#include #include "AP_NavEKF3.h" #include "AP_NavEKF3_core.h" #include #include #include extern const AP_HAL::HAL& hal; /******************************************************** * RESET FUNCTIONS * ********************************************************/ /******************************************************** * FUSE MEASURED_DATA * ********************************************************/ // select fusion of optical flow measurements void NavEKF3_core::SelectFlowFusion() { // start performance timer hal.util->perf_begin(_perf_FuseOptFlow); // Check for data at the fusion time horizon flowDataToFuse = storedOF.recall(ofDataDelayed, imuDataDelayed.time_ms); // 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 && !optFlowFusionDelayed) { optFlowFusionDelayed = true; return; } else { optFlowFusionDelayed = false; } // Perform Data Checks // Check if the optical flow data is still valid flowDataValid = ((imuSampleTime_ms - flowValidMeaTime_ms) < 1000); // check is the terrain offset estimate is still valid - if we are using range finder as the main height reference, the ground is assumed to be at 0 gndOffsetValid = ((imuSampleTime_ms - gndHgtValidTime_ms) < 5000) || (activeHgtSource == HGT_SOURCE_RNG); // Perform tilt check bool tiltOK = (prevTnb.c.z > frontend->DCM33FlowMin); // Constrain measurements to zero if takeoff is not detected and the height above ground // is insuffient to achieve acceptable focus. This allows the vehicle to be picked up // and carried to test optical flow operation if (!takeOffDetected && ((terrainState - stateStruct.position.z) < 0.5f)) { ofDataDelayed.flowRadXYcomp.zero(); ofDataDelayed.flowRadXY.zero(); flowDataValid = true; } // if have valid flow or range measurements, fuse data into a 1-state EKF to estimate terrain height if (((flowDataToFuse && (frontend->_flowUse == FLOW_USE_TERRAIN)) || rangeDataToFuse) && tiltOK) { // Estimate the terrain offset (runs a one state EKF) EstimateTerrainOffset(); } // Fuse optical flow data into the main filter if (flowDataToFuse && tiltOK) { if (frontend->_flowUse == FLOW_USE_NAV) { // Set the flow noise used by the fusion processes R_LOS = sq(MAX(frontend->_flowNoise, 0.05f)); // Fuse the optical flow X and Y axis data into the main filter sequentially FuseOptFlow(); } // reset flag to indicate that no new flow data is available for fusion flowDataToFuse = false; } // stop the performance timer hal.util->perf_end(_perf_FuseOptFlow); } /* Estimation of terrain offset using a single state EKF The filter can fuse motion compensated optical flow rates and range finder measurements Equations generated using https://github.com/PX4/ecl/tree/master/EKF/matlab/scripts/Terrain%20Estimator */ void NavEKF3_core::EstimateTerrainOffset() { // start performance timer hal.util->perf_begin(_perf_TerrainOffset); // horizontal velocity squared float velHorizSq = sq(stateStruct.velocity.x) + sq(stateStruct.velocity.y); // don't fuse flow data if LOS rate is misaligned, without GPS, or insufficient velocity, as it is poorly observable // don't fuse flow data if it exceeds validity limits // don't update terrain offset if ground is being used as the zero height datum in the main filter bool cantFuseFlowData = ((frontend->_flowUse != FLOW_USE_TERRAIN) || gpsNotAvailable || PV_AidingMode == AID_RELATIVE || velHorizSq < 25.0f || (MAX(ofDataDelayed.flowRadXY[0],ofDataDelayed.flowRadXY[1]) > frontend->_maxFlowRate)); if ((!rangeDataToFuse && cantFuseFlowData) || (activeHgtSource == HGT_SOURCE_RNG)) { // skip update inhibitGndState = true; } else { inhibitGndState = false; // record the time we last updated the terrain offset state gndHgtValidTime_ms = imuSampleTime_ms; // propagate ground position state noise each time this is called using the difference in position since the last observations and an RMS gradient assumption // limit distance to prevent intialisation afer bad gps causing bad numerical conditioning float distanceTravelledSq = sq(stateStruct.position[0] - prevPosN) + sq(stateStruct.position[1] - prevPosE); distanceTravelledSq = MIN(distanceTravelledSq, 100.0f); prevPosN = stateStruct.position[0]; prevPosE = stateStruct.position[1]; // in addition to a terrain gradient error model, we also have the growth in uncertainty due to the copters vertical velocity float timeLapsed = MIN(0.001f * (imuSampleTime_ms - timeAtLastAuxEKF_ms), 1.0f); float Pincrement = (distanceTravelledSq * sq(frontend->_terrGradMax)) + sq(timeLapsed)*P[6][6]; Popt += Pincrement; timeAtLastAuxEKF_ms = imuSampleTime_ms; // fuse range finder data if (rangeDataToFuse) { // predict range float predRngMeas = MAX((terrainState - stateStruct.position[2]),rngOnGnd) / prevTnb.c.z; // Copy required states to local variable names float q0 = stateStruct.quat[0]; // quaternion at optical flow measurement time float q1 = stateStruct.quat[1]; // quaternion at optical flow measurement time float q2 = stateStruct.quat[2]; // quaternion at optical flow measurement time float q3 = stateStruct.quat[3]; // quaternion at optical flow measurement time // Set range finder measurement noise variance. TODO make this a function of range and tilt to allow for sensor, alignment and AHRS errors float R_RNG = frontend->_rngNoise; // calculate Kalman gain float SK_RNG = sq(q0) - sq(q1) - sq(q2) + sq(q3); float K_RNG = Popt/(SK_RNG*(R_RNG + Popt/sq(SK_RNG))); // Calculate the innovation variance for data logging varInnovRng = (R_RNG + Popt/sq(SK_RNG)); // constrain terrain height to be below the vehicle terrainState = MAX(terrainState, stateStruct.position[2] + rngOnGnd); // Calculate the measurement innovation innovRng = predRngMeas - rangeDataDelayed.rng; // calculate the innovation consistency test ratio auxRngTestRatio = sq(innovRng) / (sq(MAX(0.01f * (float)frontend->_rngInnovGate, 1.0f)) * varInnovRng); // Check the innovation test ratio and don't fuse if too large if (auxRngTestRatio < 1.0f) { // correct the state terrainState -= K_RNG * innovRng; // constrain the state terrainState = MAX(terrainState, stateStruct.position[2] + rngOnGnd); // correct the covariance Popt = Popt - sq(Popt)/(SK_RNG*(R_RNG + Popt/sq(SK_RNG))*(sq(q0) - sq(q1) - sq(q2) + sq(q3))); // prevent the state variance from becoming negative Popt = MAX(Popt,0.0f); } } if (!cantFuseFlowData) { Vector3f relVelSensor; // velocity of sensor relative to ground in sensor axes Vector2f losPred; // predicted optical flow angular rate measurement float q0 = stateStruct.quat[0]; // quaternion at optical flow measurement time float q1 = stateStruct.quat[1]; // quaternion at optical flow measurement time float q2 = stateStruct.quat[2]; // quaternion at optical flow measurement time float q3 = stateStruct.quat[3]; // quaternion at optical flow measurement time float K_OPT; float H_OPT; Vector2f auxFlowObsInnovVar; // predict range to centre of image float flowRngPred = MAX((terrainState - stateStruct.position.z),rngOnGnd) / prevTnb.c.z; // constrain terrain height to be below the vehicle terrainState = MAX(terrainState, stateStruct.position.z + rngOnGnd); // calculate relative velocity in sensor frame relVelSensor = prevTnb*stateStruct.velocity; // divide velocity by range, subtract body rates and apply scale factor to // get predicted sensed angular optical rates relative to X and Y sensor axes losPred.x = relVelSensor.y / flowRngPred; losPred.y = - relVelSensor.x / flowRngPred; // calculate innovations auxFlowObsInnov = losPred - ofDataDelayed.flowRadXYcomp; // calculate observation jacobians float t2 = q0*q0; float t3 = q1*q1; float t4 = q2*q2; float t5 = q3*q3; float t6 = stateStruct.position.z - terrainState; float t7 = 1.0f / (t6*t6); float t8 = q0*q3*2.0f; float t9 = t2-t3-t4+t5; // prevent the state variances from becoming badly conditioned Popt = MAX(Popt,1E-6f); // calculate observation noise variance from parameter float flow_noise_variance = sq(MAX(frontend->_flowNoise, 0.05f)); // Fuse Y axis data // Calculate observation partial derivative H_OPT = t7*t9*(-stateStruct.velocity.z*(q0*q2*2.0-q1*q3*2.0)+stateStruct.velocity.x*(t2+t3-t4-t5)+stateStruct.velocity.y*(t8+q1*q2*2.0)); // calculate innovation variance auxFlowObsInnovVar.y = H_OPT * Popt * H_OPT + flow_noise_variance; // calculate Kalman gain K_OPT = Popt * H_OPT / auxFlowObsInnovVar.y; // calculate the innovation consistency test ratio auxFlowTestRatio.y = sq(auxFlowObsInnov.y) / (sq(MAX(0.01f * (float)frontend->_flowInnovGate, 1.0f)) * auxFlowObsInnovVar.y); // don't fuse if optical flow data is outside valid range if (auxFlowTestRatio.y < 1.0f) { // correct the state terrainState -= K_OPT * auxFlowObsInnov.y; // constrain the state terrainState = MAX(terrainState, stateStruct.position.z + rngOnGnd); // update intermediate variables used when fusing the X axis t6 = stateStruct.position.z - terrainState; t7 = 1.0f / (t6*t6); // correct the covariance Popt = Popt - K_OPT * H_OPT * Popt; // prevent the state variances from becoming badly conditioned Popt = MAX(Popt,1E-6f); } // fuse X axis data H_OPT = -t7*t9*(stateStruct.velocity.z*(q0*q1*2.0+q2*q3*2.0)+stateStruct.velocity.y*(t2-t3+t4-t5)-stateStruct.velocity.x*(t8-q1*q2*2.0)); // calculate innovation variances auxFlowObsInnovVar.x = H_OPT * Popt * H_OPT + flow_noise_variance; // calculate Kalman gain K_OPT = Popt * H_OPT / auxFlowObsInnovVar.x; // calculate the innovation consistency test ratio auxFlowTestRatio.x = sq(auxFlowObsInnov.x) / (sq(MAX(0.01f * (float)frontend->_flowInnovGate, 1.0f)) * auxFlowObsInnovVar.x); // don't fuse if optical flow data is outside valid range if (auxFlowTestRatio.x < 1.0f) { // correct the state terrainState -= K_OPT * auxFlowObsInnov.x; // constrain the state terrainState = MAX(terrainState, stateStruct.position.z + rngOnGnd); // correct the covariance Popt = Popt - K_OPT * H_OPT * Popt; // prevent the state variances from becoming badly conditioned Popt = MAX(Popt,1E-6f); } } } // stop the performance timer hal.util->perf_end(_perf_TerrainOffset); } /* * Fuse angular motion compensated optical flow rates 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 * Requires a valid terrain height estimate. */ void NavEKF3_core::FuseOptFlow() { Vector24 H_LOS; Vector3f relVelSensor; Vector14 SH_LOS; Vector2 losPred; // Copy required states to local variable names float q0 = stateStruct.quat[0]; float q1 = stateStruct.quat[1]; float q2 = stateStruct.quat[2]; float q3 = stateStruct.quat[3]; float vn = stateStruct.velocity.x; float ve = stateStruct.velocity.y; float vd = stateStruct.velocity.z; float pd = stateStruct.position.z; // constrain height above ground to be above range measured on ground float heightAboveGndEst = MAX((terrainState - pd), rngOnGnd); float ptd = pd + heightAboveGndEst; // Calculate common expressions for observation jacobians SH_LOS[0] = sq(q0) - sq(q1) - sq(q2) + sq(q3); SH_LOS[1] = vn*(sq(q0) + sq(q1) - sq(q2) - sq(q3)) - vd*(2*q0*q2 - 2*q1*q3) + ve*(2*q0*q3 + 2*q1*q2); SH_LOS[2] = ve*(sq(q0) - sq(q1) + sq(q2) - sq(q3)) + vd*(2*q0*q1 + 2*q2*q3) - vn*(2*q0*q3 - 2*q1*q2); SH_LOS[3] = 1/(pd - ptd); SH_LOS[4] = vd*SH_LOS[0] - ve*(2*q0*q1 - 2*q2*q3) + vn*(2*q0*q2 + 2*q1*q3); SH_LOS[5] = 2.0f*q0*q2 - 2.0f*q1*q3; SH_LOS[6] = 2.0f*q0*q1 + 2.0f*q2*q3; SH_LOS[7] = q0*q0; SH_LOS[8] = q1*q1; SH_LOS[9] = q2*q2; SH_LOS[10] = q3*q3; SH_LOS[11] = q0*q3*2.0f; SH_LOS[12] = pd-ptd; SH_LOS[13] = 1.0f/(SH_LOS[12]*SH_LOS[12]); // Fuse X and Y axis measurements sequentially assuming observation errors are uncorrelated for (uint8_t obsIndex=0; obsIndex<=1; obsIndex++) { // fuse X axis data first // calculate range from ground plain to centre of sensor fov assuming flat earth float range = constrain_float((heightAboveGndEst/prevTnb.c.z),rngOnGnd,1000.0f); // correct range for flow sensor offset body frame position offset // the corrected value is the predicted range from the sensor focal point to the // centre of the image on the ground assuming flat terrain Vector3f posOffsetBody = (*ofDataDelayed.body_offset) - accelPosOffset; if (!posOffsetBody.is_zero()) { Vector3f posOffsetEarth = prevTnb.mul_transpose(posOffsetBody); range -= posOffsetEarth.z / prevTnb.c.z; } // calculate relative velocity in sensor frame including the relative motion due to rotation relVelSensor = (prevTnb * stateStruct.velocity) + (ofDataDelayed.bodyRadXYZ % posOffsetBody); // divide velocity by range to get predicted angular LOS rates relative to X and Y axes losPred[0] = relVelSensor.y/range; losPred[1] = -relVelSensor.x/range; // calculate observation jacobians and Kalman gains memset(&H_LOS[0], 0, sizeof(H_LOS)); if (obsIndex == 0) { // calculate X axis observation Jacobian float t2 = 1.0f / range; H_LOS[0] = t2*(q1*vd*2.0f+q0*ve*2.0f-q3*vn*2.0f); H_LOS[1] = t2*(q0*vd*2.0f-q1*ve*2.0f+q2*vn*2.0f); H_LOS[2] = t2*(q3*vd*2.0f+q2*ve*2.0f+q1*vn*2.0f); H_LOS[3] = -t2*(q2*vd*-2.0f+q3*ve*2.0f+q0*vn*2.0f); H_LOS[4] = -t2*(q0*q3*2.0f-q1*q2*2.0f); H_LOS[5] = t2*(q0*q0-q1*q1+q2*q2-q3*q3); H_LOS[6] = t2*(q0*q1*2.0f+q2*q3*2.0f); // calculate intermediate variables for the X observation innovation variance and Kalman gains float t3 = q1*vd*2.0f; float t4 = q0*ve*2.0f; float t11 = q3*vn*2.0f; float t5 = t3+t4-t11; float t6 = q0*q3*2.0f; float t29 = q1*q2*2.0f; float t7 = t6-t29; float t8 = q0*q1*2.0f; float t9 = q2*q3*2.0f; float t10 = t8+t9; float t12 = P[0][0]*t2*t5; float t13 = q0*vd*2.0f; float t14 = q2*vn*2.0f; float t28 = q1*ve*2.0f; float t15 = t13+t14-t28; float t16 = q3*vd*2.0f; float t17 = q2*ve*2.0f; float t18 = q1*vn*2.0f; float t19 = t16+t17+t18; float t20 = q3*ve*2.0f; float t21 = q0*vn*2.0f; float t30 = q2*vd*2.0f; float t22 = t20+t21-t30; float t23 = q0*q0; float t24 = q1*q1; float t25 = q2*q2; float t26 = q3*q3; float t27 = t23-t24+t25-t26; float t31 = P[1][1]*t2*t15; float t32 = P[6][0]*t2*t10; float t33 = P[1][0]*t2*t15; float t34 = P[2][0]*t2*t19; float t35 = P[5][0]*t2*t27; float t79 = P[4][0]*t2*t7; float t80 = P[3][0]*t2*t22; float t36 = t12+t32+t33+t34+t35-t79-t80; float t37 = t2*t5*t36; float t38 = P[6][1]*t2*t10; float t39 = P[0][1]*t2*t5; float t40 = P[2][1]*t2*t19; float t41 = P[5][1]*t2*t27; float t81 = P[4][1]*t2*t7; float t82 = P[3][1]*t2*t22; float t42 = t31+t38+t39+t40+t41-t81-t82; float t43 = t2*t15*t42; float t44 = P[6][2]*t2*t10; float t45 = P[0][2]*t2*t5; float t46 = P[1][2]*t2*t15; float t47 = P[2][2]*t2*t19; float t48 = P[5][2]*t2*t27; float t83 = P[4][2]*t2*t7; float t84 = P[3][2]*t2*t22; float t49 = t44+t45+t46+t47+t48-t83-t84; float t50 = t2*t19*t49; float t51 = P[6][3]*t2*t10; float t52 = P[0][3]*t2*t5; float t53 = P[1][3]*t2*t15; float t54 = P[2][3]*t2*t19; float t55 = P[5][3]*t2*t27; float t85 = P[4][3]*t2*t7; float t86 = P[3][3]*t2*t22; float t56 = t51+t52+t53+t54+t55-t85-t86; float t57 = P[6][5]*t2*t10; float t58 = P[0][5]*t2*t5; float t59 = P[1][5]*t2*t15; float t60 = P[2][5]*t2*t19; float t61 = P[5][5]*t2*t27; float t88 = P[4][5]*t2*t7; float t89 = P[3][5]*t2*t22; float t62 = t57+t58+t59+t60+t61-t88-t89; float t63 = t2*t27*t62; float t64 = P[6][4]*t2*t10; float t65 = P[0][4]*t2*t5; float t66 = P[1][4]*t2*t15; float t67 = P[2][4]*t2*t19; float t68 = P[5][4]*t2*t27; float t90 = P[4][4]*t2*t7; float t91 = P[3][4]*t2*t22; float t69 = t64+t65+t66+t67+t68-t90-t91; float t70 = P[6][6]*t2*t10; float t71 = P[0][6]*t2*t5; float t72 = P[1][6]*t2*t15; float t73 = P[2][6]*t2*t19; float t74 = P[5][6]*t2*t27; float t93 = P[4][6]*t2*t7; float t94 = P[3][6]*t2*t22; float t75 = t70+t71+t72+t73+t74-t93-t94; float t76 = t2*t10*t75; float t87 = t2*t22*t56; float t92 = t2*t7*t69; float t77 = R_LOS+t37+t43+t50+t63+t76-t87-t92; float t78; // calculate innovation variance for X axis observation and protect against a badly conditioned calculation if (t77 > R_LOS) { t78 = 1.0f/t77; faultStatus.bad_xflow = false; } else { t77 = R_LOS; t78 = 1.0f/R_LOS; faultStatus.bad_xflow = true; return; } varInnovOptFlow[0] = t77; // calculate innovation for X axis observation innovOptFlow[0] = losPred[0] - ofDataDelayed.flowRadXYcomp.x; // calculate Kalman gains for X-axis observation Kfusion[0] = t78*(t12-P[0][4]*t2*t7+P[0][1]*t2*t15+P[0][6]*t2*t10+P[0][2]*t2*t19-P[0][3]*t2*t22+P[0][5]*t2*t27); Kfusion[1] = t78*(t31+P[1][0]*t2*t5-P[1][4]*t2*t7+P[1][6]*t2*t10+P[1][2]*t2*t19-P[1][3]*t2*t22+P[1][5]*t2*t27); Kfusion[2] = t78*(t47+P[2][0]*t2*t5-P[2][4]*t2*t7+P[2][1]*t2*t15+P[2][6]*t2*t10-P[2][3]*t2*t22+P[2][5]*t2*t27); Kfusion[3] = t78*(-t86+P[3][0]*t2*t5-P[3][4]*t2*t7+P[3][1]*t2*t15+P[3][6]*t2*t10+P[3][2]*t2*t19+P[3][5]*t2*t27); Kfusion[4] = t78*(-t90+P[4][0]*t2*t5+P[4][1]*t2*t15+P[4][6]*t2*t10+P[4][2]*t2*t19-P[4][3]*t2*t22+P[4][5]*t2*t27); Kfusion[5] = t78*(t61+P[5][0]*t2*t5-P[5][4]*t2*t7+P[5][1]*t2*t15+P[5][6]*t2*t10+P[5][2]*t2*t19-P[5][3]*t2*t22); Kfusion[6] = t78*(t70+P[6][0]*t2*t5-P[6][4]*t2*t7+P[6][1]*t2*t15+P[6][2]*t2*t19-P[6][3]*t2*t22+P[6][5]*t2*t27); Kfusion[7] = t78*(P[7][0]*t2*t5-P[7][4]*t2*t7+P[7][1]*t2*t15+P[7][6]*t2*t10+P[7][2]*t2*t19-P[7][3]*t2*t22+P[7][5]*t2*t27); Kfusion[8] = t78*(P[8][0]*t2*t5-P[8][4]*t2*t7+P[8][1]*t2*t15+P[8][6]*t2*t10+P[8][2]*t2*t19-P[8][3]*t2*t22+P[8][5]*t2*t27); Kfusion[9] = t78*(P[9][0]*t2*t5-P[9][4]*t2*t7+P[9][1]*t2*t15+P[9][6]*t2*t10+P[9][2]*t2*t19-P[9][3]*t2*t22+P[9][5]*t2*t27); if (!inhibitDelAngBiasStates) { Kfusion[10] = t78*(P[10][0]*t2*t5-P[10][4]*t2*t7+P[10][1]*t2*t15+P[10][6]*t2*t10+P[10][2]*t2*t19-P[10][3]*t2*t22+P[10][5]*t2*t27); Kfusion[11] = t78*(P[11][0]*t2*t5-P[11][4]*t2*t7+P[11][1]*t2*t15+P[11][6]*t2*t10+P[11][2]*t2*t19-P[11][3]*t2*t22+P[11][5]*t2*t27); Kfusion[12] = t78*(P[12][0]*t2*t5-P[12][4]*t2*t7+P[12][1]*t2*t15+P[12][6]*t2*t10+P[12][2]*t2*t19-P[12][3]*t2*t22+P[12][5]*t2*t27); } else { // zero indexes 10 to 12 = 3*4 bytes memset(&Kfusion[10], 0, 12); } if (!inhibitDelVelBiasStates) { Kfusion[13] = t78*(P[13][0]*t2*t5-P[13][4]*t2*t7+P[13][1]*t2*t15+P[13][6]*t2*t10+P[13][2]*t2*t19-P[13][3]*t2*t22+P[13][5]*t2*t27); Kfusion[14] = t78*(P[14][0]*t2*t5-P[14][4]*t2*t7+P[14][1]*t2*t15+P[14][6]*t2*t10+P[14][2]*t2*t19-P[14][3]*t2*t22+P[14][5]*t2*t27); Kfusion[15] = t78*(P[15][0]*t2*t5-P[15][4]*t2*t7+P[15][1]*t2*t15+P[15][6]*t2*t10+P[15][2]*t2*t19-P[15][3]*t2*t22+P[15][5]*t2*t27); } else { // zero indexes 13 to 15 = 3*4 bytes memset(&Kfusion[13], 0, 12); } if (!inhibitMagStates) { Kfusion[16] = t78*(P[16][0]*t2*t5-P[16][4]*t2*t7+P[16][1]*t2*t15+P[16][6]*t2*t10+P[16][2]*t2*t19-P[16][3]*t2*t22+P[16][5]*t2*t27); Kfusion[17] = t78*(P[17][0]*t2*t5-P[17][4]*t2*t7+P[17][1]*t2*t15+P[17][6]*t2*t10+P[17][2]*t2*t19-P[17][3]*t2*t22+P[17][5]*t2*t27); Kfusion[18] = t78*(P[18][0]*t2*t5-P[18][4]*t2*t7+P[18][1]*t2*t15+P[18][6]*t2*t10+P[18][2]*t2*t19-P[18][3]*t2*t22+P[18][5]*t2*t27); Kfusion[19] = t78*(P[19][0]*t2*t5-P[19][4]*t2*t7+P[19][1]*t2*t15+P[19][6]*t2*t10+P[19][2]*t2*t19-P[19][3]*t2*t22+P[19][5]*t2*t27); Kfusion[20] = t78*(P[20][0]*t2*t5-P[20][4]*t2*t7+P[20][1]*t2*t15+P[20][6]*t2*t10+P[20][2]*t2*t19-P[20][3]*t2*t22+P[20][5]*t2*t27); Kfusion[21] = t78*(P[21][0]*t2*t5-P[21][4]*t2*t7+P[21][1]*t2*t15+P[21][6]*t2*t10+P[21][2]*t2*t19-P[21][3]*t2*t22+P[21][5]*t2*t27); } else { // zero indexes 16 to 21 = 6*4 bytes memset(&Kfusion[16], 0, 24); } if (!inhibitWindStates) { Kfusion[22] = t78*(P[22][0]*t2*t5-P[22][4]*t2*t7+P[22][1]*t2*t15+P[22][6]*t2*t10+P[22][2]*t2*t19-P[22][3]*t2*t22+P[22][5]*t2*t27); Kfusion[23] = t78*(P[23][0]*t2*t5-P[23][4]*t2*t7+P[23][1]*t2*t15+P[23][6]*t2*t10+P[23][2]*t2*t19-P[23][3]*t2*t22+P[23][5]*t2*t27); } else { // zero indexes 22 to 23 = 2*4 bytes memset(&Kfusion[22], 0, 8); } } else { // calculate Y axis observation Jacobian float t2 = 1.0f / range; H_LOS[0] = -t2*(q2*vd*-2.0f+q3*ve*2.0f+q0*vn*2.0f); H_LOS[1] = -t2*(q3*vd*2.0f+q2*ve*2.0f+q1*vn*2.0f); H_LOS[2] = t2*(q0*vd*2.0f-q1*ve*2.0f+q2*vn*2.0f); H_LOS[3] = -t2*(q1*vd*2.0f+q0*ve*2.0f-q3*vn*2.0f); H_LOS[4] = -t2*(q0*q0+q1*q1-q2*q2-q3*q3); H_LOS[5] = -t2*(q0*q3*2.0f+q1*q2*2.0f); H_LOS[6] = t2*(q0*q2*2.0f-q1*q3*2.0f); // calculate intermediate variables for the Y observation innovation variance and Kalman gains float t3 = q3*ve*2.0f; float t4 = q0*vn*2.0f; float t11 = q2*vd*2.0f; float t5 = t3+t4-t11; float t6 = q0*q3*2.0f; float t7 = q1*q2*2.0f; float t8 = t6+t7; float t9 = q0*q2*2.0f; float t28 = q1*q3*2.0f; float t10 = t9-t28; float t12 = P[0][0]*t2*t5; float t13 = q3*vd*2.0f; float t14 = q2*ve*2.0f; float t15 = q1*vn*2.0f; float t16 = t13+t14+t15; float t17 = q0*vd*2.0f; float t18 = q2*vn*2.0f; float t29 = q1*ve*2.0f; float t19 = t17+t18-t29; float t20 = q1*vd*2.0f; float t21 = q0*ve*2.0f; float t30 = q3*vn*2.0f; float t22 = t20+t21-t30; float t23 = q0*q0; float t24 = q1*q1; float t25 = q2*q2; float t26 = q3*q3; float t27 = t23+t24-t25-t26; float t31 = P[1][1]*t2*t16; float t32 = P[5][0]*t2*t8; float t33 = P[1][0]*t2*t16; float t34 = P[3][0]*t2*t22; float t35 = P[4][0]*t2*t27; float t80 = P[6][0]*t2*t10; float t81 = P[2][0]*t2*t19; float t36 = t12+t32+t33+t34+t35-t80-t81; float t37 = t2*t5*t36; float t38 = P[5][1]*t2*t8; float t39 = P[0][1]*t2*t5; float t40 = P[3][1]*t2*t22; float t41 = P[4][1]*t2*t27; float t82 = P[6][1]*t2*t10; float t83 = P[2][1]*t2*t19; float t42 = t31+t38+t39+t40+t41-t82-t83; float t43 = t2*t16*t42; float t44 = P[5][2]*t2*t8; float t45 = P[0][2]*t2*t5; float t46 = P[1][2]*t2*t16; float t47 = P[3][2]*t2*t22; float t48 = P[4][2]*t2*t27; float t79 = P[2][2]*t2*t19; float t84 = P[6][2]*t2*t10; float t49 = t44+t45+t46+t47+t48-t79-t84; float t50 = P[5][3]*t2*t8; float t51 = P[0][3]*t2*t5; float t52 = P[1][3]*t2*t16; float t53 = P[3][3]*t2*t22; float t54 = P[4][3]*t2*t27; float t86 = P[6][3]*t2*t10; float t87 = P[2][3]*t2*t19; float t55 = t50+t51+t52+t53+t54-t86-t87; float t56 = t2*t22*t55; float t57 = P[5][4]*t2*t8; float t58 = P[0][4]*t2*t5; float t59 = P[1][4]*t2*t16; float t60 = P[3][4]*t2*t22; float t61 = P[4][4]*t2*t27; float t88 = P[6][4]*t2*t10; float t89 = P[2][4]*t2*t19; float t62 = t57+t58+t59+t60+t61-t88-t89; float t63 = t2*t27*t62; float t64 = P[5][5]*t2*t8; float t65 = P[0][5]*t2*t5; float t66 = P[1][5]*t2*t16; float t67 = P[3][5]*t2*t22; float t68 = P[4][5]*t2*t27; float t90 = P[6][5]*t2*t10; float t91 = P[2][5]*t2*t19; float t69 = t64+t65+t66+t67+t68-t90-t91; float t70 = t2*t8*t69; float t71 = P[5][6]*t2*t8; float t72 = P[0][6]*t2*t5; float t73 = P[1][6]*t2*t16; float t74 = P[3][6]*t2*t22; float t75 = P[4][6]*t2*t27; float t92 = P[6][6]*t2*t10; float t93 = P[2][6]*t2*t19; float t76 = t71+t72+t73+t74+t75-t92-t93; float t85 = t2*t19*t49; float t94 = t2*t10*t76; float t77 = R_LOS+t37+t43+t56+t63+t70-t85-t94; float t78; // calculate innovation variance for Y axis observation and protect against a badly conditioned calculation if (t77 > R_LOS) { t78 = 1.0f/t77; faultStatus.bad_yflow = false; } else { t77 = R_LOS; t78 = 1.0f/R_LOS; faultStatus.bad_yflow = true; return; } varInnovOptFlow[1] = t77; // calculate innovation for Y observation innovOptFlow[1] = losPred[1] - ofDataDelayed.flowRadXYcomp.y; // calculate Kalman gains for the Y-axis observation Kfusion[0] = -t78*(t12+P[0][5]*t2*t8-P[0][6]*t2*t10+P[0][1]*t2*t16-P[0][2]*t2*t19+P[0][3]*t2*t22+P[0][4]*t2*t27); Kfusion[1] = -t78*(t31+P[1][0]*t2*t5+P[1][5]*t2*t8-P[1][6]*t2*t10-P[1][2]*t2*t19+P[1][3]*t2*t22+P[1][4]*t2*t27); Kfusion[2] = -t78*(-t79+P[2][0]*t2*t5+P[2][5]*t2*t8-P[2][6]*t2*t10+P[2][1]*t2*t16+P[2][3]*t2*t22+P[2][4]*t2*t27); Kfusion[3] = -t78*(t53+P[3][0]*t2*t5+P[3][5]*t2*t8-P[3][6]*t2*t10+P[3][1]*t2*t16-P[3][2]*t2*t19+P[3][4]*t2*t27); Kfusion[4] = -t78*(t61+P[4][0]*t2*t5+P[4][5]*t2*t8-P[4][6]*t2*t10+P[4][1]*t2*t16-P[4][2]*t2*t19+P[4][3]*t2*t22); Kfusion[5] = -t78*(t64+P[5][0]*t2*t5-P[5][6]*t2*t10+P[5][1]*t2*t16-P[5][2]*t2*t19+P[5][3]*t2*t22+P[5][4]*t2*t27); Kfusion[6] = -t78*(-t92+P[6][0]*t2*t5+P[6][5]*t2*t8+P[6][1]*t2*t16-P[6][2]*t2*t19+P[6][3]*t2*t22+P[6][4]*t2*t27); Kfusion[7] = -t78*(P[7][0]*t2*t5+P[7][5]*t2*t8-P[7][6]*t2*t10+P[7][1]*t2*t16-P[7][2]*t2*t19+P[7][3]*t2*t22+P[7][4]*t2*t27); Kfusion[8] = -t78*(P[8][0]*t2*t5+P[8][5]*t2*t8-P[8][6]*t2*t10+P[8][1]*t2*t16-P[8][2]*t2*t19+P[8][3]*t2*t22+P[8][4]*t2*t27); Kfusion[9] = -t78*(P[9][0]*t2*t5+P[9][5]*t2*t8-P[9][6]*t2*t10+P[9][1]*t2*t16-P[9][2]*t2*t19+P[9][3]*t2*t22+P[9][4]*t2*t27); if (!inhibitDelAngBiasStates) { Kfusion[10] = -t78*(P[10][0]*t2*t5+P[10][5]*t2*t8-P[10][6]*t2*t10+P[10][1]*t2*t16-P[10][2]*t2*t19+P[10][3]*t2*t22+P[10][4]*t2*t27); Kfusion[11] = -t78*(P[11][0]*t2*t5+P[11][5]*t2*t8-P[11][6]*t2*t10+P[11][1]*t2*t16-P[11][2]*t2*t19+P[11][3]*t2*t22+P[11][4]*t2*t27); Kfusion[12] = -t78*(P[12][0]*t2*t5+P[12][5]*t2*t8-P[12][6]*t2*t10+P[12][1]*t2*t16-P[12][2]*t2*t19+P[12][3]*t2*t22+P[12][4]*t2*t27); } else { // zero indexes 10 to 12 = 3*4 bytes memset(&Kfusion[10], 0, 12); } if (!inhibitDelVelBiasStates) { Kfusion[13] = -t78*(P[13][0]*t2*t5+P[13][5]*t2*t8-P[13][6]*t2*t10+P[13][1]*t2*t16-P[13][2]*t2*t19+P[13][3]*t2*t22+P[13][4]*t2*t27); Kfusion[14] = -t78*(P[14][0]*t2*t5+P[14][5]*t2*t8-P[14][6]*t2*t10+P[14][1]*t2*t16-P[14][2]*t2*t19+P[14][3]*t2*t22+P[14][4]*t2*t27); Kfusion[15] = -t78*(P[15][0]*t2*t5+P[15][5]*t2*t8-P[15][6]*t2*t10+P[15][1]*t2*t16-P[15][2]*t2*t19+P[15][3]*t2*t22+P[15][4]*t2*t27); } else { // zero indexes 13 to 15 = 3*4 bytes memset(&Kfusion[13], 0, 12); } if (!inhibitMagStates) { Kfusion[16] = -t78*(P[16][0]*t2*t5+P[16][5]*t2*t8-P[16][6]*t2*t10+P[16][1]*t2*t16-P[16][2]*t2*t19+P[16][3]*t2*t22+P[16][4]*t2*t27); Kfusion[17] = -t78*(P[17][0]*t2*t5+P[17][5]*t2*t8-P[17][6]*t2*t10+P[17][1]*t2*t16-P[17][2]*t2*t19+P[17][3]*t2*t22+P[17][4]*t2*t27); Kfusion[18] = -t78*(P[18][0]*t2*t5+P[18][5]*t2*t8-P[18][6]*t2*t10+P[18][1]*t2*t16-P[18][2]*t2*t19+P[18][3]*t2*t22+P[18][4]*t2*t27); Kfusion[19] = -t78*(P[19][0]*t2*t5+P[19][5]*t2*t8-P[19][6]*t2*t10+P[19][1]*t2*t16-P[19][2]*t2*t19+P[19][3]*t2*t22+P[19][4]*t2*t27); Kfusion[20] = -t78*(P[20][0]*t2*t5+P[20][5]*t2*t8-P[20][6]*t2*t10+P[20][1]*t2*t16-P[20][2]*t2*t19+P[20][3]*t2*t22+P[20][4]*t2*t27); Kfusion[21] = -t78*(P[21][0]*t2*t5+P[21][5]*t2*t8-P[21][6]*t2*t10+P[21][1]*t2*t16-P[21][2]*t2*t19+P[21][3]*t2*t22+P[21][4]*t2*t27); } else { // zero indexes 16 to 21 = 6*4 bytes memset(&Kfusion[16], 0, 24); } if (!inhibitWindStates) { Kfusion[22] = -t78*(P[22][0]*t2*t5+P[22][5]*t2*t8-P[22][6]*t2*t10+P[22][1]*t2*t16-P[22][2]*t2*t19+P[22][3]*t2*t22+P[22][4]*t2*t27); Kfusion[23] = -t78*(P[23][0]*t2*t5+P[23][5]*t2*t8-P[23][6]*t2*t10+P[23][1]*t2*t16-P[23][2]*t2*t19+P[23][3]*t2*t22+P[23][4]*t2*t27); } else { // zero indexes 22 to 23 = 2*4 bytes memset(&Kfusion[22], 0, 8); } } // calculate the innovation consistency test ratio flowTestRatio[obsIndex] = sq(innovOptFlow[obsIndex]) / (sq(MAX(0.01f * (float)frontend->_flowInnovGate, 1.0f)) * varInnovOptFlow[obsIndex]); // Check the innovation for consistency and don't fuse if out of bounds or flow is too fast to be reliable if ((flowTestRatio[obsIndex]) < 1.0f && (ofDataDelayed.flowRadXY.x < frontend->_maxFlowRate) && (ofDataDelayed.flowRadXY.y < frontend->_maxFlowRate)) { // record the last time observations were accepted for fusion prevFlowFuseTime_ms = imuSampleTime_ms; // notify first time only if (!flowFusionActive) { flowFusionActive = true; gcs().send_text(MAV_SEVERITY_INFO, "EKF3 IMU%u fusing optical flow",(unsigned)imu_index); } // 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] = Kfusion[i] * H_LOS[j]; } for (unsigned j = 7; j<=stateIndexLim; 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][4] * P[4][j]; res += KH[i][5] * P[5][j]; res += KH[i][6] * P[6][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] * innovOptFlow[obsIndex]; } stateStruct.quat.normalize(); } else { // record bad axis if (obsIndex == 0) { faultStatus.bad_xflow = true; } else if (obsIndex == 1) { faultStatus.bad_yflow = true; } } } } } /******************************************************** * MISC FUNCTIONS * ********************************************************/