#include #if HAL_CPU_CLASS >= HAL_CPU_CLASS_150 #include "AP_NavEKF3.h" #include "AP_NavEKF3_core.h" #include #include #include #include extern const AP_HAL::HAL& hal; /******************************************************** * FUSE MEASURED_DATA * ********************************************************/ // select fusion of range beacon measurements void NavEKF3_core::SelectRngBcnFusion() { // read range data from the sensor and check for new data in the buffer readRngBcnData(); // Determine if we need to fuse range beacon data on this time step if (rngBcnDataToFuse) { if (PV_AidingMode == AID_ABSOLUTE) { // Normal operating mode is to fuse the range data into the main filter FuseRngBcn(); } else { // If we aren't able to use the data in the main filter, use a simple 3-state filter to estimte position only FuseRngBcnStatic(); } } } void NavEKF3_core::FuseRngBcn() { // declarations float pn; float pe; float pd; float bcn_pn; float bcn_pe; float bcn_pd; const float R_BCN = sq(MAX(rngBcnDataDelayed.rngErr , 0.1f)); float rngPred; // health is set bad until test passed rngBcnHealth = false; if (activeHgtSource != HGT_SOURCE_BCN) { // calculate the vertical offset from EKF datum to beacon datum CalcRangeBeaconPosDownOffset(R_BCN, stateStruct.position, false); } else { bcnPosOffset = 0.0f; } // copy required states to local variable names pn = stateStruct.position.x; pe = stateStruct.position.y; pd = stateStruct.position.z; bcn_pn = rngBcnDataDelayed.beacon_posNED.x; bcn_pe = rngBcnDataDelayed.beacon_posNED.y; bcn_pd = rngBcnDataDelayed.beacon_posNED.z + bcnPosOffset; // predicted range Vector3f deltaPosNED = stateStruct.position - rngBcnDataDelayed.beacon_posNED; rngPred = deltaPosNED.length(); // calculate measurement innovation innovRngBcn = rngPred - rngBcnDataDelayed.rng; // perform fusion of range measurement if (rngPred > 0.1f) { // calculate observation jacobians float H_BCN[24]; memset(H_BCN, 0, sizeof(H_BCN)); float t2 = bcn_pd-pd; float t3 = bcn_pe-pe; float t4 = bcn_pn-pn; float t5 = t2*t2; float t6 = t3*t3; float t7 = t4*t4; float t8 = t5+t6+t7; float t9 = 1.0f/sqrtf(t8); H_BCN[7] = -t4*t9; H_BCN[8] = -t3*t9; // If we are not using the beacons as a height reference, we pretend that the beacons // are a the same height as the flight vehicle when calculating the observation derivatives // and Kalman gains // TODO - less hacky way of achieving this, preferably using an alternative derivation if (activeHgtSource != HGT_SOURCE_BCN) { t2 = 0.0f; } H_BCN[9] = -t2*t9; // calculate Kalman gains float t10 = P[9][9]*t2*t9; float t11 = P[8][9]*t3*t9; float t12 = P[7][9]*t4*t9; float t13 = t10+t11+t12; float t14 = t2*t9*t13; float t15 = P[9][8]*t2*t9; float t16 = P[8][8]*t3*t9; float t17 = P[7][8]*t4*t9; float t18 = t15+t16+t17; float t19 = t3*t9*t18; float t20 = P[9][7]*t2*t9; float t21 = P[8][7]*t3*t9; float t22 = P[7][7]*t4*t9; float t23 = t20+t21+t22; float t24 = t4*t9*t23; varInnovRngBcn = R_BCN+t14+t19+t24; float t26; if (varInnovRngBcn >= R_BCN) { t26 = 1.0f/varInnovRngBcn; faultStatus.bad_rngbcn = 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_rngbcn = true; return; } Kfusion[0] = -t26*(P[0][7]*t4*t9+P[0][8]*t3*t9+P[0][9]*t2*t9); Kfusion[1] = -t26*(P[1][7]*t4*t9+P[1][8]*t3*t9+P[1][9]*t2*t9); Kfusion[2] = -t26*(P[2][7]*t4*t9+P[2][8]*t3*t9+P[2][9]*t2*t9); Kfusion[3] = -t26*(P[3][7]*t4*t9+P[3][8]*t3*t9+P[3][9]*t2*t9); Kfusion[4] = -t26*(P[4][7]*t4*t9+P[4][8]*t3*t9+P[4][9]*t2*t9); Kfusion[5] = -t26*(P[5][7]*t4*t9+P[5][8]*t3*t9+P[5][9]*t2*t9); Kfusion[7] = -t26*(t22+P[7][8]*t3*t9+P[7][9]*t2*t9); Kfusion[8] = -t26*(t16+P[8][7]*t4*t9+P[8][9]*t2*t9); Kfusion[10] = -t26*(P[10][7]*t4*t9+P[10][8]*t3*t9+P[10][9]*t2*t9); Kfusion[11] = -t26*(P[11][7]*t4*t9+P[11][8]*t3*t9+P[11][9]*t2*t9); Kfusion[12] = -t26*(P[12][7]*t4*t9+P[12][8]*t3*t9+P[12][9]*t2*t9); Kfusion[13] = -t26*(P[13][7]*t4*t9+P[13][8]*t3*t9+P[13][9]*t2*t9); Kfusion[14] = -t26*(P[14][7]*t4*t9+P[14][8]*t3*t9+P[14][9]*t2*t9); Kfusion[15] = -t26*(P[15][7]*t4*t9+P[15][8]*t3*t9+P[15][9]*t2*t9); // only allow the range observations to modify the vertical states if we are using it as a height reference if (activeHgtSource == HGT_SOURCE_BCN) { Kfusion[6] = -t26*(P[6][7]*t4*t9+P[6][8]*t3*t9+P[6][9]*t2*t9); Kfusion[9] = -t26*(t10+P[9][7]*t4*t9+P[9][8]*t3*t9); } else { Kfusion[6] = 0.0f; Kfusion[9] = 0.0f; } if (!inhibitMagStates) { Kfusion[16] = -t26*(P[16][7]*t4*t9+P[16][8]*t3*t9+P[16][9]*t2*t9); Kfusion[17] = -t26*(P[17][7]*t4*t9+P[17][8]*t3*t9+P[17][9]*t2*t9); Kfusion[18] = -t26*(P[18][7]*t4*t9+P[18][8]*t3*t9+P[18][9]*t2*t9); Kfusion[19] = -t26*(P[19][7]*t4*t9+P[19][8]*t3*t9+P[19][9]*t2*t9); Kfusion[20] = -t26*(P[20][7]*t4*t9+P[20][8]*t3*t9+P[20][9]*t2*t9); Kfusion[21] = -t26*(P[21][7]*t4*t9+P[21][8]*t3*t9+P[21][9]*t2*t9); } else { // zero indexes 16 to 21 = 6*4 bytes memset(&Kfusion[16], 0, 24); } Kfusion[22] = -t26*(P[22][7]*t4*t9+P[22][8]*t3*t9+P[22][9]*t2*t9); Kfusion[23] = -t26*(P[23][7]*t4*t9+P[23][8]*t3*t9+P[23][9]*t2*t9); // Calculate innovation using the selected offset value Vector3f delta = stateStruct.position - rngBcnDataDelayed.beacon_posNED; innovRngBcn = delta.length() - rngBcnDataDelayed.rng; // calculate the innovation consistency test ratio rngBcnTestRatio = sq(innovRngBcn) / (sq(MAX(0.01f * (float)frontend->_rngBcnInnovGate, 1.0f)) * varInnovRngBcn); // fail if the ratio is > 1, but don't fail if bad IMU data rngBcnHealth = ((rngBcnTestRatio < 1.0f) || badIMUdata); // test the ratio before fusing data if (rngBcnHealth) { // restart the counter lastRngBcnPassTime_ms = imuSampleTime_ms; // 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<=6; j++) { KH[i][j] = 0.0f; } for (unsigned j = 7; j<=9; j++) { KH[i][j] = Kfusion[i] * H_BCN[j]; } for (unsigned j = 10; 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][7] * P[7][j]; res += KH[i][8] * P[8][j]; res += KH[i][9] * P[9][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-condiioning. ForceSymmetry(); ConstrainVariances(); // correct the state vector for (uint8_t j= 0; j<=stateIndexLim; j++) { statesArray[j] = statesArray[j] - Kfusion[j] * innovRngBcn; } // record healthy fusion faultStatus.bad_rngbcn = false; } else { // record bad fusion faultStatus.bad_rngbcn = true; } } // Update the fusion report rngBcnFusionReport[rngBcnDataDelayed.beacon_ID].beaconPosNED = rngBcnDataDelayed.beacon_posNED; rngBcnFusionReport[rngBcnDataDelayed.beacon_ID].innov = innovRngBcn; rngBcnFusionReport[rngBcnDataDelayed.beacon_ID].innovVar = varInnovRngBcn; rngBcnFusionReport[rngBcnDataDelayed.beacon_ID].rng = rngBcnDataDelayed.rng; rngBcnFusionReport[rngBcnDataDelayed.beacon_ID].testRatio = rngBcnTestRatio; } } /* Use range beaon measurements to calculate a static position using a 3-state EKF algorithm. Algorihtm based on the following: https://github.com/priseborough/InertialNav/blob/master/derivations/range_beacon.m */ void NavEKF3_core::FuseRngBcnStatic() { // get the estimated range measurement variance const float R_RNG = sq(MAX(rngBcnDataDelayed.rngErr , 0.1f)); /* The first thing to do is to check if we have started the alignment and if not, initialise the states and covariance to a first guess. To do this iterate through the avilable beacons and then initialise the initial position to the mean beacon position. The initial position uncertainty is set to the mean range measurement. */ if (!rngBcnAlignmentStarted) { if (rngBcnDataDelayed.beacon_ID != lastBeaconIndex) { rngBcnPosSum += rngBcnDataDelayed.beacon_posNED; lastBeaconIndex = rngBcnDataDelayed.beacon_ID; rngSum += rngBcnDataDelayed.rng; numBcnMeas++; // capture the beacon vertical spread if (rngBcnDataDelayed.beacon_posNED.z > maxBcnPosD) { maxBcnPosD = rngBcnDataDelayed.beacon_posNED.z; } else if(rngBcnDataDelayed.beacon_posNED.z < minBcnPosD) { minBcnPosD = rngBcnDataDelayed.beacon_posNED.z; } } if (numBcnMeas >= 100) { rngBcnAlignmentStarted = true; float tempVar = 1.0f / (float)numBcnMeas; // initialise the receiver position to the centre of the beacons and at zero height receiverPos.x = rngBcnPosSum.x * tempVar; receiverPos.y = rngBcnPosSum.y * tempVar; receiverPos.z = 0.0f; receiverPosCov[2][2] = receiverPosCov[1][1] = receiverPosCov[0][0] = rngSum * tempVar; lastBeaconIndex = 0; numBcnMeas = 0; rngBcnPosSum.zero(); rngSum = 0.0f; } } if (rngBcnAlignmentStarted) { numBcnMeas++; if (numBcnMeas >= 100) { // 100 observations is enough for a stable estimate under most conditions // TODO monitor stability of the position estimate rngBcnAlignmentCompleted = true; } if (rngBcnAlignmentCompleted) { if (activeHgtSource != HGT_SOURCE_BCN) { // We are using a different height reference for the main EKF so need to estimate a vertical // position offset to be applied to the beacon system that minimises the range innovations // The position estimate should be stable after 100 iterations so we use a simple dual // hypothesis 1-state EKF to estiate the offset Vector3f refPosNED; refPosNED.x = receiverPos.x; refPosNED.y = receiverPos.y; refPosNED.z = stateStruct.position.z; CalcRangeBeaconPosDownOffset(R_RNG, refPosNED, true); } else { // we are using the beacons as the primary height source, so don't modify their vertical position bcnPosOffset = 0.0f; } } else { if (activeHgtSource != HGT_SOURCE_BCN) { // The position estimate is not yet stable so we cannot run the 1-state EKF to estimate // beacon system vertical position offset. Instead we initialise the dual hypothesis offset states // using the beacon vertical position, vertical position estimate relative to the beacon origin // and the main EKF vertical position // Calculate the mid vertical position of all beacons float bcnMidPosD = 0.5f * (minBcnPosD + maxBcnPosD); // calculate the delta to the estimated receiver position float delta = receiverPos.z - bcnMidPosD; // calcuate the two hypothesis for our vertical position float receverPosDownMax; float receverPosDownMin; if (delta >= 0.0f) { receverPosDownMax = receiverPos.z; receverPosDownMin = receiverPos.z - 2.0f * delta; } else { receverPosDownMax = receiverPos.z - 2.0f * delta; receverPosDownMin = receiverPos.z; } bcnPosDownOffsetMax = stateStruct.position.z - receverPosDownMin; bcnPosDownOffsetMin = stateStruct.position.z - receverPosDownMax; } else { // We are using the beacons as the primary height reference, so don't modify their vertical position bcnPosOffset = 0.0f; } } // Add some process noise to the states at each time step for (uint8_t i= 0; i<=2; i++) { receiverPosCov[i][i] += 0.1f; } // calculate the observation jacobian float t2 = rngBcnDataDelayed.beacon_posNED.z - receiverPos.z + bcnPosOffset; float t3 = rngBcnDataDelayed.beacon_posNED.y - receiverPos.y; float t4 = rngBcnDataDelayed.beacon_posNED.x - receiverPos.x; float t5 = t2*t2; float t6 = t3*t3; float t7 = t4*t4; float t8 = t5+t6+t7; if (t8 < 0.1f) { // calculation will be badly conditioned return; } float t9 = 1.0f/sqrtf(t8); float t10 = rngBcnDataDelayed.beacon_posNED.x*2.0f; float t15 = receiverPos.x*2.0f; float t11 = t10-t15; float t12 = rngBcnDataDelayed.beacon_posNED.y*2.0f; float t14 = receiverPos.y*2.0f; float t13 = t12-t14; float t16 = rngBcnDataDelayed.beacon_posNED.z*2.0f; float t18 = receiverPos.z*2.0f; float t17 = t16-t18; float H_RNG[3]; H_RNG[0] = -t9*t11*0.5f; H_RNG[1] = -t9*t13*0.5f; H_RNG[2] = -t9*t17*0.5f; // calculate the Kalman gains float t19 = receiverPosCov[0][0]*t9*t11*0.5f; float t20 = receiverPosCov[1][1]*t9*t13*0.5f; float t21 = receiverPosCov[0][1]*t9*t11*0.5f; float t22 = receiverPosCov[2][1]*t9*t17*0.5f; float t23 = t20+t21+t22; float t24 = t9*t13*t23*0.5f; float t25 = receiverPosCov[1][2]*t9*t13*0.5f; float t26 = receiverPosCov[0][2]*t9*t11*0.5f; float t27 = receiverPosCov[2][2]*t9*t17*0.5f; float t28 = t25+t26+t27; float t29 = t9*t17*t28*0.5f; float t30 = receiverPosCov[1][0]*t9*t13*0.5f; float t31 = receiverPosCov[2][0]*t9*t17*0.5f; float t32 = t19+t30+t31; float t33 = t9*t11*t32*0.5f; varInnovRngBcn = R_RNG+t24+t29+t33; float t35 = 1.0f/varInnovRngBcn; float K_RNG[3]; K_RNG[0] = -t35*(t19+receiverPosCov[0][1]*t9*t13*0.5f+receiverPosCov[0][2]*t9*t17*0.5f); K_RNG[1] = -t35*(t20+receiverPosCov[1][0]*t9*t11*0.5f+receiverPosCov[1][2]*t9*t17*0.5f); K_RNG[2] = -t35*(t27+receiverPosCov[2][0]*t9*t11*0.5f+receiverPosCov[2][1]*t9*t13*0.5f); // calculate range measurement innovation Vector3f deltaPosNED = receiverPos - rngBcnDataDelayed.beacon_posNED; deltaPosNED.z -= bcnPosOffset; innovRngBcn = deltaPosNED.length() - rngBcnDataDelayed.rng; // update the state receiverPos.x -= K_RNG[0] * innovRngBcn; receiverPos.y -= K_RNG[1] * innovRngBcn; receiverPos.z -= K_RNG[2] * innovRngBcn; receiverPos.z = MAX(receiverPos.z, minBcnPosD + 1.2f); // calculate the covariance correction for (unsigned i = 0; i<=2; i++) { for (unsigned j = 0; j<=2; j++) { KH[i][j] = K_RNG[i] * H_RNG[j]; } } for (unsigned j = 0; j<=2; j++) { for (unsigned i = 0; i<=2; i++) { ftype res = 0; res += KH[i][0] * receiverPosCov[0][j]; res += KH[i][1] * receiverPosCov[1][j]; res += KH[i][2] * receiverPosCov[2][j]; KHP[i][j] = res; } } // prevent negative variances for (uint8_t i= 0; i<=2; i++) { if (receiverPosCov[i][i] < 0.0f) { receiverPosCov[i][i] = 0.0f; KHP[i][i] = 0.0f; } else if (KHP[i][i] > receiverPosCov[i][i]) { KHP[i][i] = receiverPosCov[i][i]; } } // apply the covariance correction for (uint8_t i= 0; i<=2; i++) { for (uint8_t j= 0; j<=2; j++) { receiverPosCov[i][j] -= KHP[i][j]; } } // ensure the covariance matrix is symmetric for (uint8_t i=1; i<=2; i++) { for (uint8_t j=0; j<=i-1; j++) { float temp = 0.5f*(receiverPosCov[i][j] + receiverPosCov[j][i]); receiverPosCov[i][j] = temp; receiverPosCov[j][i] = temp; } } if (numBcnMeas >= 100) { // 100 observations is enough for a stable estimate under most conditions // TODO monitor stability of the position estimate rngBcnAlignmentCompleted = true; } } } /* Run a single state Kalman filter to estimate the vertical position offset of the range beacon constellation Calculate using a high and low hypothesis and select the hypothesis with the lowest innovation sequence */ void NavEKF3_core::CalcRangeBeaconPosDownOffset(float obsVar, Vector3f &vehiclePosNED, bool aligning) { // Handle height offsets between the primary height source and the range beacons by estimating // the beacon systems global vertical position offset using a single state Kalman filter // The estimated offset is used to correct the beacon height when calculating innovations // A high and low estimate is calculated to handle the ambiguity in height associated with beacon positions that are co-planar // The main filter then uses the offset with the smaller innovations float innov; // range measurement innovation (m) float innovVar; // range measurement innovation variance (m^2) float gain; // Kalman gain float obsDeriv; // derivative of observation relative to state const float stateNoiseVar = 0.1f; // State process noise variance const float filtAlpha = 0.01f; // LPF constant const float innovGateWidth = 5.0f; // width of innovation consistency check gate in std // estimate upper value for offset // calculate observation derivative float t2 = rngBcnDataDelayed.beacon_posNED.z - vehiclePosNED.z + bcnPosDownOffsetMax; float t3 = rngBcnDataDelayed.beacon_posNED.y - vehiclePosNED.y; float t4 = rngBcnDataDelayed.beacon_posNED.x - vehiclePosNED.x; float t5 = t2*t2; float t6 = t3*t3; float t7 = t4*t4; float t8 = t5+t6+t7; float t9; if (t8 > 0.1f) { t9 = 1.0f/sqrtf(t8); obsDeriv = t2*t9; // Calculate innovation innov = sqrtf(t8) - rngBcnDataDelayed.rng; // calculate a filtered innovation magnitude to be used to select between the high or low offset OffsetMaxInnovFilt = (1.0f - filtAlpha) * bcnPosOffsetMaxVar + filtAlpha * fabsf(innov); // covariance prediction bcnPosOffsetMaxVar += stateNoiseVar; // calculate the innovation variance innovVar = obsDeriv * bcnPosOffsetMaxVar * obsDeriv + obsVar; innovVar = MAX(innovVar, obsVar); // Reject range innovation spikes using a 5-sigma threshold unless aligning if ((sq(innov) < sq(innovGateWidth) * innovVar) || aligning) { // calculate the Kalman gain gain = (bcnPosOffsetMaxVar * obsDeriv) / innovVar; // state update bcnPosDownOffsetMax -= innov * gain; // covariance update bcnPosOffsetMaxVar -= gain * obsDeriv * bcnPosOffsetMaxVar; bcnPosOffsetMaxVar = MAX(bcnPosOffsetMaxVar, 0.0f); } } // estimate lower value for offset // calculate observation derivative t2 = rngBcnDataDelayed.beacon_posNED.z - vehiclePosNED.z + bcnPosDownOffsetMin; t5 = t2*t2; t8 = t5+t6+t7; if (t8 > 0.1f) { t9 = 1.0f/sqrtf(t8); obsDeriv = t2*t9; // Calculate innovation innov = sqrtf(t8) - rngBcnDataDelayed.rng; // calculate a filtered innovation magnitude to be used to select between the high or low offset OffsetMinInnovFilt = (1.0f - filtAlpha) * OffsetMinInnovFilt + filtAlpha * fabsf(innov); // covariance prediction bcnPosOffsetMinVar += stateNoiseVar; // calculate the innovation variance innovVar = obsDeriv * bcnPosOffsetMinVar * obsDeriv + obsVar; innovVar = MAX(innovVar, obsVar); // Reject range innovation spikes using a 5-sigma threshold unless aligning if ((sq(innov) < sq(innovGateWidth) * innovVar) || aligning) { // calculate the Kalman gain gain = (bcnPosOffsetMinVar * obsDeriv) / innovVar; // state update bcnPosDownOffsetMin -= innov * gain; // covariance update bcnPosOffsetMinVar -= gain * obsDeriv * bcnPosOffsetMinVar; bcnPosOffsetMinVar = MAX(bcnPosOffsetMinVar, 0.0f); } } // calculate the mid vertical position of all beacons float bcnMidPosD = 0.5f * (minBcnPosD + maxBcnPosD); // ensure the two beacon vertical offset hypothesis place the mid point of the beacons below and above the flight vehicle bcnPosDownOffsetMax = MAX(bcnPosDownOffsetMax, vehiclePosNED.z - bcnMidPosD + 0.5f); bcnPosDownOffsetMin = MIN(bcnPosDownOffsetMin, vehiclePosNED.z - bcnMidPosD - 0.5f); // calculate the innovation for the main filter using the offset with the smallest innovation history // apply hysteresis to prevent rapid switching if (!usingMinHypothesis && OffsetMinInnovFilt < 0.8f * OffsetMaxInnovFilt) { bcnPosOffset = bcnPosDownOffsetMin; usingMinHypothesis = true; } else if (usingMinHypothesis && OffsetMaxInnovFilt < 0.8f * OffsetMinInnovFilt) { bcnPosOffset = bcnPosDownOffsetMax; usingMinHypothesis = false; } } #endif // HAL_CPU_CLASS