px4_autopilot/EKF/optflow_fusion.cpp

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/**
 * @file vel_pos_fusion.cpp
 * Function for fusing gps and baro measurements/
 *
 * @author Paul Riseborough <p_riseborough@live.com.au>
 * @author Siddharth Bharat Purohit <siddharthbharatpurohit@gmail.com>
 *
 */

#include "ekf.h"
#include <ecl.h>
#include <mathlib/mathlib.h>
#include <float.h>

void Ekf::fuseOptFlow()
{
	float gndclearance = fmaxf(_params.rng_gnd_clearance, 0.1f);

	// get latest estimated orientation
	const float q0 = _state.quat_nominal(0);
	const float q1 = _state.quat_nominal(1);
	const float q2 = _state.quat_nominal(2);
	const float q3 = _state.quat_nominal(3);

	// get latest velocity in earth frame
	const float vn = _state.vel(0);
	const float ve = _state.vel(1);
	const float vd = _state.vel(2);

	// calculate the optical flow observation variance
	const float R_LOS = calcOptFlowMeasVar();

	float H_LOS[2][24] = {}; // Optical flow observation Jacobians
	float Kfusion[24][2] = {}; // Optical flow Kalman gains

	// get rotation matrix from earth to body
	const Dcmf earth_to_body = quat_to_invrotmat(_state.quat_nominal);

	// calculate the sensor position relative to the IMU
	const Vector3f pos_offset_body = _params.flow_pos_body - _params.imu_pos_body;

	// calculate the velocity of the sensor relative to the imu in body frame
	// Note: _flow_sample_delayed.gyroXYZ is the negative of the body angular velocity, thus use minus sign
	const Vector3f vel_rel_imu_body = Vector3f(-_flow_sample_delayed.gyroXYZ / _flow_sample_delayed.dt) % pos_offset_body;

	// calculate the velocity of the sensor in the earth frame
	const Vector3f vel_rel_earth = _state.vel + _R_to_earth * vel_rel_imu_body;

	// rotate into body frame
	const Vector3f vel_body = earth_to_body * vel_rel_earth;

	// height above ground of the IMU
	float heightAboveGndEst = _terrain_vpos - _state.pos(2);

	// calculate the sensor position relative to the IMU in earth frame
	const Vector3f pos_offset_earth = _R_to_earth * pos_offset_body;

	// calculate the height above the ground of the optical flow camera. Since earth frame is NED
	// a positive offset in earth frame leads to a smaller height above the ground.
	heightAboveGndEst -= pos_offset_earth(2);

	// constrain minimum height above ground
	heightAboveGndEst = math::max(heightAboveGndEst, gndclearance);

	// calculate range from focal point to centre of image
	const float range = heightAboveGndEst / earth_to_body(2, 2); // absolute distance to the frame region in view

	// calculate optical LOS rates using optical flow rates that have had the body angular rate contribution removed
	// correct for gyro bias errors in the data used to do the motion compensation
	// Note the sign convention used: A positive LOS rate is a RH rotation of the scene about that axis.
	Vector2f opt_flow_rate;
	opt_flow_rate(0) = _flowRadXYcomp(0) / _flow_sample_delayed.dt + _flow_gyro_bias(0);
	opt_flow_rate(1) = _flowRadXYcomp(1) / _flow_sample_delayed.dt + _flow_gyro_bias(1);

	if (opt_flow_rate.norm() < _flow_max_rate) {
		_flow_innov[0] =  vel_body(1) / range - opt_flow_rate(0); // flow around the X axis
		_flow_innov[1] = -vel_body(0) / range - opt_flow_rate(1); // flow around the Y axis

	} else {
		return;
	}


	// Fuse X and Y axis measurements sequentially assuming observation errors are uncorrelated
	// Calculate Obser ation Jacobians and Kalman gans for each measurement axis
	for (uint8_t obs_index = 0; obs_index <= 1; obs_index++) {

		if (obs_index == 0) {

			// calculate X axis observation Jacobian
			float t2 = 1.0f / range;
			H_LOS[0][0] = t2*(q1*vd*2.0f+q0*ve*2.0f-q3*vn*2.0f);
			H_LOS[0][1] = t2*(q0*vd*2.0f-q1*ve*2.0f+q2*vn*2.0f);
			H_LOS[0][2] = t2*(q3*vd*2.0f+q2*ve*2.0f+q1*vn*2.0f);
			H_LOS[0][3] = -t2*(q2*vd*-2.0f+q3*ve*2.0f+q0*vn*2.0f);
			H_LOS[0][4] = -t2*(q0*q3*2.0f-q1*q2*2.0f);
			H_LOS[0][5] = t2*(q0*q0-q1*q1+q2*q2-q3*q3);
			H_LOS[0][6] = t2*(q0*q1*2.0f+q2*q3*2.0f);

			// calculate intermediate variables for the X observation innovatoin 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;
				_flow_innov_var[0] = t77;

			} else {
				// we need to reinitialise the covariance matrix and abort this fusion step
				initialiseCovariance();
				return;
			}

			// calculate Kalman gains for X-axis observation
			Kfusion[0][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][0] = 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][0] = 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][0] = 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][0] = 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][0] = 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][0] = 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][0] = 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][0] = 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][0] = 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);
			Kfusion[10][0] = 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][0] = 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][0] = 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);
			Kfusion[13][0] = 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][0] = 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][0] = 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);
			Kfusion[16][0] = 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][0] = 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][0] = 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][0] = 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][0] = 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][0] = 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);
			Kfusion[22][0] = 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][0] = 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 if (obs_index == 1) {

			// calculate Y axis observation Jacobian
			float t2 = 1.0f / range;
			H_LOS[1][0] = -t2*(q2*vd*-2.0f+q3*ve*2.0f+q0*vn*2.0f);
			H_LOS[1][1] = -t2*(q3*vd*2.0f+q2*ve*2.0f+q1*vn*2.0f);
			H_LOS[1][2] = t2*(q0*vd*2.0f-q1*ve*2.0f+q2*vn*2.0f);
			H_LOS[1][3] = -t2*(q1*vd*2.0f+q0*ve*2.0f-q3*vn*2.0f);
			H_LOS[1][4] = -t2*(q0*q0+q1*q1-q2*q2-q3*q3);
			H_LOS[1][5] = -t2*(q0*q3*2.0f+q1*q2*2.0f);
			H_LOS[1][6] = t2*(q0*q2*2.0f-q1*q3*2.0f);

			// calculate intermediate variables for the Y observation innovatoin 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;
				_flow_innov_var[1] = t77;

			} else {
				// we need to reinitialise the covariance matrix and abort this fusion step
				initialiseCovariance();
				return;
			}

			// calculate Kalman gains for Y-axis observation
			Kfusion[0][1] = -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][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][1] = -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][1] = -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][1] = -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][1] = -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][1] = -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][1] = -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][1] = -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][1] = -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);
			Kfusion[10][1] = -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][1] = -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][1] = -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);
			Kfusion[13][1] = -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][1] = -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][1] = -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);
			Kfusion[16][1] = -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][1] = -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][1] = -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][1] = -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][1] = -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][1] = -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);
			Kfusion[22][1] = -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][1] = -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);

		}
	}

	// run the innovation consistency check and record result
	bool flow_fail = false;
	float test_ratio[2];
	test_ratio[0] = sq(_flow_innov[0]) / (sq(math::max(_params.flow_innov_gate, 1.0f)) * _flow_innov_var[0]);
	test_ratio[1] = sq(_flow_innov[1]) / (sq(math::max(_params.flow_innov_gate, 1.0f)) * _flow_innov_var[1]);
	_optflow_test_ratio = math::max(test_ratio[0],test_ratio[1]);

	for (uint8_t obs_index = 0; obs_index <= 1; obs_index++) {
		if (test_ratio[obs_index] > 1.0f) {
			flow_fail = true;
			_innov_check_fail_status.value |= (1 << (obs_index + 10));

		} else {
			_innov_check_fail_status.value &= ~(1 << (obs_index + 10));

		}
	}

	// if either axis fails we abort the fusion
	if (flow_fail) {
		return;

	}

	for (uint8_t obs_index = 0; obs_index <= 1; obs_index++) {

		// copy the Kalman gain vector for the axis we are fusing
		float gain[24];

		for (unsigned row = 0; row <= 23; row++) {
			gain[row] = Kfusion[row][obs_index];
		}

		// apply covariance correction via P_new = (I -K*H)*P
		// first calculate expression for KHP
		// then calculate P - KHP
		matrix::SquareMatrix<float, _k_num_states> KHP;
		float KH[7];

		for (unsigned row = 0; row < _k_num_states; row++) {

			KH[0] = gain[row] * H_LOS[obs_index][0];
			KH[1] = gain[row] * H_LOS[obs_index][1];
			KH[2] = gain[row] * H_LOS[obs_index][2];
			KH[3] = gain[row] * H_LOS[obs_index][3];
			KH[4] = gain[row] * H_LOS[obs_index][4];
			KH[5] = gain[row] * H_LOS[obs_index][5];
			KH[6] = gain[row] * H_LOS[obs_index][6];

			for (unsigned column = 0; column < _k_num_states; column++) {
				float tmp = KH[0] * P(0,column);
				tmp += KH[1] * P(1,column);
				tmp += KH[2] * P(2,column);
				tmp += KH[3] * P(3,column);
				tmp += KH[4] * P(4,column);
				tmp += KH[5] * P(5,column);
				tmp += KH[6] * P(6,column);
				KHP(row,column) = tmp;
			}
		}

		// if the covariance correction will result in a negative variance, then
		// the covariance matrix is unhealthy and must be corrected
		bool healthy = true;
		_fault_status.flags.bad_optflow_X = false;
		_fault_status.flags.bad_optflow_Y = false;

		for (int i = 0; i < _k_num_states; i++) {
			if (P(i,i) < KHP(i,i)) {
				// zero rows and columns
				P.uncorrelateCovarianceSetVariance<1>(i, 0.0f);

				//flag as unhealthy
				healthy = false;

				// update individual measurement health status
				if (obs_index == 0) {
					_fault_status.flags.bad_optflow_X = true;

				} else if (obs_index == 1) {
					_fault_status.flags.bad_optflow_Y = true;
				}
			}
		}

		// only apply covariance and state corrections if healthy
		if (healthy) {
			// apply the covariance corrections
			for (unsigned row = 0; row < _k_num_states; row++) {
				for (unsigned column = 0; column < _k_num_states; column++) {
					P(row,column) = P(row,column) - KHP(row,column);
				}
			}

			// correct the covariance matrix for gross errors
			fixCovarianceErrors(true);

			// apply the state corrections
			fuse(gain, _flow_innov[obs_index]);

			_time_last_of_fuse = _time_last_imu;
		}
	}
}

// calculate optical flow body angular rate compensation
// returns false if bias corrected body rate data is unavailable
bool Ekf::calcOptFlowBodyRateComp()
{
	// reset the accumulators if the time interval is too large
	if (_delta_time_of > 1.0f) {
		_imu_del_ang_of.setZero();
		_delta_time_of = 0.0f;
		return false;
	}

	const bool use_flow_sensor_gyro =  ISFINITE(_flow_sample_delayed.gyroXYZ(0)) && ISFINITE(_flow_sample_delayed.gyroXYZ(1)) && ISFINITE(_flow_sample_delayed.gyroXYZ(2));

	if (use_flow_sensor_gyro) {

		// if accumulation time differences are not excessive and accumulation time is adequate
		// compare the optical flow and and navigation rate data and calculate a bias error
		if ((fabsf(_delta_time_of - _flow_sample_delayed.dt) < 0.1f) && (_delta_time_of > FLT_EPSILON)) {

			const Vector3f reference_body_rate(_imu_del_ang_of * (1.0f / _delta_time_of));

			const Vector3f measured_body_rate(_flow_sample_delayed.gyroXYZ * (1.0f / _flow_sample_delayed.dt));

			// calculate the bias estimate using  a combined LPF and spike filter
			_flow_gyro_bias(0) = 0.99f * _flow_gyro_bias(0) + 0.01f * math::constrain((of_body_rate(0) - reference_body_rate(0)),
					     -0.1f, 0.1f);
			_flow_gyro_bias(1) = 0.99f * _flow_gyro_bias(1) + 0.01f * math::constrain((of_body_rate(1) - reference_body_rate(1)),
					     -0.1f, 0.1f);
			_flow_gyro_bias(2) = 0.99f * _flow_gyro_bias(2) + 0.01f * math::constrain((of_body_rate(2) - reference_body_rate(2)),
					     -0.1f, 0.1f);
		}

	} else {
		// Use the EKF gyro data if optical flow sensor gyro data is not available
		// for clarification of the sign see definition of flowSample and imuSample in common.h
		_flow_sample_delayed.gyroXYZ = - _imu_del_ang_of;
		_flow_gyro_bias.zero();
	}

	// reset the accumulators
	_imu_del_ang_of.setZero();
	_delta_time_of = 0.0f;
	return true;
}

// calculate the measurement variance for the optical flow sensor (rad/sec)^2
float Ekf::calcOptFlowMeasVar()
{
	// calculate the observation noise variance - scaling noise linearly across flow quality range
	const float R_LOS_best = fmaxf(_params.flow_noise, 0.05f);
	const float R_LOS_worst = fmaxf(_params.flow_noise_qual_min, 0.05f);

	// calculate a weighting that varies between 1 when flow quality is best and 0 when flow quality is worst
	float weighting = (255.0f - (float)_params.flow_qual_min);

	if (weighting >= 1.0f) {
		weighting = math::constrain(((float)_flow_sample_delayed.quality - (float)_params.flow_qual_min) / weighting, 0.0f,
					    1.0f);

	} else {
		weighting = 0.0f;
	}

	// take the weighted average of the observation noise for the best and wort flow quality
	const float R_LOS = sq(R_LOS_best * weighting + R_LOS_worst * (1.0f - weighting));

	return R_LOS;
}