#include #include "AP_NavEKF2.h" #include "AP_NavEKF2_core.h" extern const AP_HAL::HAL& hal; /******************************************************** * RESET FUNCTIONS * ********************************************************/ /******************************************************** * FUSE MEASURED_DATA * ********************************************************/ /* * Fuse true airspeed 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::FuseAirspeed() { // declarations float vn; float ve; float vd; float vwn; float vwe; float EAS2TAS = dal.get_EAS2TAS(); const float R_TAS = sq(constrain_float(frontend->_easNoise, 0.5f, 5.0f) * constrain_float(EAS2TAS, 0.9f, 10.0f)); Vector3 SH_TAS; float SK_TAS; Vector24 H_TAS; float VtasPred; // copy required states to local variable names vn = stateStruct.velocity.x; ve = stateStruct.velocity.y; vd = stateStruct.velocity.z; vwn = stateStruct.wind_vel.x; vwe = stateStruct.wind_vel.y; // calculate the predicted airspeed VtasPred = norm((ve - vwe) , (vn - vwn) , vd); // perform fusion of True Airspeed measurement if (VtasPred > 1.0f) { // calculate observation jacobians SH_TAS[0] = 1.0f/(sqrtf(sq(ve - vwe) + sq(vn - vwn) + sq(vd))); SH_TAS[1] = (SH_TAS[0]*(2*ve - 2*vwe))/2; SH_TAS[2] = (SH_TAS[0]*(2*vn - 2*vwn))/2; for (uint8_t i=0; i<=2; i++) H_TAS[i] = 0.0f; H_TAS[3] = SH_TAS[2]; H_TAS[4] = SH_TAS[1]; H_TAS[5] = vd*SH_TAS[0]; H_TAS[22] = -SH_TAS[2]; H_TAS[23] = -SH_TAS[1]; for (uint8_t i=6; i<=21; i++) H_TAS[i] = 0.0f; // calculate Kalman gains float temp = (R_TAS + SH_TAS[2]*(P[3][3]*SH_TAS[2] + P[4][3]*SH_TAS[1] - P[22][3]*SH_TAS[2] - P[23][3]*SH_TAS[1] + P[5][3]*vd*SH_TAS[0]) + SH_TAS[1]*(P[3][4]*SH_TAS[2] + P[4][4]*SH_TAS[1] - P[22][4]*SH_TAS[2] - P[23][4]*SH_TAS[1] + P[5][4]*vd*SH_TAS[0]) - SH_TAS[2]*(P[3][22]*SH_TAS[2] + P[4][22]*SH_TAS[1] - P[22][22]*SH_TAS[2] - P[23][22]*SH_TAS[1] + P[5][22]*vd*SH_TAS[0]) - SH_TAS[1]*(P[3][23]*SH_TAS[2] + P[4][23]*SH_TAS[1] - P[22][23]*SH_TAS[2] - P[23][23]*SH_TAS[1] + P[5][23]*vd*SH_TAS[0]) + vd*SH_TAS[0]*(P[3][5]*SH_TAS[2] + P[4][5]*SH_TAS[1] - P[22][5]*SH_TAS[2] - P[23][5]*SH_TAS[1] + P[5][5]*vd*SH_TAS[0])); if (temp >= R_TAS) { SK_TAS = 1.0f / temp; faultStatus.bad_airspeed = false; } else { // the calculation is badly conditioned, so we cannot perform fusion on this step // we reset the covariance matrix and try again next measurement CovarianceInit(); faultStatus.bad_airspeed = true; return; } Kfusion[0] = SK_TAS*(P[0][3]*SH_TAS[2] - P[0][22]*SH_TAS[2] + P[0][4]*SH_TAS[1] - P[0][23]*SH_TAS[1] + P[0][5]*vd*SH_TAS[0]); Kfusion[1] = SK_TAS*(P[1][3]*SH_TAS[2] - P[1][22]*SH_TAS[2] + P[1][4]*SH_TAS[1] - P[1][23]*SH_TAS[1] + P[1][5]*vd*SH_TAS[0]); Kfusion[2] = SK_TAS*(P[2][3]*SH_TAS[2] - P[2][22]*SH_TAS[2] + P[2][4]*SH_TAS[1] - P[2][23]*SH_TAS[1] + P[2][5]*vd*SH_TAS[0]); Kfusion[3] = SK_TAS*(P[3][3]*SH_TAS[2] - P[3][22]*SH_TAS[2] + P[3][4]*SH_TAS[1] - P[3][23]*SH_TAS[1] + P[3][5]*vd*SH_TAS[0]); Kfusion[4] = SK_TAS*(P[4][3]*SH_TAS[2] - P[4][22]*SH_TAS[2] + P[4][4]*SH_TAS[1] - P[4][23]*SH_TAS[1] + P[4][5]*vd*SH_TAS[0]); Kfusion[5] = SK_TAS*(P[5][3]*SH_TAS[2] - P[5][22]*SH_TAS[2] + P[5][4]*SH_TAS[1] - P[5][23]*SH_TAS[1] + P[5][5]*vd*SH_TAS[0]); Kfusion[6] = SK_TAS*(P[6][3]*SH_TAS[2] - P[6][22]*SH_TAS[2] + P[6][4]*SH_TAS[1] - P[6][23]*SH_TAS[1] + P[6][5]*vd*SH_TAS[0]); Kfusion[7] = SK_TAS*(P[7][3]*SH_TAS[2] - P[7][22]*SH_TAS[2] + P[7][4]*SH_TAS[1] - P[7][23]*SH_TAS[1] + P[7][5]*vd*SH_TAS[0]); Kfusion[8] = SK_TAS*(P[8][3]*SH_TAS[2] - P[8][22]*SH_TAS[2] + P[8][4]*SH_TAS[1] - P[8][23]*SH_TAS[1] + P[8][5]*vd*SH_TAS[0]); Kfusion[9] = SK_TAS*(P[9][3]*SH_TAS[2] - P[9][22]*SH_TAS[2] + P[9][4]*SH_TAS[1] - P[9][23]*SH_TAS[1] + P[9][5]*vd*SH_TAS[0]); Kfusion[10] = SK_TAS*(P[10][3]*SH_TAS[2] - P[10][22]*SH_TAS[2] + P[10][4]*SH_TAS[1] - P[10][23]*SH_TAS[1] + P[10][5]*vd*SH_TAS[0]); Kfusion[11] = SK_TAS*(P[11][3]*SH_TAS[2] - P[11][22]*SH_TAS[2] + P[11][4]*SH_TAS[1] - P[11][23]*SH_TAS[1] + P[11][5]*vd*SH_TAS[0]); Kfusion[12] = SK_TAS*(P[12][3]*SH_TAS[2] - P[12][22]*SH_TAS[2] + P[12][4]*SH_TAS[1] - P[12][23]*SH_TAS[1] + P[12][5]*vd*SH_TAS[0]); Kfusion[13] = SK_TAS*(P[13][3]*SH_TAS[2] - P[13][22]*SH_TAS[2] + P[13][4]*SH_TAS[1] - P[13][23]*SH_TAS[1] + P[13][5]*vd*SH_TAS[0]); Kfusion[14] = SK_TAS*(P[14][3]*SH_TAS[2] - P[14][22]*SH_TAS[2] + P[14][4]*SH_TAS[1] - P[14][23]*SH_TAS[1] + P[14][5]*vd*SH_TAS[0]); Kfusion[15] = SK_TAS*(P[15][3]*SH_TAS[2] - P[15][22]*SH_TAS[2] + P[15][4]*SH_TAS[1] - P[15][23]*SH_TAS[1] + P[15][5]*vd*SH_TAS[0]); Kfusion[22] = SK_TAS*(P[22][3]*SH_TAS[2] - P[22][22]*SH_TAS[2] + P[22][4]*SH_TAS[1] - P[22][23]*SH_TAS[1] + P[22][5]*vd*SH_TAS[0]); Kfusion[23] = SK_TAS*(P[23][3]*SH_TAS[2] - P[23][22]*SH_TAS[2] + P[23][4]*SH_TAS[1] - P[23][23]*SH_TAS[1] + P[23][5]*vd*SH_TAS[0]); // zero Kalman gains to inhibit magnetic field state estimation if (!inhibitMagStates) { Kfusion[16] = SK_TAS*(P[16][3]*SH_TAS[2] - P[16][22]*SH_TAS[2] + P[16][4]*SH_TAS[1] - P[16][23]*SH_TAS[1] + P[16][5]*vd*SH_TAS[0]); Kfusion[17] = SK_TAS*(P[17][3]*SH_TAS[2] - P[17][22]*SH_TAS[2] + P[17][4]*SH_TAS[1] - P[17][23]*SH_TAS[1] + P[17][5]*vd*SH_TAS[0]); Kfusion[18] = SK_TAS*(P[18][3]*SH_TAS[2] - P[18][22]*SH_TAS[2] + P[18][4]*SH_TAS[1] - P[18][23]*SH_TAS[1] + P[18][5]*vd*SH_TAS[0]); Kfusion[19] = SK_TAS*(P[19][3]*SH_TAS[2] - P[19][22]*SH_TAS[2] + P[19][4]*SH_TAS[1] - P[19][23]*SH_TAS[1] + P[19][5]*vd*SH_TAS[0]); Kfusion[20] = SK_TAS*(P[20][3]*SH_TAS[2] - P[20][22]*SH_TAS[2] + P[20][4]*SH_TAS[1] - P[20][23]*SH_TAS[1] + P[20][5]*vd*SH_TAS[0]); Kfusion[21] = SK_TAS*(P[21][3]*SH_TAS[2] - P[21][22]*SH_TAS[2] + P[21][4]*SH_TAS[1] - P[21][23]*SH_TAS[1] + P[21][5]*vd*SH_TAS[0]); } else { for (uint8_t i=16; i<=21; i++) { Kfusion[i] = 0.0f; } } // calculate measurement innovation variance varInnovVtas = 1.0f/SK_TAS; // calculate measurement innovation innovVtas = VtasPred - tasDataDelayed.tas; // calculate the innovation consistency test ratio tasTestRatio = sq(innovVtas) / (sq(MAX(0.01f * (float)frontend->_tasInnovGate, 1.0f)) * varInnovVtas); // fail if the ratio is > 1, but don't fail if bad IMU data bool tasHealth = ((tasTestRatio < 1.0f) || badIMUdata); tasTimeout = (imuSampleTime_ms - lastTasPassTime_ms) > frontend->tasRetryTime_ms; // test the ratio before fusing data, forcing fusion if airspeed and position are timed out as we have no choice but to try and use airspeed to constrain error growth if (tasHealth || (tasTimeout && posTimeout)) { // restart the counter lastTasPassTime_ms = imuSampleTime_ms; // zero the attitude error state - by definition it is assumed to be zero before each observation fusion stateStruct.angErr.zero(); // correct the state vector for (uint8_t j= 0; j<=stateIndexLim; j++) { statesArray[j] = statesArray[j] - Kfusion[j] * innovVtas; } // the first 3 states represent the angular misalignment vector. // This 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 (unsigned i = 0; i<=stateIndexLim; i++) { for (unsigned j = 0; j<=2; j++) { KH[i][j] = 0.0f; } for (unsigned j = 3; j<=5; j++) { KH[i][j] = Kfusion[i] * H_TAS[j]; } for (unsigned j = 6; j<=21; j++) { KH[i][j] = 0.0f; } for (unsigned j = 22; j<=23; j++) { KH[i][j] = Kfusion[i] * H_TAS[j]; } } for (unsigned j = 0; j<=stateIndexLim; j++) { for (unsigned i = 0; i<=stateIndexLim; i++) { ftype res = 0; res += KH[i][3] * P[3][j]; res += KH[i][4] * P[4][j]; res += KH[i][5] * P[5][j]; res += KH[i][22] * P[22][j]; res += KH[i][23] * P[23][j]; KHP[i][j] = res; } } for (unsigned i = 0; i<=stateIndexLim; i++) { for (unsigned 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(); } // select fusion of true airspeed measurements void NavEKF2_core::SelectTasFusion() { // Check if the magnetometer has been fused on that time step and the filter is running at faster than 200 Hz // If so, don't fuse measurements on this time step to reduce frame over-runs // Only allow one time slip to prevent high rate magnetometer data locking out fusion of other measurements if (magFusePerformed && dtIMUavg < 0.005f && !airSpdFusionDelayed) { airSpdFusionDelayed = true; return; } else { airSpdFusionDelayed = false; } // get true airspeed measurement readAirSpdData(); // If we haven't received airspeed data for a while, then declare the airspeed data as being timed out if (imuSampleTime_ms - tasDataNew.time_ms > frontend->tasRetryTime_ms) { tasTimeout = true; } // if the filter is initialised, wind states are not inhibited and we have data to fuse, then perform TAS fusion if (tasDataToFuse && statesInitialised && !inhibitWindStates) { FuseAirspeed(); prevTasStep_ms = imuSampleTime_ms; } } // select fusion of synthetic sideslip measurements // synthetic sidelip fusion only works for fixed wing aircraft and relies on the average sideslip being close to zero // it requires a stable wind for best results and should not be used for aerobatic flight with manoeuvres that induce large sidslip angles (eg knife-edge, spins, etc) void NavEKF2_core::SelectBetaFusion() { // Check if the magnetometer has been fused on that time step and the filter is running at faster than 200 Hz // If so, don't fuse measurements on this time step to reduce frame over-runs // Only allow one time slip to prevent high rate magnetometer data preventing fusion of other measurements if (magFusePerformed && dtIMUavg < 0.005f && !sideSlipFusionDelayed) { sideSlipFusionDelayed = true; return; } else { sideSlipFusionDelayed = false; } // set true when the fusion time interval has triggered bool f_timeTrigger = ((imuSampleTime_ms - prevBetaStep_ms) >= frontend->betaAvg_ms); // set true when use of synthetic sideslip fusion is necessary because we have limited sensor data or are dead reckoning position bool f_required = !(use_compass() && useAirspeed() && ((imuSampleTime_ms - lastPosPassTime_ms) < frontend->posRetryTimeNoVel_ms)); // set true when sideslip fusion is feasible (requires zero sideslip assumption to be valid and use of wind states) bool f_feasible = (assume_zero_sideslip() && !inhibitWindStates); // use synthetic sideslip fusion if feasible, required and enough time has lapsed since the last fusion if (f_feasible && f_required && f_timeTrigger) { FuseSideslip(); prevBetaStep_ms = imuSampleTime_ms; } } /* * Fuse synthetic sideslip measurement of zero 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::FuseSideslip() { // declarations float q0; float q1; float q2; float q3; float vn; float ve; float vd; float vwn; float vwe; const float R_BETA = 0.03f; // assume a sideslip angle RMS of ~10 deg Vector10 SH_BETA; Vector5 SK_BETA; Vector3f vel_rel_wind; Vector24 H_BETA; float innovBeta; // copy required states to local variable names q0 = stateStruct.quat[0]; q1 = stateStruct.quat[1]; q2 = stateStruct.quat[2]; q3 = stateStruct.quat[3]; vn = stateStruct.velocity.x; ve = stateStruct.velocity.y; vd = stateStruct.velocity.z; vwn = stateStruct.wind_vel.x; vwe = stateStruct.wind_vel.y; // calculate predicted wind relative velocity in NED vel_rel_wind.x = vn - vwn; vel_rel_wind.y = ve - vwe; vel_rel_wind.z = vd; // rotate into body axes vel_rel_wind = prevTnb * vel_rel_wind; // perform fusion of assumed sideslip = 0 if (vel_rel_wind.x > 5.0f) { // Calculate observation jacobians SH_BETA[0] = (vn - vwn)*(sq(q0) + sq(q1) - sq(q2) - sq(q3)) - vd*(2*q0*q2 - 2*q1*q3) + (ve - vwe)*(2*q0*q3 + 2*q1*q2); if (fabsf(SH_BETA[0]) <= 1e-9f) { faultStatus.bad_sideslip = true; return; } else { faultStatus.bad_sideslip = false; } SH_BETA[0] = (vn - vwn)*(sq(q0) + sq(q1) - sq(q2) - sq(q3)) - vd*(2*q0*q2 - 2*q1*q3) + (ve - vwe)*(2*q0*q3 + 2*q1*q2); SH_BETA[1] = (ve - vwe)*(sq(q0) - sq(q1) + sq(q2) - sq(q3)) + vd*(2*q0*q1 + 2*q2*q3) - (vn - vwn)*(2*q0*q3 - 2*q1*q2); SH_BETA[2] = vd*(sq(q0) - sq(q1) - sq(q2) + sq(q3)) - (ve - vwe)*(2*q0*q1 - 2*q2*q3) + (vn - vwn)*(2*q0*q2 + 2*q1*q3); SH_BETA[3] = 1/sq(SH_BETA[0]); SH_BETA[4] = (sq(q0) - sq(q1) + sq(q2) - sq(q3))/SH_BETA[0]; SH_BETA[5] = sq(q0) + sq(q1) - sq(q2) - sq(q3); SH_BETA[6] = 1/SH_BETA[0]; SH_BETA[7] = 2*q0*q3; SH_BETA[8] = SH_BETA[7] + 2*q1*q2; SH_BETA[9] = SH_BETA[7] - 2*q1*q2; H_BETA[0] = SH_BETA[2]*SH_BETA[6]; H_BETA[1] = SH_BETA[1]*SH_BETA[2]*SH_BETA[3]; H_BETA[2] = - sq(SH_BETA[1])*SH_BETA[3] - 1; H_BETA[3] = - SH_BETA[6]*SH_BETA[9] - SH_BETA[1]*SH_BETA[3]*SH_BETA[5]; H_BETA[4] = SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]; H_BETA[5] = SH_BETA[6]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[3]*(2*q0*q2 - 2*q1*q3); for (uint8_t i=6; i<=21; i++) { H_BETA[i] = 0.0f; } H_BETA[22] = SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]; H_BETA[23] = SH_BETA[1]*SH_BETA[3]*SH_BETA[8] - SH_BETA[4]; // Calculate Kalman gains float temp = (R_BETA + (SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8])*(P[22][4]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[3][4]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[2][4]*(sq(SH_BETA[1])*SH_BETA[3] + 1) + P[5][4]*(SH_BETA[6]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[3]*(2*q0*q2 - 2*q1*q3)) + P[4][4]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) - P[23][4]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) + P[0][4]*SH_BETA[2]*SH_BETA[6] + P[1][4]*SH_BETA[1]*SH_BETA[2]*SH_BETA[3]) - (SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8])*(P[22][23]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[3][23]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[2][23]*(sq(SH_BETA[1])*SH_BETA[3] + 1) + P[5][23]*(SH_BETA[6]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[3]*(2*q0*q2 - 2*q1*q3)) + P[4][23]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) - P[23][23]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) + P[0][23]*SH_BETA[2]*SH_BETA[6] + P[1][23]*SH_BETA[1]*SH_BETA[2]*SH_BETA[3]) - (SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5])*(P[22][3]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[3][3]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[2][3]*(sq(SH_BETA[1])*SH_BETA[3] + 1) + P[5][3]*(SH_BETA[6]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[3]*(2*q0*q2 - 2*q1*q3)) + P[4][3]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) - P[23][3]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) + P[0][3]*SH_BETA[2]*SH_BETA[6] + P[1][3]*SH_BETA[1]*SH_BETA[2]*SH_BETA[3]) + (SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5])*(P[22][22]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[3][22]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[2][22]*(sq(SH_BETA[1])*SH_BETA[3] + 1) + P[5][22]*(SH_BETA[6]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[3]*(2*q0*q2 - 2*q1*q3)) + P[4][22]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) - P[23][22]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) + P[0][22]*SH_BETA[2]*SH_BETA[6] + P[1][22]*SH_BETA[1]*SH_BETA[2]*SH_BETA[3]) - (sq(SH_BETA[1])*SH_BETA[3] + 1)*(P[22][2]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[3][2]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[2][2]*(sq(SH_BETA[1])*SH_BETA[3] + 1) + P[5][2]*(SH_BETA[6]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[3]*(2*q0*q2 - 2*q1*q3)) + P[4][2]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) - P[23][2]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) + P[0][2]*SH_BETA[2]*SH_BETA[6] + P[1][2]*SH_BETA[1]*SH_BETA[2]*SH_BETA[3]) + (SH_BETA[6]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[3]*(2*q0*q2 - 2*q1*q3))*(P[22][5]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[3][5]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[2][5]*(sq(SH_BETA[1])*SH_BETA[3] + 1) + P[5][5]*(SH_BETA[6]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[3]*(2*q0*q2 - 2*q1*q3)) + P[4][5]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) - P[23][5]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) + P[0][5]*SH_BETA[2]*SH_BETA[6] + P[1][5]*SH_BETA[1]*SH_BETA[2]*SH_BETA[3]) + SH_BETA[2]*SH_BETA[6]*(P[22][0]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[3][0]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[2][0]*(sq(SH_BETA[1])*SH_BETA[3] + 1) + P[5][0]*(SH_BETA[6]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[3]*(2*q0*q2 - 2*q1*q3)) + P[4][0]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) - P[23][0]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) + P[0][0]*SH_BETA[2]*SH_BETA[6] + P[1][0]*SH_BETA[1]*SH_BETA[2]*SH_BETA[3]) + SH_BETA[1]*SH_BETA[2]*SH_BETA[3]*(P[22][1]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[3][1]*(SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]) - P[2][1]*(sq(SH_BETA[1])*SH_BETA[3] + 1) + P[5][1]*(SH_BETA[6]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[3]*(2*q0*q2 - 2*q1*q3)) + P[4][1]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) - P[23][1]*(SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]) + P[0][1]*SH_BETA[2]*SH_BETA[6] + P[1][1]*SH_BETA[1]*SH_BETA[2]*SH_BETA[3])); if (temp >= R_BETA) { SK_BETA[0] = 1.0f / temp; faultStatus.bad_sideslip = false; } else { // the calculation is badly conditioned, so we cannot perform fusion on this step // we reset the covariance matrix and try again next measurement CovarianceInit(); faultStatus.bad_sideslip = true; return; } SK_BETA[1] = SH_BETA[6]*(2*q0*q1 + 2*q2*q3) + SH_BETA[1]*SH_BETA[3]*(2*q0*q2 - 2*q1*q3); SK_BETA[2] = SH_BETA[6]*SH_BETA[9] + SH_BETA[1]*SH_BETA[3]*SH_BETA[5]; SK_BETA[3] = SH_BETA[4] - SH_BETA[1]*SH_BETA[3]*SH_BETA[8]; SK_BETA[4] = sq(SH_BETA[1])*SH_BETA[3] + 1; Kfusion[0] = SK_BETA[0]*(P[0][5]*SK_BETA[1] - P[0][2]*SK_BETA[4] - P[0][3]*SK_BETA[2] + P[0][4]*SK_BETA[3] + P[0][22]*SK_BETA[2] - P[0][23]*SK_BETA[3] + P[0][0]*SH_BETA[6]*SH_BETA[2] + P[0][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[1] = SK_BETA[0]*(P[1][5]*SK_BETA[1] - P[1][2]*SK_BETA[4] - P[1][3]*SK_BETA[2] + P[1][4]*SK_BETA[3] + P[1][22]*SK_BETA[2] - P[1][23]*SK_BETA[3] + P[1][0]*SH_BETA[6]*SH_BETA[2] + P[1][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[2] = SK_BETA[0]*(P[2][5]*SK_BETA[1] - P[2][2]*SK_BETA[4] - P[2][3]*SK_BETA[2] + P[2][4]*SK_BETA[3] + P[2][22]*SK_BETA[2] - P[2][23]*SK_BETA[3] + P[2][0]*SH_BETA[6]*SH_BETA[2] + P[2][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[3] = SK_BETA[0]*(P[3][5]*SK_BETA[1] - P[3][2]*SK_BETA[4] - P[3][3]*SK_BETA[2] + P[3][4]*SK_BETA[3] + P[3][22]*SK_BETA[2] - P[3][23]*SK_BETA[3] + P[3][0]*SH_BETA[6]*SH_BETA[2] + P[3][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[4] = SK_BETA[0]*(P[4][5]*SK_BETA[1] - P[4][2]*SK_BETA[4] - P[4][3]*SK_BETA[2] + P[4][4]*SK_BETA[3] + P[4][22]*SK_BETA[2] - P[4][23]*SK_BETA[3] + P[4][0]*SH_BETA[6]*SH_BETA[2] + P[4][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[5] = SK_BETA[0]*(P[5][5]*SK_BETA[1] - P[5][2]*SK_BETA[4] - P[5][3]*SK_BETA[2] + P[5][4]*SK_BETA[3] + P[5][22]*SK_BETA[2] - P[5][23]*SK_BETA[3] + P[5][0]*SH_BETA[6]*SH_BETA[2] + P[5][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[6] = SK_BETA[0]*(P[6][5]*SK_BETA[1] - P[6][2]*SK_BETA[4] - P[6][3]*SK_BETA[2] + P[6][4]*SK_BETA[3] + P[6][22]*SK_BETA[2] - P[6][23]*SK_BETA[3] + P[6][0]*SH_BETA[6]*SH_BETA[2] + P[6][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[7] = SK_BETA[0]*(P[7][5]*SK_BETA[1] - P[7][2]*SK_BETA[4] - P[7][3]*SK_BETA[2] + P[7][4]*SK_BETA[3] + P[7][22]*SK_BETA[2] - P[7][23]*SK_BETA[3] + P[7][0]*SH_BETA[6]*SH_BETA[2] + P[7][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[8] = SK_BETA[0]*(P[8][5]*SK_BETA[1] - P[8][2]*SK_BETA[4] - P[8][3]*SK_BETA[2] + P[8][4]*SK_BETA[3] + P[8][22]*SK_BETA[2] - P[8][23]*SK_BETA[3] + P[8][0]*SH_BETA[6]*SH_BETA[2] + P[8][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[9] = SK_BETA[0]*(P[9][5]*SK_BETA[1] - P[9][2]*SK_BETA[4] - P[9][3]*SK_BETA[2] + P[9][4]*SK_BETA[3] + P[9][22]*SK_BETA[2] - P[9][23]*SK_BETA[3] + P[9][0]*SH_BETA[6]*SH_BETA[2] + P[9][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[10] = SK_BETA[0]*(P[10][5]*SK_BETA[1] - P[10][2]*SK_BETA[4] - P[10][3]*SK_BETA[2] + P[10][4]*SK_BETA[3] + P[10][22]*SK_BETA[2] - P[10][23]*SK_BETA[3] + P[10][0]*SH_BETA[6]*SH_BETA[2] + P[10][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[11] = SK_BETA[0]*(P[11][5]*SK_BETA[1] - P[11][2]*SK_BETA[4] - P[11][3]*SK_BETA[2] + P[11][4]*SK_BETA[3] + P[11][22]*SK_BETA[2] - P[11][23]*SK_BETA[3] + P[11][0]*SH_BETA[6]*SH_BETA[2] + P[11][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[12] = SK_BETA[0]*(P[12][5]*SK_BETA[1] - P[12][2]*SK_BETA[4] - P[12][3]*SK_BETA[2] + P[12][4]*SK_BETA[3] + P[12][22]*SK_BETA[2] - P[12][23]*SK_BETA[3] + P[12][0]*SH_BETA[6]*SH_BETA[2] + P[12][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[13] = SK_BETA[0]*(P[13][5]*SK_BETA[1] - P[13][2]*SK_BETA[4] - P[13][3]*SK_BETA[2] + P[13][4]*SK_BETA[3] + P[13][22]*SK_BETA[2] - P[13][23]*SK_BETA[3] + P[13][0]*SH_BETA[6]*SH_BETA[2] + P[13][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[14] = SK_BETA[0]*(P[14][5]*SK_BETA[1] - P[14][2]*SK_BETA[4] - P[14][3]*SK_BETA[2] + P[14][4]*SK_BETA[3] + P[14][22]*SK_BETA[2] - P[14][23]*SK_BETA[3] + P[14][0]*SH_BETA[6]*SH_BETA[2] + P[14][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[15] = SK_BETA[0]*(P[15][5]*SK_BETA[1] - P[15][2]*SK_BETA[4] - P[15][3]*SK_BETA[2] + P[15][4]*SK_BETA[3] + P[15][22]*SK_BETA[2] - P[15][23]*SK_BETA[3] + P[15][0]*SH_BETA[6]*SH_BETA[2] + P[15][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[22] = SK_BETA[0]*(P[22][5]*SK_BETA[1] - P[22][2]*SK_BETA[4] - P[22][3]*SK_BETA[2] + P[22][4]*SK_BETA[3] + P[22][22]*SK_BETA[2] - P[22][23]*SK_BETA[3] + P[22][0]*SH_BETA[6]*SH_BETA[2] + P[22][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[23] = SK_BETA[0]*(P[23][5]*SK_BETA[1] - P[23][2]*SK_BETA[4] - P[23][3]*SK_BETA[2] + P[23][4]*SK_BETA[3] + P[23][22]*SK_BETA[2] - P[23][23]*SK_BETA[3] + P[23][0]*SH_BETA[6]*SH_BETA[2] + P[23][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); // zero Kalman gains to inhibit magnetic field state estimation if (!inhibitMagStates) { Kfusion[16] = SK_BETA[0]*(P[16][5]*SK_BETA[1] - P[16][2]*SK_BETA[4] - P[16][3]*SK_BETA[2] + P[16][4]*SK_BETA[3] + P[16][22]*SK_BETA[2] - P[16][23]*SK_BETA[3] + P[16][0]*SH_BETA[6]*SH_BETA[2] + P[16][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[17] = SK_BETA[0]*(P[17][5]*SK_BETA[1] - P[17][2]*SK_BETA[4] - P[17][3]*SK_BETA[2] + P[17][4]*SK_BETA[3] + P[17][22]*SK_BETA[2] - P[17][23]*SK_BETA[3] + P[17][0]*SH_BETA[6]*SH_BETA[2] + P[17][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[18] = SK_BETA[0]*(P[18][5]*SK_BETA[1] - P[18][2]*SK_BETA[4] - P[18][3]*SK_BETA[2] + P[18][4]*SK_BETA[3] + P[18][22]*SK_BETA[2] - P[18][23]*SK_BETA[3] + P[18][0]*SH_BETA[6]*SH_BETA[2] + P[18][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[19] = SK_BETA[0]*(P[19][5]*SK_BETA[1] - P[19][2]*SK_BETA[4] - P[19][3]*SK_BETA[2] + P[19][4]*SK_BETA[3] + P[19][22]*SK_BETA[2] - P[19][23]*SK_BETA[3] + P[19][0]*SH_BETA[6]*SH_BETA[2] + P[19][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[20] = SK_BETA[0]*(P[20][5]*SK_BETA[1] - P[20][2]*SK_BETA[4] - P[20][3]*SK_BETA[2] + P[20][4]*SK_BETA[3] + P[20][22]*SK_BETA[2] - P[20][23]*SK_BETA[3] + P[20][0]*SH_BETA[6]*SH_BETA[2] + P[20][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); Kfusion[21] = SK_BETA[0]*(P[21][5]*SK_BETA[1] - P[21][2]*SK_BETA[4] - P[21][3]*SK_BETA[2] + P[21][4]*SK_BETA[3] + P[21][22]*SK_BETA[2] - P[21][23]*SK_BETA[3] + P[21][0]*SH_BETA[6]*SH_BETA[2] + P[21][1]*SH_BETA[1]*SH_BETA[3]*SH_BETA[2]); } else { for (uint8_t i=16; i<=21; i++) { Kfusion[i] = 0.0f; } } // calculate predicted sideslip angle and innovation using small angle approximation innovBeta = vel_rel_wind.y / vel_rel_wind.x; // reject measurement if greater than 3-sigma inconsistency if (innovBeta > 0.5f) { return; } // zero the attitude error state - by definition it is assumed to be zero before each observation fusion stateStruct.angErr.zero(); // correct the state vector for (uint8_t j= 0; j<=stateIndexLim; j++) { statesArray[j] = statesArray[j] - Kfusion[j] * innovBeta; } // the first 3 states represent the angular misalignment vector. // This 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 (unsigned i = 0; i<=stateIndexLim; i++) { for (unsigned j = 0; j<=5; j++) { KH[i][j] = Kfusion[i] * H_BETA[j]; } for (unsigned j = 6; j<=21; j++) { KH[i][j] = 0.0f; } for (unsigned j = 22; j<=23; j++) { KH[i][j] = Kfusion[i] * H_BETA[j]; } } 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][4] * P[4][j]; res += KH[i][5] * P[5][j]; res += KH[i][22] * P[22][j]; res += KH[i][23] * P[23][j]; KHP[i][j] = res; } } for (unsigned i = 0; i<=stateIndexLim; i++) { for (unsigned 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(); } /******************************************************** * MISC FUNCTIONS * ********************************************************/