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ardupilot/libraries/AP_NavEKF3/AP_NavEKF3_OptFlowFusion.cpp

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#include <AP_HAL/AP_HAL.h>
#include "AP_NavEKF3.h"
#include "AP_NavEKF3_core.h"
#include <AP_AHRS/AP_AHRS.h>
#include <AP_Vehicle/AP_Vehicle.h>
#include <GCS_MAVLink/GCS.h>
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 *
********************************************************/