WindEstimator.cpp

Go to the documentation of this file.

/****************************************************************************
 *
 *   Copyright (c) 2018 PX4 Development Team. All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in
 *    the documentation and/or other materials provided with the
 *    distribution.
 * 3. Neither the name PX4 nor the names of its contributors may be
 *    used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
 * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
 * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 *
 ****************************************************************************/

/**
 * @file WindEstimator.cpp
 * A wind and airspeed scale estimator.
 */

#include "WindEstimator.hpp"

bool
WindEstimator::initialise(const matrix::Vector3f &velI, const matrix::Vector2f &velIvar, const float tas_meas)
{
    // do no initialise if ground velocity is low
    // this should prevent the filter from initialising on the ground
    if (sqrtf(velI(0) * velI(0) + velI(1) * velI(1)) < 3.0f) {
        return false;
    }

    const float v_n = velI(0);
    const float v_e = velI(1);

    // estimate heading from ground velocity
    const float heading_est = atan2f(v_e, v_n);

    // initilaise wind states assuming zero side slip and horizontal flight
    _state(w_n) = velI(w_n) - tas_meas * cosf(heading_est);
    _state(w_e) = velI(w_e) - tas_meas * sinf(heading_est);
    _state(tas) = 1.0f;

    // compute jacobian of states wrt north/each earth velocity states and true airspeed measurement
    float L0 = v_e * v_e;
    float L1 = v_n * v_n;
    float L2 = L0 + L1;
    float L3 = tas_meas / (L2 * sqrtf(L2));
    float L4 = L3 * v_e * v_n + 1.0f;
    float L5 = 1.0f / sqrtf(L2);
    float L6 = -L5 * tas_meas;

    matrix::Matrix3f L;
    L.setZero();
    L(0, 0) = L4;
    L(0, 1) = L0 * L3 + L6;
    L(1, 0) = L1 * L3 + L6;
    L(1, 1) = L4;
    L(2, 2) = 1.0f;

    // get an estimate of the state covariance matrix given the estimated variance of ground velocity
    // and measured airspeed
    _P.setZero();
    _P(w_n, w_n) = velIvar(0);
    _P(w_e, w_e) = velIvar(1);
    _P(tas, tas) = 0.0001f;

    _P = L * _P * L.transpose();

    // reset the timestamp for measurement rejection
    _time_rejected_tas = 0;
    _time_rejected_beta = 0;

    _wind_estimator_reset = true;

    return true;
}

void
WindEstimator::update(uint64_t time_now)
{
    if (!_initialised) {
        return;
    }

    // set reset state to false (is set to true when initialise fuction is called later)
    _wind_estimator_reset = false;

    // run covariance prediction at 1Hz
    if (time_now - _time_last_update < 1000 * 1000 || _time_last_update == 0) {
        if (_time_last_update == 0) {
            _time_last_update = time_now;
        }

        return;
    }

    float dt = (float)(time_now - _time_last_update) * 1e-6f;
    _time_last_update = time_now;

    float q_w = _wind_p_var;
    float q_k_tas = _tas_scale_p_var;

    float SPP0 = dt * dt;
    float SPP1 = SPP0 * q_w;
    float SPP2 = SPP1 + _P(0, 1);

    matrix::Matrix3f P_next;

    P_next(0, 0) = SPP1 + _P(0, 0);
    P_next(0, 1) = SPP2;
    P_next(0, 2) = _P(0, 2);
    P_next(1, 0) = SPP2;
    P_next(1, 1) = SPP1 + _P(1, 1);
    P_next(1, 2) = _P(1, 2);
    P_next(2, 0) = _P(0, 2);
    P_next(2, 1) = _P(1, 2);
    P_next(2, 2) = SPP0 * q_k_tas + _P(2, 2);
    _P = P_next;
}

void
WindEstimator::fuse_airspeed(uint64_t time_now, const float true_airspeed, const matrix::Vector3f &velI,
                 const matrix::Vector2f &velIvar)
{
    matrix::Vector2f velIvar_constrained = { math::max(0.01f, velIvar(0)), math::max(0.01f, velIvar(1)) };

    if (!_initialised) {
        // try to initialise
        _initialised =  initialise(velI, velIvar_constrained, true_airspeed);
        return;
    }

    // don't fuse faster than 10Hz
    if (time_now - _time_last_airspeed_fuse < 100 * 1000) {
        return;
    }

    _time_last_airspeed_fuse = time_now;

    // assign helper variables
    const float v_n = velI(0);
    const float v_e = velI(1);
    const float v_d = velI(2);

    const float k_tas = _state(tas);

    // compute kalman gain K
    const float HH0 = sqrtf(v_d * v_d + (v_e - w_e) * (v_e - w_e) + (v_n - w_n) * (v_n - w_n));
    const float HH1 = k_tas / HH0;

    matrix::Matrix<float, 1, 3> H_tas;
    H_tas(0, 0) = HH1 * (-v_n + w_n);
    H_tas(0, 1) = HH1 * (-v_e + w_e);
    H_tas(0, 2) = HH0;

    matrix::Matrix<float, 3, 1> K = _P * H_tas.transpose();

    const matrix::Matrix<float, 1, 1> S = H_tas * _P * H_tas.transpose() + _tas_var;

    K /= S(0,0);
    // compute innovation
    const float airspeed_pred = _state(tas) * sqrtf((v_n - _state(w_n)) * (v_n - _state(w_n)) + (v_e - _state(w_e)) *
                    (v_e - _state(w_e)) + v_d * v_d);

    _tas_innov = true_airspeed - airspeed_pred;

    // innovation variance
    _tas_innov_var = S(0,0);

    bool reinit_filter = false;
    bool meas_is_rejected = false;

    meas_is_rejected = check_if_meas_is_rejected(time_now, _tas_innov, _tas_innov_var, _tas_gate, _time_rejected_tas, reinit_filter);

    reinit_filter |= _tas_innov_var < 0.0f;

    if (meas_is_rejected || reinit_filter) {
        if (reinit_filter) {
            _initialised =  initialise(velI, matrix::Vector2f(0.1f, 0.1f), true_airspeed);
        }

        // we either did a filter reset or the current measurement was rejected so do not fuse
        return;
    }

    // apply correction to state
    _state(w_n) += _tas_innov * K(0, 0);
    _state(w_e) += _tas_innov * K(1, 0);
    _state(tas) += _tas_innov * K(2, 0);

    // update covariance matrix
    _P = _P - K * H_tas * _P;

    run_sanity_checks();
}

void
WindEstimator::fuse_beta(uint64_t time_now, const matrix::Vector3f &velI, const matrix::Quatf &q_att)
{
    if (!_initialised) {
        _initialised =  initialise(velI, matrix::Vector2f(0.1f, 0.1f), velI.length());
        return;
    }

    // don't fuse faster than 10Hz
    if (time_now - _time_last_beta_fuse < 100 * 1000) {
        return;
    }

    _time_last_beta_fuse = time_now;

    const float v_n = velI(0);
    const float v_e = velI(1);
    const float v_d = velI(2);

    // compute sideslip observation vector
    float HB0 = 2.0f * q_att(0);
    float HB1 = HB0 * q_att(3);
    float HB2 = 2.0f * q_att(1);
    float HB3 = HB2 * q_att(2);
    float HB4 = v_e - w_e;
    float HB5 = HB1 + HB3;
    float HB6 = v_n - w_n;
    float HB7 = q_att(0) * q_att(0);
    float HB8 = q_att(3) * q_att(3);
    float HB9 = HB7 - HB8;
    float HB10 = q_att(1) * q_att(1);
    float HB11 = q_att(2) * q_att(2);
    float HB12 = HB10 - HB11;
    float HB13 = HB12 + HB9;
    float HB14 = HB13 * HB6 + HB4 * HB5 + v_d * (-HB0 * q_att(2) + HB2 * q_att(3));
    float HB15 = 1.0f / HB14;
    float HB16 = (HB4 * (-HB10 + HB11 + HB9) + HB6 * (-HB1 + HB3) + v_d * (HB0 * q_att(1) + 2.0f * q_att(2) * q_att(3))) /
             (HB14 * HB14);

    matrix::Matrix<float, 1, 3> H_beta;
    H_beta(0, 0) = HB13 * HB16 + HB15 * (HB1 - HB3);
    H_beta(0, 1) = HB15 * (HB12 - HB7 + HB8) + HB16 * HB5;
    H_beta(0, 2) = 0;

    // compute kalman gain
    matrix::Matrix<float, 3, 1> K = _P * H_beta.transpose();

    const matrix::Matrix<float, 1, 1> S = H_beta * _P * H_beta.transpose() + _beta_var;

    K /= S(0,0);

    // compute predicted side slip angle
    matrix::Vector3f rel_wind(velI(0) - _state(w_n), velI(1) - _state(w_e), velI(2));
    matrix::Dcmf R_body_to_earth(q_att);
    rel_wind = R_body_to_earth.transpose() * rel_wind;

    if (fabsf(rel_wind(0)) < 0.1f) {
        return;
    }

    // use small angle approximation, sin(x) = x for small x
    const float beta_pred = rel_wind(1) / rel_wind(0);

    _beta_innov = 0.0f - beta_pred;
    _beta_innov_var = S(0,0);

    bool reinit_filter = false;
    bool meas_is_rejected = false;

    meas_is_rejected = check_if_meas_is_rejected(time_now, _beta_innov, _beta_innov_var, _beta_gate, _time_rejected_beta,
               reinit_filter);

    reinit_filter |= _beta_innov_var < 0.0f;

    if (meas_is_rejected || reinit_filter) {
        if (reinit_filter) {
            _initialised =  initialise(velI, matrix::Vector2f(0.1f, 0.1f), velI.length());
        }

        // we either did a filter reset or the current measurement was rejected so do not fuse
        return;
    }

    // apply correction to state
    _state(w_n) += _beta_innov * K(0, 0);
    _state(w_e) += _beta_innov * K(1, 0);
    _state(tas) += _beta_innov * K(2, 0);

    // update covariance matrix
    _P = _P - K * H_beta * _P;

    run_sanity_checks();
}

void
WindEstimator::run_sanity_checks()
{
    for (unsigned i = 0; i < 3; i++) {
        if (_P(i, i) < 0.0f) {
            // ill-conditioned covariance matrix, reset filter
            _initialised = false;
            return;
        }

        // limit covariance diagonals if they grow too large
        if (i < 2) {
            _P(i, i) = _P(i, i) > 25.0f ? 25.0f : _P(i, i);

        } else if (i == 2) {
            _P(i, i) = _P(i, i) > 0.1f ? 0.1f : _P(i, i);
        }
    }

    if (!ISFINITE(_state(w_n)) || !ISFINITE(_state(w_e)) || !ISFINITE(_state(tas))) {
        _initialised = false;
        return;
    }

    // check if we should inhibit learning of airspeed scale factor and rather use a pre-set value.
    // airspeed scale factor errors arise from sensor installation which does not change and only needs
    // to be computed once for a perticular installation.
    if (_enforced_airspeed_scale < 0) {
        _state(tas) = math::max(0.0f, _state(tas));
    } else {
        _state(tas) = _enforced_airspeed_scale;
    }

    // attain symmetry
    for (unsigned row = 0; row < 3; row++) {
        for (unsigned column = 0; column < row; column++) {
            float tmp = (_P(row, column) + _P(column, row)) / 2;
            _P(row, column) = tmp;
            _P(column, row) = tmp;
        }
    }
}

bool
WindEstimator::check_if_meas_is_rejected(uint64_t time_now, float innov, float innov_var, uint8_t gate_size,
        uint64_t &time_meas_rejected, bool &reinit_filter)
{
    if (innov * innov > gate_size * gate_size * innov_var) {
        time_meas_rejected = time_meas_rejected == 0 ? time_now : time_meas_rejected;

    } else {
        time_meas_rejected = 0;
    }

    reinit_filter = time_now - time_meas_rejected > 5 * 1000 * 1000 && time_meas_rejected != 0;

    return time_meas_rejected != 0;
}