px4-firmware/EKF/airspeed_fusion.cpp

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/**
 * @file airspeed_fusion.cpp
 * airspeed fusion methods.
 *
 * @author Carl Olsson <carlolsson.co@gmail.com>
 * @author Roman Bast <bapstroman@gmail.com>
 * @author Paul Riseborough <p_riseborough@live.com.au>
 *
 */
#include "../ecl.h"
#include "ekf.h"
#include "mathlib.h"

void Ekf::fuseAirspeed()
{
	// Initialize variables
	float vn; // Velocity in north direction
	float ve; // Velocity in east direction
	float vd; // Velocity in downwards direction
	float vwn; // Wind speed in north direction
	float vwe; // Wind speed in east direction
	float v_tas_pred; // Predicted measurement
	float R_TAS = sq(math::constrain(_params.eas_noise, 0.5f, 5.0f) * math::constrain(_airspeed_sample_delayed.eas2tas, 0.9f,
			 10.0f)); // Variance for true airspeed measurement - (m/sec)^2
	float SH_TAS[3] = {}; // Varialbe used to optimise calculations of measurement jacobian
	float H_TAS[24] = {}; // Observation Jacobian
	float SK_TAS[2] = {}; // Varialbe used to optimise calculations of the Kalman gain vector
	float Kfusion[24] = {}; // Kalman gain vector

	// Copy required states to local variable names
	vn = _state.vel(0);
	ve = _state.vel(1);
	vd = _state.vel(2);
	vwn = _state.wind_vel(0);
	vwe = _state.wind_vel(1);

	// Calculate the predicted airspeed
	v_tas_pred = sqrtf((ve - vwe) * (ve - vwe) + (vn - vwn) * (vn - vwn) + vd * vd);

	// Perform fusion of True Airspeed measurement
	if (v_tas_pred > 1.0f) {
		// Calculate the observation jacobian
		// intermediate variable from algebraic optimisation
		SH_TAS[0] = 1.0f/v_tas_pred;
		SH_TAS[1] = (SH_TAS[0]*(2.0f*ve - 2.0f*vwe))*0.5f;
		SH_TAS[2] = (SH_TAS[0]*(2.0f*vn - 2.0f*vwn))*0.5f;

		for (uint8_t i = 0; i < _k_num_states; i++) { H_TAS[i] = 0.0f; }

		H_TAS[4] = SH_TAS[2];
		H_TAS[5] = SH_TAS[1];
		H_TAS[6] = vd*SH_TAS[0];
		H_TAS[22] = -SH_TAS[2];
		H_TAS[23] = -SH_TAS[1];

		// We don't want to update the innovation variance if the calculation is ill conditioned
		float _airspeed_innov_var_temp = (R_TAS + SH_TAS[2]*(P[4][4]*SH_TAS[2] + P[5][4]*SH_TAS[1] - P[22][4]*SH_TAS[2] - P[23][4]*SH_TAS[1] + P[6][4]*vd*SH_TAS[0]) + SH_TAS[1]*(P[4][5]*SH_TAS[2] + P[5][5]*SH_TAS[1] - P[22][5]*SH_TAS[2] - P[23][5]*SH_TAS[1] + P[6][5]*vd*SH_TAS[0]) - SH_TAS[2]*(P[4][22]*SH_TAS[2] + P[5][22]*SH_TAS[1] - P[22][22]*SH_TAS[2] - P[23][22]*SH_TAS[1] + P[6][22]*vd*SH_TAS[0]) - SH_TAS[1]*(P[4][23]*SH_TAS[2] + P[5][23]*SH_TAS[1] - P[22][23]*SH_TAS[2] - P[23][23]*SH_TAS[1] + P[6][23]*vd*SH_TAS[0]) + vd*SH_TAS[0]*(P[4][6]*SH_TAS[2] + P[5][6]*SH_TAS[1] - P[22][6]*SH_TAS[2] - P[23][6]*SH_TAS[1] + P[6][6]*vd*SH_TAS[0]));

		if (_airspeed_innov_var_temp >= R_TAS) { // Check for badly conditioned calculation
			SK_TAS[0] = 1.0f / _airspeed_innov_var_temp;
			_fault_status.flags.bad_airspeed = false;

		} else { // Reset the estimator covarinace matrix
			_fault_status.flags.bad_airspeed = true;
			initialiseCovariance();
			ECL_ERR("EKF airspeed fusion numerical error - covariance reset");
			return;
		}

		SK_TAS[1] = SH_TAS[1];

		Kfusion[0] = SK_TAS[0]*(P[0][4]*SH_TAS[2] - P[0][22]*SH_TAS[2] + P[0][5]*SK_TAS[1] - P[0][23]*SK_TAS[1] + P[0][6]*vd*SH_TAS[0]);
		Kfusion[1] = SK_TAS[0]*(P[1][4]*SH_TAS[2] - P[1][22]*SH_TAS[2] + P[1][5]*SK_TAS[1] - P[1][23]*SK_TAS[1] + P[1][6]*vd*SH_TAS[0]);
		Kfusion[2] = SK_TAS[0]*(P[2][4]*SH_TAS[2] - P[2][22]*SH_TAS[2] + P[2][5]*SK_TAS[1] - P[2][23]*SK_TAS[1] + P[2][6]*vd*SH_TAS[0]);
		Kfusion[3] = SK_TAS[0]*(P[3][4]*SH_TAS[2] - P[3][22]*SH_TAS[2] + P[3][5]*SK_TAS[1] - P[3][23]*SK_TAS[1] + P[3][6]*vd*SH_TAS[0]);
		Kfusion[4] = SK_TAS[0]*(P[4][4]*SH_TAS[2] - P[4][22]*SH_TAS[2] + P[4][5]*SK_TAS[1] - P[4][23]*SK_TAS[1] + P[4][6]*vd*SH_TAS[0]);
		Kfusion[5] = SK_TAS[0]*(P[5][4]*SH_TAS[2] - P[5][22]*SH_TAS[2] + P[5][5]*SK_TAS[1] - P[5][23]*SK_TAS[1] + P[5][6]*vd*SH_TAS[0]);
		Kfusion[6] = SK_TAS[0]*(P[6][4]*SH_TAS[2] - P[6][22]*SH_TAS[2] + P[6][5]*SK_TAS[1] - P[6][23]*SK_TAS[1] + P[6][6]*vd*SH_TAS[0]);
		Kfusion[7] = SK_TAS[0]*(P[7][4]*SH_TAS[2] - P[7][22]*SH_TAS[2] + P[7][5]*SK_TAS[1] - P[7][23]*SK_TAS[1] + P[7][6]*vd*SH_TAS[0]);
		Kfusion[8] = SK_TAS[0]*(P[8][4]*SH_TAS[2] - P[8][22]*SH_TAS[2] + P[8][5]*SK_TAS[1] - P[8][23]*SK_TAS[1] + P[8][6]*vd*SH_TAS[0]);
		Kfusion[9] = SK_TAS[0]*(P[9][4]*SH_TAS[2] - P[9][22]*SH_TAS[2] + P[9][5]*SK_TAS[1] - P[9][23]*SK_TAS[1] + P[9][6]*vd*SH_TAS[0]);
		Kfusion[10] = SK_TAS[0]*(P[10][4]*SH_TAS[2] - P[10][22]*SH_TAS[2] + P[10][5]*SK_TAS[1] - P[10][23]*SK_TAS[1] + P[10][6]*vd*SH_TAS[0]);
		Kfusion[11] = SK_TAS[0]*(P[11][4]*SH_TAS[2] - P[11][22]*SH_TAS[2] + P[11][5]*SK_TAS[1] - P[11][23]*SK_TAS[1] + P[11][6]*vd*SH_TAS[0]);
		Kfusion[12] = SK_TAS[0]*(P[12][4]*SH_TAS[2] - P[12][22]*SH_TAS[2] + P[12][5]*SK_TAS[1] - P[12][23]*SK_TAS[1] + P[12][6]*vd*SH_TAS[0]);
		Kfusion[13] = SK_TAS[0]*(P[13][4]*SH_TAS[2] - P[13][22]*SH_TAS[2] + P[13][5]*SK_TAS[1] - P[13][23]*SK_TAS[1] + P[13][6]*vd*SH_TAS[0]);
		Kfusion[14] = SK_TAS[0]*(P[14][4]*SH_TAS[2] - P[14][22]*SH_TAS[2] + P[14][5]*SK_TAS[1] - P[14][23]*SK_TAS[1] + P[14][6]*vd*SH_TAS[0]);
		Kfusion[15] = SK_TAS[0]*(P[15][4]*SH_TAS[2] - P[15][22]*SH_TAS[2] + P[15][5]*SK_TAS[1] - P[15][23]*SK_TAS[1] + P[15][6]*vd*SH_TAS[0]);
		Kfusion[16] = SK_TAS[0]*(P[16][4]*SH_TAS[2] - P[16][22]*SH_TAS[2] + P[16][5]*SK_TAS[1] - P[16][23]*SK_TAS[1] + P[16][6]*vd*SH_TAS[0]);
		Kfusion[17] = SK_TAS[0]*(P[17][4]*SH_TAS[2] - P[17][22]*SH_TAS[2] + P[17][5]*SK_TAS[1] - P[17][23]*SK_TAS[1] + P[17][6]*vd*SH_TAS[0]);
		Kfusion[18] = SK_TAS[0]*(P[18][4]*SH_TAS[2] - P[18][22]*SH_TAS[2] + P[18][5]*SK_TAS[1] - P[18][23]*SK_TAS[1] + P[18][6]*vd*SH_TAS[0]);
		Kfusion[19] = SK_TAS[0]*(P[19][4]*SH_TAS[2] - P[19][22]*SH_TAS[2] + P[19][5]*SK_TAS[1] - P[19][23]*SK_TAS[1] + P[19][6]*vd*SH_TAS[0]);
		Kfusion[20] = SK_TAS[0]*(P[20][4]*SH_TAS[2] - P[20][22]*SH_TAS[2] + P[20][5]*SK_TAS[1] - P[20][23]*SK_TAS[1] + P[20][6]*vd*SH_TAS[0]);
		Kfusion[21] = SK_TAS[0]*(P[21][4]*SH_TAS[2] - P[21][22]*SH_TAS[2] + P[21][5]*SK_TAS[1] - P[21][23]*SK_TAS[1] + P[21][6]*vd*SH_TAS[0]);
		Kfusion[22] = SK_TAS[0]*(P[22][4]*SH_TAS[2] - P[22][22]*SH_TAS[2] + P[22][5]*SK_TAS[1] - P[22][23]*SK_TAS[1] + P[22][6]*vd*SH_TAS[0]);
		Kfusion[23] = SK_TAS[0]*(P[23][4]*SH_TAS[2] - P[23][22]*SH_TAS[2] + P[23][5]*SK_TAS[1] - P[23][23]*SK_TAS[1] + P[23][6]*vd*SH_TAS[0]);


		// Calculate measurement innovation
		_airspeed_innov = v_tas_pred -
				  _airspeed_sample_delayed.true_airspeed;

		// Calculate the innovation variance
		_airspeed_innov_var = 1.0f / SK_TAS[0];

		// Compute the ratio of innovation to gate size
		_tas_test_ratio = sq(_airspeed_innov) / (sq(fmaxf(_params.tas_innov_gate, 1.0f)) * _airspeed_innov_var);

		// If the innovation consistency check fails then don't fuse the sample and indicate bad airspeed health
		if (_tas_test_ratio > 1.0f) {
			_innov_check_fail_status.flags.reject_airspeed = true;
			return;
		}
		else {
			_innov_check_fail_status.flags.reject_airspeed = false;
		}

		// Airspeed measurement sample has passed check so record it
		_time_last_arsp_fuse = _time_last_imu;

		// update covariance matrix via Pnew = (I - KH)P = P - KHP
		for (unsigned row = 0; row < _k_num_states; row++) {
			for (unsigned column = 0; column < _k_num_states; column++) { // Here it will be a lot of zeros, should optimize that...
				KH[row][column] = Kfusion[row] * H_TAS[column];
			}
		}

		for (unsigned row = 0; row < _k_num_states; row++) {
			for (unsigned column = 0; column < _k_num_states; column++) {
				for (unsigned i = 0; i < _k_num_states; i++) { // Check if this is correct matrix multiplication!
					KHP[row][column] += KH[row][i] * P[i][column];
				}
			}
		}

		// if the covariance correction will result in a negative variance, then
		// the covariance marix is unhealthy and must be corrected
		bool healthy = true;
		_fault_status.flags.bad_airspeed = false;
		for (int i = 0; i < _k_num_states; i++) {
			if (P[i][i] < KHP[i][i]) {
				// zero rows and columns
				zeroRows(P,i,i);
				zeroCols(P,i,i);

				//flag as unhealthy
				healthy = false;

				// update individual measurement health status
				_fault_status.flags.bad_airspeed = true;

			}
		}

		// only apply covariance and state corrrections 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 marix for gross errors
			fixCovarianceErrors();

			// apply the state corrections
			fuse(Kfusion, _airspeed_innov);

		}
	}
}