK_MY[0]*(P[6][20] + P[6][17]*SH_MAG[0] + P[6][18]*SH_MAG[3] + P[6][0]*SK_MY[2] - P[6][2]*SK_MY[1] - P[6][16]*SK_MY[3]); Kfusion[7] = SK_MY[0]*(P[7][20] + P[7][17]*SH_MAG[0] + P[7][18]*SH_MAG[3] + P[7][0]*SK_MY[2] - P[7][2]*SK_MY[1] - P[7][16]*SK_MY[3]); Kfusion[8] = SK_MY[0]*(P[8][20] + P[8][17]*SH_MAG[0] + P[8][18]*SH_MAG[3] + P[8][0]*SK_MY[2] - P[8][2]*SK_MY[1] - P[8][16]*SK_MY[3]); Kfusion[9] = SK_MY[0]*(P[9][20] + P[9][17]*SH_MAG[0] + P[9][18]*SH_MAG[3] + P[9][0]*SK_MY[2] - P[9][2]*SK_MY[1] - P[9][16]*SK_MY[3]); Kfusion[10] = SK_MY[0]*(P[10][20] + P[10][17]*SH_MAG[0] + P[10][18]*SH_MAG[3] + P[10][0]*SK_MY[2] - P[10][2]*SK_MY[1] - P[10][16]*SK_MY[3]); Kfusion[11] = SK_MY[0]*(P[11][20] + P[11][17]*SH_MAG[0] + P[11][18]*SH_MAG[3] + P[11][0]*SK_MY[2] - P[11][2]*SK_MY[1] - P[11][16]*SK_MY[3]); Kfusion[12] = SK_MY[0]*(P[12][20] + P[12][17]*SH_MAG[0] + P[12][18]*SH_MAG[3] + P[12][0]*SK_MY[2] - P[12][2]*SK_MY[1] - P[12][16]*SK_MY[3]); Kfusion[13] = SK_MY[0]*(P[13][20] + P[13][17]*SH_MAG[0] + P[13][18]*SH_MAG[3] + P[13][0]*SK_MY[2] - P[13][2]*SK_MY[1] - P[13][16]*SK_MY[3]); Kfusion[14] = SK_MY[0]*(P[14][20] + P[14][17]*SH_MAG[0] + P[14][18]*SH_MAG[3] + P[14][0]*SK_MY[2] - P[14][2]*SK_MY[1] - P[14][16]*SK_MY[3]); Kfusion[15] = SK_MY[0]*(P[15][20] + P[15][17]*SH_MAG[0] + P[15][18]*SH_MAG[3] + P[15][0]*SK_MY[2] - P[15][2]*SK_MY[1] - P[15][16]*SK_MY[3]); // zero Kalman gains to inhibit wind state estimation if (!inhibitWindStates) { Kfusion[22] = SK_MY[0]*(P[22][20] + P[22][17]*SH_MAG[0] + P[22][18]*SH_MAG[3] + P[22][0]*SK_MY[2] - P[22][2]*SK_MY[1] - P[22][16]*SK_MY[3]); Kfusion[23] = SK_MY[0]*(P[23][20] + P[23][17]*SH_MAG[0] + P[23][18]*SH_MAG[3] + P[23][0]*SK_MY[2] - P[23][2]*SK_MY[1] - P[23][16]*SK_MY[3]); } else { Kfusion[22] = 0.0f; Kfusion[23] = 0.0f; } // zero Kalman gains to inhibit magnetic field state estimation if (!inhibitMagStates) { Kfusion[16] = SK_MY[0]*(P[16][20] + P[16][17]*SH_MAG[0] + P[16][18]*SH_MAG[3] + P[16][0]*SK_MY[2] - P[16][2]*SK_MY[1] - P[16][16]*SK_MY[3]); Kfusion[17] = SK_MY[0]*(P[17][20] + P[17][17]*SH_MAG[0] + P[17][18]*SH_MAG[3] + P[17][0]*SK_MY[2] - P[17][2]*SK_MY[1] - P[17][16]*SK_MY[3]); Kfusion[18] = SK_MY[0]*(P[18][20] + P[18][17]*SH_MAG[0] + P[18][18]*SH_MAG[3] + P[18][0]*SK_MY[2] - P[18][2]*SK_MY[1] - P[18][16]*SK_MY[3]); Kfusion[19] = SK_MY[0]*(P[19][20] + P[19][17]*SH_MAG[0] + P[19][18]*SH_MAG[3] + P[19][0]*SK_MY[2] - P[19][2]*SK_MY[1] - P[19][16]*SK_MY[3]); Kfusion[20] = SK_MY[0]*(P[20][20] + P[20][17]*SH_MAG[0] + P[20][18]*SH_MAG[3] + P[20][0]*SK_MY[2] - P[20][2]*SK_MY[1] - P[20][16]*SK_MY[3]); Kfusion[21] = SK_MY[0]*(P[21][20] + P[21][17]*SH_MAG[0] + P[21][18]*SH_MAG[3] + P[21][0]*SK_MY[2] - P[21][2]*SK_MY[1] - P[21][16]*SK_MY[3]); } else { for (uint8_t i=16; i<=21; i++) { Kfusion[i] = 0.0f; } } // set flags to indicate to other processes that fusion has been performede and is required on the next frame // this can be used by other fusion processes to avoid fusing on the same frame as this expensive step magFusePerformed = true; magFuseRequired = true; } else if (obsIndex == 2) // we are now fusing the Z measurement { // calculate observation jacobians for (uint8_t i = 0; i<=stateIndexLim; i++) H_MAG[i] = 0.0f; H_MAG[0] = magN*(SH_MAG[8] - 2*q1*q2) - magD*SH_MAG[3] - magE*SH_MAG[0]; H_MAG[1] = magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]; H_MAG[16] = SH_MAG[5]; H_MAG[17] = 2*q2*q3 - 2*q0*q1; H_MAG[18] = SH_MAG[2]; H_MAG[21] = 1; // calculate Kalman gain varInnovMag[2] = (P[21][21] + R_MAG + P[16][21]*SH_MAG[5] + P[18][21]*SH_MAG[2] - (2*q0*q1 - 2*q2*q3)*(P[21][17] + P[16][17]*SH_MAG[5] + P[18][17]*SH_MAG[2] - P[0][17]*(magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2)) + P[1][17]*(magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]) - P[17][17]*(2*q0*q1 - 2*q2*q3)) - P[0][21]*(magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2)) + P[1][21]*(magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]) + SH_MAG[5]*(P[21][16] + P[16][16]*SH_MAG[5] + P[18][16]*SH_MAG[2] - P[0][16]*(magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2)) + P[1][16]*(magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]) - P[17][16]*(2*q0*q1 - 2*q2*q3)) + SH_MAG[2]*(P[21][18] + P[16][18]*SH_MAG[5] + P[18][18]*SH_MAG[2] - P[0][18]*(magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2)) + P[1][18]*(magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]) - P[17][18]*(2*q0*q1 - 2*q2*q3)) - (magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2))*(P[21][0] + P[16][0]*SH_MAG[5] + P[18][0]*SH_MAG[2] - P[0][0]*(magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2)) + P[1][0]*(magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]) - P[17][0]*(2*q0*q1 - 2*q2*q3)) - P[17][21]*(2*q0*q1 - 2*q2*q3) + (magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1])*(P[21][1] + P[16][1]*SH_MAG[5] + P[18][1]*SH_MAG[2] - P[0][1]*(magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2)) + P[1][1]*(magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]) - P[17][1]*(2*q0*q1 - 2*q2*q3))); if (varInnovMag[2] >= R_MAG) { SK_MZ[0] = 1.0f / varInnovMag[2]; 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(); obsIndex = 3; faultStatus.bad_zmag = true; return; } SK_MZ[1] = magE*SH_MAG[0] + magD*SH_MAG[3] - magN*(SH_MAG[8] - 2*q1*q2); SK_MZ[2] = magE*SH_MAG[4] + magD*SH_MAG[7] + magN*SH_MAG[1]; SK_MZ[3] = 2*q0*q1 - 2*q2*q3; Kfusion[0] = SK_MZ[0]*(P[0][21] + P[0][18]*SH_MAG[2] + P[0][16]*SH_MAG[5] - P[0][0]*SK_MZ[1] + P[0][1]*SK_MZ[2] - P[0][17]*SK_MZ[3]); Kfusion[1] = SK_MZ[0]*(P[1][21] + P[1][18]*SH_MAG[2] + P[1][16]*SH_MAG[5] - P[1][0]*SK_MZ[1] + P[1][1]*SK_MZ[2] - P[1][17]*SK_MZ[3]); Kfusion[2] = SK_MZ[0]*(P[2][21] + P[2][18]*SH_MAG[2] + P[2][16]*SH_MAG[5] - P[2][0]*SK_MZ[1] + P[2][1]*SK_MZ[2] - P[2][17]*SK_MZ[3]); Kfusion[3] = SK_MZ[0]*(P[3][21] + P[3][18]*SH_MAG[2] + P[3][16]*SH_MAG[5] - P[3][0]*SK_MZ[1] + P[3][1]*SK_MZ[2] - P[3][17]*SK_MZ[3]); Kfusion[4] = SK_MZ[0]*(P[4][21] + P[4][18]*SH_MAG[2] + P[4][16]*SH_MAG[5] - P[4][0]*SK_MZ[1] + P[4][1]*SK_MZ[2] - P[4][17]*SK_MZ[3]); Kfusion[5] = SK_MZ[0]*(P[5][21] + P[5][18]*SH_MAG[2] + P[5][16]*SH_MAG[5] - P[5][0]*SK_MZ[1] + P[5][1]*SK_MZ[2] - P[5][17]*SK_MZ[3]); Kfusion[6] = SK_MZ[0]*(P[6][21] + P[6][18]*SH_MAG[2] + P[6][16]*SH_MAG[5] - P[6][0]*SK_MZ[1] + P[6][1]*SK_MZ[2] - P[6][17]*SK_MZ[3]); Kfusion[7] = SK_MZ[0]*(P[7][21] + P[7][18]*SH_MAG[2] + P[7][16]*SH_MAG[5] - P[7][0]*SK_MZ[1] + P[7][1]*SK_MZ[2] - P[7][17]*SK_MZ[3]); Kfusion[8] = SK_MZ[0]*(P[8][21] + P[8][18]*SH_MAG[2] + P[8][16]*SH_MAG[5] - P[8][0]*SK_MZ[1] + P[8][1]*SK_MZ[2] - P[8][17]*SK_MZ[3]); Kfusion[9] = SK_MZ[0]*(P[9][21] + P[9][18]*SH_MAG[2] + P[9][16]*SH_MAG[5] - P[9][0]*SK_MZ[1] + P[9][1]*SK_MZ[2] - P[9][17]*SK_MZ[3]); Kfusion[10] = SK_MZ[0]*(P[10][21] + P[10][18]*SH_MAG[2] + P[10][16]*SH_MAG[5] - P[10][0]*SK_MZ[1] + P[10][1]*SK_MZ[2] - P[10][17]*SK_MZ[3]); Kfusion[11] = SK_MZ[0]*(P[11][21] + P[11][18]*SH_MAG[2] + P[11][16]*SH_MAG[5] - P[11][0]*SK_MZ[1] + P[11][1]*SK_MZ[2] - P[11][17]*SK_MZ[3]); Kfusion[12] = SK_MZ[0]*(P[12][21] + P[12][18]*SH_MAG[2] + P[12][16]*SH_MAG[5] - P[12][0]*SK_MZ[1] + P[12][1]*SK_MZ[2] - P[12][17]*SK_MZ[3]); Kfusion[13] = SK_MZ[0]*(P[13][21] + P[13][18]*SH_MAG[2] + P[13][16]*SH_MAG[5] - P[13][0]*SK_MZ[1] + P[13][1]*SK_MZ[2] - P[13][17]*SK_MZ[3]); Kfusion[14] = SK_MZ[0]*(P[14][21] + P[14][18]*SH_MAG[2] + P[14][16]*SH_MAG[5] - P[14][0]*SK_MZ[1] + P[14][1]*SK_MZ[2] - P[14][17]*SK_MZ[3]); Kfusion[15] = SK_MZ[0]*(P[15][21] + P[15][18]*SH_MAG[2] + P[15][16]*SH_MAG[5] - P[15][0]*SK_MZ[1] + P[15][1]*SK_MZ[2] - P[15][17]*SK_MZ[3]); // zero Kalman gains to inhibit wind state estimation if (!inhibitWindStates) { Kfusion[22] = SK_MZ[0]*(P[22][21] + P[22][18]*SH_MAG[2] + P[22][16]*SH_MAG[5] - P[22][0]*SK_MZ[1] + P[22][1]*SK_MZ[2] - P[22][17]*SK_MZ[3]); Kfusion[23] = SK_MZ[0]*(P[23][21] + P[23][18]*SH_MAG[2] + P[23][16]*SH_MAG[5] - P[23][0]*SK_MZ[1] + P[23][1]*SK_MZ[2] - P[23][17]*SK_MZ[3]); } else { Kfusion[22] = 0.0f; Kfusion[23] = 0.0f; } // zero Kalman gains to inhibit magnetic field state estimation if (!inhibitMagStates) { Kfusion[16] = SK_MZ[0]*(P[16][21] + P[16][18]*SH_MAG[2] + P[16][16]*SH_MAG[5] - P[16][0]*SK_MZ[1] + P[16][1]*SK_MZ[2] - P[16][17]*SK_MZ[3]); Kfusion[17] = SK_MZ[0]*(P[17][21] + P[17][18]*SH_MAG[2] + P[17][16]*SH_MAG[5] - P[17][0]*SK_MZ[1] + P[17][1]*SK_MZ[2] - P[17][17]*SK_MZ[3]); Kfusion[18] = SK_MZ[0]*(P[18][21] + P[18][18]*SH_MAG[2] + P[18][16]*SH_MAG[5] - P[18][0]*SK_MZ[1] + P[18][1]*SK_MZ[2] - P[18][17]*SK_MZ[3]); Kfusion[19] = SK_MZ[0]*(P[19][21] + P[19][18]*SH_MAG[2] + P[19][16]*SH_MAG[5] - P[19][0]*SK_MZ[1] + P[19][1]*SK_MZ[2] - P[19][17]*SK_MZ[3]); Kfusion[20] = SK_MZ[0]*(P[20][21] + P[20][18]*SH_MAG[2] + P[20][16]*SH_MAG[5] - P[20][0]*SK_MZ[1] + P[20][1]*SK_MZ[2] - P[20][17]*SK_MZ[3]); Kfusion[21] = SK_MZ[0]*(P[21][21] + P[21][18]*SH_MAG[2] + P[21][16]*SH_MAG[5] - P[21][0]*SK_MZ[1] + P[21][1]*SK_MZ[2] - P[21][17]*SK_MZ[3]); } else { for (uint8_t i=16; i<=21; i++) { Kfusion[i] = 0.0f; } } // set flags to indicate to other processes that fusion has been performede and is required on the next frame // this can be used by other fusion processes to avoid fusing on the same frame as this expensive step magFusePerformed = true; magFuseRequired = false; } // calculate the measurement innovation innovMag[obsIndex] = MagPred[obsIndex] - magDataDelayed.mag[obsIndex]; // calculate the innovation test ratio magTestRatio[obsIndex] = sq(innovMag[obsIndex]) / (sq(frontend._magInnovGate) * varInnovMag[obsIndex]); // check the last values from all components and set magnetometer health accordingly magHealth = (magTestRatio[0] < 1.0f && magTestRatio[1] < 1.0f && magTestRatio[2] < 1.0f); // Don't fuse unless all componenets pass. The exception is if the bad health has timed out and we are not a fly forward vehicle // In this case we might as well try using the magnetometer, but with a reduced weighting if (magHealth || ((magTestRatio[obsIndex] < 1.0f) && !assume_zero_sideslip() && magTimeout)) { // zero the attitude error state - by definition it is assumed to be zero before each observaton fusion stateStruct.angErr.zero(); // correct the state vector for (uint8_t j= 0; j<=stateIndexLim; j++) { // If we are forced to use a bad compass in flight, we reduce the weighting by a factor of 4 if (!magHealth && (PV_AidingMode == AID_ABSOLUTE)) { Kfusion[j] *= 0.25f; } // If in the air and there is no other form of heading reference or we are yawing rapidly which creates larger inertial yaw errors, // we strengthen the magnetometer attitude correction if (motorsArmed && ((PV_AidingMode == AID_NONE) || highYawRate) && j <= 3) { Kfusion[j] *= 4.0f; } statesArray[j] = statesArray[j] - Kfusion[j] * innovMag[obsIndex]; } // the first 3 states represent the angular misalignment vector. This is // is used to correct the estimated quaternion on the current time step stateStruct.quat.rotate(stateStruct.angErr); // correct the covariance P = (I - K*H)*P // take advantage of the empty columns in KH to reduce the // number of operations for (uint8_t i = 0; i<=stateIndexLim; i++) { for (uint8_t j = 0; j<=2; j++) { KH[i][j] = Kfusion[i] * H_MAG[j]; } for (uint8_t j = 3; j<=15; j++) { KH[i][j] = 0.0f; } for (uint8_t j = 16; j<=21; j++) { if (!inhibitMagStates) { KH[i][j] = Kfusion[i] * H_MAG[j]; } else { KH[i][j] = 0.0f; } } for (uint8_t j = 22; j<=23; j++) { KH[i][j] = 0.0f; } } for (uint8_t i = 0; i<=stateIndexLim; i++) { for (uint8_t j = 0; j<=stateIndexLim; j++) { KHP[i][j] = 0; for (uint8_t k = 0; k<=2; k++) { KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j]; } if (!inhibitMagStates) { for (uint8_t k = 16; k<=21; k++) { KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j]; } } } } for (uint8_t i = 0; i<=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-condiioning. ForceSymmetry(); ConstrainVariances(); } /* * Fuse compass 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/priseborough/InertialNav/blob/master/derivations/RotationVectorAttitudeParameterisation/GenerateNavFilterEquations.m */ void NavEKF2_core::fuseCompass() { float q0 = stateStruct.quat[0]; float q1 = stateStruct.quat[1]; float q2 = stateStruct.quat[2]; float q3 = stateStruct.quat[3]; float magX = magDataDelayed.mag.x; float magY = magDataDelayed.mag.y; float magZ = magDataDelayed.mag.z; // compass measurement error variance (rad^2) const float R_MAG = 3e-2f; // Calculate observation Jacobian float t2 = q0*q0; float t3 = q1*q1; float t4 = q2*q2; float t5 = q3*q3; float t6 = q0*q2*2.0f; float t7 = q1*q3*2.0f; float t8 = t6+t7; float t9 = q0*q3*2.0f; float t13 = q1*q2*2.0f; float t10 = t9-t13; float t11 = t2+t3-t4-t5; float t12 = magX*t11; float t14 = magZ*t8; float t19 = magY*t10; float t15 = t12+t14-t19; float t16 = t2-t3+t4-t5; float t17 = q0*q1*2.0f; float t24 = q2*q3*2.0f; float t18 = t17-t24; float t20 = 1.0f/t15; float t21 = magY*t16; float t22 = t9+t13; float t23 = magX*t22; float t28 = magZ*t18; float t25 = t21+t23-t28; float t29 = t20*t25; float t26 = tan(t29); float t27 = 1.0f/(t15*t15); float t30 = t26*t26; float t31 = t30+1.0f; float H_MAG[3]; H_MAG[0] = -t31*(t20*(magZ*t16+magY*t18)+t25*t27*(magY*t8+magZ*t10)); H_MAG[1] = t31*(t20*(magX*t18+magZ*t22)+t25*t27*(magX*t8-magZ*t11)); H_MAG[2] = t31*(t20*(magX*t16-magY*t22)+t25*t27*(magX*t10+magY*t11)); // Calculate innovation variance and Kalman gains, taking advantage of the fact that only the first 3 elements in H are non zero float PH[3]; float varInnov = R_MAG; for (uint8_t rowIndex=0; rowIndex<=2; rowIndex++) { PH[rowIndex] = 0.0f; for (uint8_t colIndex=0; colIndex<=2; colIndex++) { PH[rowIndex] += P[rowIndex][colIndex]*H_MAG[colIndex]; } varInnov += H_MAG[rowIndex]*PH[rowIndex]; } float varInnovInv = 1.0f / varInnov; for (uint8_t rowIndex=0; rowIndex<=stateIndexLim; rowIndex++) { Kfusion[rowIndex] = 0.0f; for (uint8_t colIndex=0; colIndex<=2; colIndex++) { Kfusion[rowIndex] += P[rowIndex][colIndex]*H_MAG[colIndex]; } Kfusion[rowIndex] *= varInnovInv; } // Calculate the innovation float innovation = calcMagHeadingInnov(); // Copy raw value to output variable used for data logging innovYaw = innovation; // limit the innovation so that initial corrections are not too large if (innovation > 0.5f) { innovation = 0.5f; } else if (innovation < -0.5f) { innovation = -0.5f; } // correct the state vector stateStruct.angErr.zero(); for (uint8_t i=0; i<=stateIndexLim; i++) { statesArray[i] -= Kfusion[i] * innovation; } // the first 3 states represent the angular misalignment vector. This is // is used to correct the estimated quaternion on the current time step stateStruct.quat.rotate(stateStruct.angErr); // 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 float HP[24]; for (uint8_t colIndex=0; colIndex<=stateIndexLim; colIndex++) { HP[colIndex] = 0.0f; for (uint8_t rowIndex=0; rowIndex<=2; rowIndex++) { HP[colIndex] += H_MAG[rowIndex]*P[rowIndex][colIndex]; } } for (uint8_t rowIndex=0; rowIndex<=stateIndexLim; rowIndex++) { for (uint8_t colIndex=0; colIndex<=stateIndexLim; colIndex++) { P[rowIndex][colIndex] -= Kfusion[rowIndex] * HP[colIndex]; } } // force the covariance matrix to be symmetrical and limit the variances to prevent // ill-condiioning. ForceSymmetry(); ConstrainVariances(); } /* * 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/priseborough/InertialNav/blob/master/derivations/RotationVectorAttitudeParameterisation/GenerateNavFilterEquations.m * This is used to prevent the declination of the EKF earth field states from drifting during peraton without GPS * or some other absolute position or velocity reference */ void NavEKF2_core::FuseDeclination() { // declination error variance (rad^2) const float R_DECL = 1e-2f; // copy required states to local variables float magN = stateStruct.earth_magfield.x; float magE = stateStruct.earth_magfield.y; // prevent bad earth field states from causing numerical errors or exceptions if (magN < 1e-3f) { return; } // Calculate observation Jacobian and Kalman gains float t2 = 1.0f/magN; float t4 = magE*t2; float t3 = tanf(t4); float t5 = t3*t3; float t6 = t5+1.0; float t7 = 1.0f/(magN*magN); float t8 = P[17][17]*t2*t6; float t15 = P[16][17]*magE*t6*t7; float t9 = t8-t15; float t10 = t2*t6*t9; float t11 = P[17][16]*t2*t6; float t16 = P[16][16]*magE*t6*t7; float t12 = t11-t16; float t17 = magE*t6*t7*t12; float t13 = R_DECL+t10-t17; float t14 = 1.0/t13; float t18 = magE; float t19 = magN; float t21 = 1.0f/t19; float t22 = t18*t21; float t20 = tanf(t22); float t23 = t20*t20; float t24 = t23+1.0; float H_MAG[24]; H_MAG[16] = -t18*1.0/(t19*t19)*t24; H_MAG[17] = t21*t24; for (uint8_t i=0; i<=15; i++) { Kfusion[i] = t14*(P[i][17]*t2*t6-P[i][16]*magE*t6*t7); } Kfusion[16] = -t14*(t16-P[16][17]*t2*t6); Kfusion[17] = t14*(t8-P[17][16]*magE*t6*t7); for (uint8_t i=17; i<=23; i++) { Kfusion[i] = t14*(P[i][17]*t2*t6-P[i][16]*magE*t6*t7); } // get the magnetic declination float magDecAng = use_compass() ? _ahrs->get_compass()->get_declination() : 0; // Calculate the innovation float innovation = atanf(t4) - magDecAng; // limit the innovation to protect against data errors if (innovation > 0.5f) { innovation = 0.5f; } else if (innovation < -0.5f) { innovation = -0.5f; } // zero the attitude error state - by definition it is assumed to be zero before each observaton fusion stateStruct.angErr.zero(); // correct the state vector for (uint8_t j= 0; j<=stateIndexLim; j++) { statesArray[j] = statesArray[j] - Kfusion[j] * innovation; } // the first 3 states represent the angular misalignment vector. This is // is used to correct the estimated quaternion on the current time step stateStruct.quat.rotate(stateStruct.angErr); // correct the covariance P = (I - K*H)*P // take advantage of the empty columns in KH to reduce the // number of operations for (uint8_t i = 0; i<=stateIndexLim; i++) { for (uint8_t j = 0; j<=15; j++) { KH[i][j] = 0.0f; } for (uint8_t j = 16; j<=17; j++) { if (!inhibitMagStates) { KH[i][j] = Kfusion[i] * H_MAG[j]; } else { KH[i][j] = 0.0f; } } for (uint8_t j = 18; j<=23; j++) { KH[i][j] = 0.0f; } } for (uint8_t i = 0; i<=stateIndexLim; i++) { for (uint8_t j = 0; j<=stateIndexLim; j++) { KHP[i][j] = 0; for (uint8_t k = 16; k<=17; k++) { KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j]; } } } 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-condiioning. ForceSymmetry(); ConstrainVariances(); } // Calculate magnetic heading innovation float NavEKF2_core::calcMagHeadingInnov() { // rotate predicted earth components into body axes and calculate // predicted measurements Matrix3f Tbn_temp; stateStruct.quat.rotation_matrix(Tbn_temp); Vector3f magMeasNED = Tbn_temp*magDataDelayed.mag; // calculate the innovation where the predicted measurement is the angle wrt magnetic north of the horizontal component of the measured field float innovation = atan2f(magMeasNED.y,magMeasNED.x) - _ahrs->get_compass()->get_declination(); // wrap the innovation so it sits on the range from +-pi if (innovation > M_PI) { innovation = innovation - 2*M_PI; } else if (innovation < -M_PI) { innovation = innovation + 2*M_PI; } // Unwrap so that a large yaw gyro bias offset that causes the heading to wrap does not lead to continual uncontrolled heading drift if (innovation - lastInnovation > M_PI) { // Angle has wrapped in the positive direction to subtract an additional 2*Pi innovationIncrement -= 2*M_PI; } else if (innovation -innovationIncrement < -M_PI) { // Angle has wrapped in the negative direction so add an additional 2*Pi innovationIncrement += 2*M_PI; } lastInnovation = innovation; return innovation + innovationIncrement; } /******************************************************** * MISC FUNCTIONS * ********************************************************/ // align the NE earth magnetic field states with the published declination void NavEKF2_core::alignMagStateDeclination() { // get the magnetic declination float magDecAng = use_compass() ? _ahrs->get_compass()->get_declination() : 0; // rotate the NE values so that the declination matches the published value Vector3f initMagNED = stateStruct.earth_magfield; float magLengthNE = pythagorous2(initMagNED.x,initMagNED.y); stateStruct.earth_magfield.x = magLengthNE * cosf(magDecAng); stateStruct.earth_magfield.y = magLengthNE * sinf(magDecAng); } #endif // HAL_CPU_CLASS