gps_yaw_fusion.cpp

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/**
 * @file gps_yaw_fusion.cpp
 * Definition of functions required to use yaw obtained from GPS dual antenna measurements.
 *
 * @author Paul Riseborough <p_riseborough@live.com.au>
 *
 */

#include "ekf.h"

#include <ecl.h>
#include <mathlib/mathlib.h>
#include <cstdlib>

void Ekf::fuseGpsAntYaw()
{
    // assign intermediate state variables
    float q0 = _state.quat_nominal(0);
    float q1 = _state.quat_nominal(1);
    float q2 = _state.quat_nominal(2);
    float q3 = _state.quat_nominal(3);

    float R_YAW = 1.0f;
    float predicted_hdg;
    float H_YAW[4];
    float measured_hdg;

    // check if data has been set to NAN indicating no measurement
    if (ISFINITE(_gps_sample_delayed.yaw)) {
        // calculate the observed yaw angle of antenna array, converting a from body to antenna yaw measurement
        measured_hdg = _gps_sample_delayed.yaw + _gps_yaw_offset;

        // define the predicted antenna array vector and rotate into earth frame
        Vector3f ant_vec_bf = {cosf(_gps_yaw_offset), sinf(_gps_yaw_offset), 0.0f};
        Vector3f ant_vec_ef = _R_to_earth * ant_vec_bf;

        // check if antenna array vector is within 30 degrees of vertical and therefore unable to provide a reliable heading
        if (fabsf(ant_vec_ef(2)) > cosf(math::radians(30.0f)))  {
            return;
        }

        // calculate predicted antenna yaw angle
        predicted_hdg =  atan2f(ant_vec_ef(1),ant_vec_ef(0));

        // calculate observation jacobian
        float t2 = sinf(_gps_yaw_offset);
        float t3 = cosf(_gps_yaw_offset);
        float t4 = q0*q3*2.0f;
        float t5 = q0*q0;
        float t6 = q1*q1;
        float t7 = q2*q2;
        float t8 = q3*q3;
        float t9 = q1*q2*2.0f;
        float t10 = t5+t6-t7-t8;
        float t11 = t3*t10;
        float t12 = t4+t9;
        float t13 = t3*t12;
        float t14 = t5-t6+t7-t8;
        float t15 = t2*t14;
        float t16 = t13+t15;
        float t17 = t4-t9;
        float t19 = t2*t17;
        float t20 = t11-t19;
        float t18 = (t20*t20);
        if (t18 < 1e-6f) {
            return;
        }
        t18 = 1.0f / t18;
        float t21 = t16*t16;
        float t22 = sq(t11-t19);
        if (t22 < 1e-6f) {
            return;
        }
        t22 = 1.0f/t22;
        float t23 = q1*t3*2.0f;
        float t24 = q2*t2*2.0f;
        float t25 = t23+t24;
        float t26 = 1.0f/t20;
        float t27 = q1*t2*2.0f;
        float t28 = t21*t22;
        float t29 = t28+1.0f;
        if (fabsf(t29) < 1e-6f) {
            return;
        }
        float t30 = 1.0f/t29;
        float t31 = q0*t3*2.0f;
        float t32 = t31-q3*t2*2.0f;
        float t33 = q3*t3*2.0f;
        float t34 = q0*t2*2.0f;
        float t35 = t33+t34;

        H_YAW[0] = (t35/(t11-t2*(t4-q1*q2*2.0f))-t16*t18*t32)/(t18*t21+1.0f);
        H_YAW[1] = -t30*(t26*(t27-q2*t3*2.0f)+t16*t22*t25);
        H_YAW[2] = t30*(t25*t26-t16*t22*(t27-q2*t3*2.0f));
        H_YAW[3] = t30*(t26*t32+t16*t22*t35);

        // using magnetic heading tuning parameter
        R_YAW = sq(fmaxf(_params.mag_heading_noise, 1.0e-2f));

    } else {
        // there is nothing to fuse
        return;
    }

    // wrap the heading to the interval between +-pi
    measured_hdg = wrap_pi(measured_hdg);

    // calculate the innovation and define the innovation gate
    float innov_gate = math::max(_params.heading_innov_gate, 1.0f);
    _heading_innov = predicted_hdg - measured_hdg;

    // wrap the innovation to the interval between +-pi
    _heading_innov = wrap_pi(_heading_innov);

    // Calculate innovation variance and Kalman gains, taking advantage of the fact that only the first 3 elements in H are non zero
    // calculate the innovation variance
    float PH[4];
    _heading_innov_var = R_YAW;

    for (unsigned row = 0; row <= 3; row++) {
        PH[row] = 0.0f;

        for (uint8_t col = 0; col <= 3; col++) {
            PH[row] += P[row][col] * H_YAW[col];
        }

        _heading_innov_var += H_YAW[row] * PH[row];
    }

    float heading_innov_var_inv;

    // check if the innovation variance calculation is badly conditioned
    if (_heading_innov_var >= R_YAW) {
        // the innovation variance contribution from the state covariances is not negative, no fault
        _fault_status.flags.bad_hdg = false;
        heading_innov_var_inv = 1.0f / _heading_innov_var;

    } else {
        // the innovation variance contribution from the state covariances is negative which means the covariance matrix is badly conditioned
        _fault_status.flags.bad_hdg = true;

        // we reinitialise the covariance matrix and abort this fusion step
        initialiseCovariance();
        ECL_ERR_TIMESTAMPED("EKF GPS yaw fusion numerical error - covariance reset");
        return;
    }

    // calculate the Kalman gains
    // only calculate gains for states we are using
    float Kfusion[_k_num_states] = {};

    for (uint8_t row = 0; row <= 15; row++) {
        Kfusion[row] = 0.0f;

        for (uint8_t col = 0; col <= 3; col++) {
            Kfusion[row] += P[row][col] * H_YAW[col];
        }

        Kfusion[row] *= heading_innov_var_inv;
    }

    if (_control_status.flags.wind) {
        for (uint8_t row = 22; row <= 23; row++) {
            Kfusion[row] = 0.0f;

            for (uint8_t col = 0; col <= 3; col++) {
                Kfusion[row] += P[row][col] * H_YAW[col];
            }

            Kfusion[row] *= heading_innov_var_inv;
        }
    }

    // innovation test ratio
    _yaw_test_ratio = sq(_heading_innov) / (sq(innov_gate) * _heading_innov_var);

    // we are no longer using 3-axis fusion so set the reported test levels to zero
    memset(_mag_test_ratio, 0, sizeof(_mag_test_ratio));

    // set the magnetometer unhealthy if the test fails
    if (_yaw_test_ratio > 1.0f) {
        _innov_check_fail_status.flags.reject_yaw = true;

        // if we are in air we don't want to fuse the measurement
        // we allow to use it when on the ground because the large innovation could be caused
        // by interference or a large initial gyro bias
        if (_control_status.flags.in_air) {
            return;

        } else {
            // constrain the innovation to the maximum set by the gate
            float gate_limit = sqrtf((sq(innov_gate) * _heading_innov_var));
            _heading_innov = math::constrain(_heading_innov, -gate_limit, gate_limit);
        }

    } else {
        _innov_check_fail_status.flags.reject_yaw = false;
    }

    // apply covariance correction via P_new = (I -K*H)*P
    // first calculate expression for KHP
    // then calculate P - KHP
    float KHP[_k_num_states][_k_num_states];
    float KH[4];

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

        KH[0] = Kfusion[row] * H_YAW[0];
        KH[1] = Kfusion[row] * H_YAW[1];
        KH[2] = Kfusion[row] * H_YAW[2];
        KH[3] = Kfusion[row] * H_YAW[3];

        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];
            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_hdg = 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_hdg = 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();

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

    }
}

bool Ekf::resetGpsAntYaw()
{
    // check if data has been set to NAN indicating no measurement
    if (ISFINITE(_gps_sample_delayed.yaw)) {

        // define the predicted antenna array vector and rotate into earth frame
        Vector3f ant_vec_bf = {cosf(_gps_yaw_offset), sinf(_gps_yaw_offset), 0.0f};
        Vector3f ant_vec_ef = _R_to_earth * ant_vec_bf;

        // check if antenna array vector is within 30 degrees of vertical and therefore unable to provide a reliable heading
        if (fabsf(ant_vec_ef(2)) > cosf(math::radians(30.0f)))  {
            return false;
        }

        float predicted_yaw =  atan2f(ant_vec_ef(1),ant_vec_ef(0));

        // get measurement and correct for antenna array yaw offset
        float measured_yaw = _gps_sample_delayed.yaw + _gps_yaw_offset;

        // calculate the amount the yaw needs to be rotated by
        float yaw_delta = wrap_pi(measured_yaw - predicted_yaw);

        // save a copy of the quaternion state for later use in calculating the amount of reset change
        Quatf quat_before_reset = _state.quat_nominal;
        Quatf quat_after_reset = _state.quat_nominal;

        // obtain the yaw angle using the best conditioned from either a Tait-Bryan 321 or 312 sequence
        // to avoid gimbal lock
        if (fabsf(_R_to_earth(2, 0)) < fabsf(_R_to_earth(2, 1))) {
            // get the roll, pitch, yaw estimates from the quaternion states using a 321 Tait-Bryan rotation sequence
            Quatf q_init(_state.quat_nominal);
            Eulerf euler_init(q_init);

            // correct the yaw angle
            euler_init(2) += yaw_delta;
            euler_init(2) = wrap_pi(euler_init(2));

            // update the quaternions
            quat_after_reset = Quatf(euler_init);

        } else {
            // Calculate the 312 Tait-Bryan sequence euler angles that rotate from earth to body frame
            // PX4 math library does not support this so are using equations from
            // http://www.atacolorado.com/eulersequences.doc
            Vector3f euler312;
            euler312(0) = atan2f(-_R_to_earth(0, 1), _R_to_earth(1, 1));  // first rotation (yaw)
            euler312(1) = asinf(_R_to_earth(2, 1)); // second rotation (roll)
            euler312(2) = atan2f(-_R_to_earth(2, 0), _R_to_earth(2, 2));  // third rotation (pitch)

            // correct the yaw angle
            euler312(0) += yaw_delta;
            euler312(0) = wrap_pi(euler312(0));

            // Calculate the body to earth frame rotation matrix from the corrected euler angles
            float c2 = cosf(euler312(2));
            float s2 = sinf(euler312(2));
            float s1 = sinf(euler312(1));
            float c1 = cosf(euler312(1));
            float s0 = sinf(euler312(0));
            float c0 = cosf(euler312(0));

            Dcmf R_to_earth;
            R_to_earth(0, 0) = c0 * c2 - s0 * s1 * s2;
            R_to_earth(1, 1) = c0 * c1;
            R_to_earth(2, 2) = c2 * c1;
            R_to_earth(0, 1) = -c1 * s0;
            R_to_earth(0, 2) = s2 * c0 + c2 * s1 * s0;
            R_to_earth(1, 0) = c2 * s0 + s2 * s1 * c0;
            R_to_earth(1, 2) = s0 * s2 - s1 * c0 * c2;
            R_to_earth(2, 0) = -s2 * c1;
            R_to_earth(2, 1) = s1;

            // update the quaternions
            quat_after_reset = Quatf(R_to_earth);
        }

        // calculate the amount that the quaternion has changed by
        Quatf q_error =  _state.quat_nominal * quat_before_reset.inversed();
        q_error.normalize();

        // convert the quaternion delta to a delta angle
        Vector3f delta_ang_error;
        float scalar;

        if (q_error(0) >= 0.0f) {
            scalar = -2.0f;

        } else {
            scalar = 2.0f;
        }

        delta_ang_error(0) = scalar * q_error(1);
        delta_ang_error(1) = scalar * q_error(2);
        delta_ang_error(2) = scalar * q_error(3);

        // update the quaternion state estimates and corresponding covariances only if the change in angle has been large or the yaw is not yet aligned
        if (delta_ang_error.norm() > math::radians(15.0f) || !_control_status.flags.yaw_align) {
            // update quaternion states
            _state.quat_nominal = quat_after_reset;
            uncorrelateQuatStates();

            // record the state change
            _state_reset_status.quat_change = q_error;

            // update transformation matrix from body to world frame using the current estimate
            _R_to_earth = Dcmf(_state.quat_nominal);

            // reset the rotation from the EV to EKF frame of reference if it is being used
            if ((_params.fusion_mode & MASK_ROTATE_EV) && (_params.fusion_mode & MASK_USE_EVPOS)) {
                resetExtVisRotMat();
            }

            // update the yaw angle variance using the variance of the measurement
            increaseQuatYawErrVariance(sq(fmaxf(_params.mag_heading_noise, 1.0e-2f)));

            // add the reset amount to the output observer buffered data
            for (uint8_t i = 0; i < _output_buffer.get_length(); i++) {
                _output_buffer[i].quat_nominal = _state_reset_status.quat_change * _output_buffer[i].quat_nominal;
            }

            // apply the change in attitude quaternion to our newest quaternion estimate
            // which was already taken out from the output buffer
            _output_new.quat_nominal = _state_reset_status.quat_change * _output_new.quat_nominal;

            // capture the reset event
            _state_reset_status.quat_counter++;

        }

        return true;
    }

    return false;
}