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px4-firmware/EKF/ekf.cpp

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/****************************************************************************
*
* Copyright (c) 2015 Estimation and Control Library (ECL). 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 ECL 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 ekf.cpp
* Core functions for ekf attitude and position estimator.
*
* @author Roman Bast <bapstroman@gmail.com>
* @author Paul Riseborough <p_riseborough@live.com.au>
*/
#include "ekf.h"
#include "mathlib.h"
#ifndef __PX4_QURT
#if defined(__cplusplus) && !defined(__PX4_NUTTX)
#include <cmath>
#define ISFINITE(x) std::isfinite(x)
#else
#define ISFINITE(x) isfinite(x)
#endif
#endif
#if defined(__PX4_QURT)
// Missing math.h defines
#define ISFINITE(x) __builtin_isfinite(x)
#endif
Ekf::Ekf():
_filter_initialised(false),
_earth_rate_initialised(false),
_fuse_height(false),
_fuse_pos(false),
_fuse_hor_vel(false),
_fuse_vert_vel(false),
_fuse_flow(false),
_fuse_hagl_data(false),
_time_last_fake_gps(0),
_time_last_pos_fuse(0),
_time_last_vel_fuse(0),
_time_last_hgt_fuse(0),
_time_last_of_fuse(0),
_time_last_arsp_fuse(0),
_last_disarmed_posD(0.0f),
_last_dt_overrun(0.0f),
_airspeed_innov(0.0f),
_airspeed_innov_var(0.0f),
_heading_innov(0.0f),
_heading_innov_var(0.0f),
_delta_time_of(0.0f),
_mag_declination(0.0f),
_gpsDriftVelN(0.0f),
_gpsDriftVelE(0.0f),
_gps_drift_velD(0.0f),
_gps_velD_diff_filt(0.0f),
_gps_velN_filt(0.0f),
_gps_velE_filt(0.0f),
_last_gps_fail_us(0),
_last_gps_origin_time_us(0),
_gps_alt_ref(0.0f),
_hgt_counter(0),
_rng_filt_state(0.0f),
_mag_counter(0),
_time_last_mag(0),
_hgt_sensor_offset(0.0f),
_terrain_vpos(0.0f),
_terrain_var(1.e4f),
_hagl_innov(0.0f),
_hagl_innov_var(0.0f),
_time_last_hagl_fuse(0),
_baro_hgt_faulty(false),
_gps_hgt_faulty(false),
_rng_hgt_faulty(false),
_baro_hgt_offset(0.0f),
_vert_pos_reset_delta(0.0f),
_time_vert_pos_reset(0),
_vert_vel_reset_delta(0.0f),
_time_vert_vel_reset(0),
_time_bad_vert_accel(0)
{
_state = {};
_last_known_posNE.setZero();
_earth_rate_NED.setZero();
_R_to_earth = matrix::Dcm<float>();
memset(_vel_pos_innov, 0, sizeof(_vel_pos_innov));
memset(_mag_innov, 0, sizeof(_mag_innov));
memset(_flow_innov, 0, sizeof(_flow_innov));
memset(_vel_pos_innov_var, 0, sizeof(_vel_pos_innov_var));
memset(_mag_innov_var, 0, sizeof(_mag_innov_var));
memset(_flow_innov_var, 0, sizeof(_flow_innov_var));
_delta_angle_corr.setZero();
_last_known_posNE.setZero();
_imu_down_sampled = {};
_q_down_sampled.setZero();
_mag_filt_state = {};
_delVel_sum = {};
_flow_gyro_bias = {};
_imu_del_ang_of = {};
_gps_check_fail_status.value = 0;
}
Ekf::~Ekf()
{
}
bool Ekf::init(uint64_t timestamp)
{
bool ret = initialise_interface(timestamp);
_state.vel.setZero();
_state.pos.setZero();
_state.gyro_bias.setZero();
_state.accel_bias.setZero();
_state.mag_I.setZero();
_state.mag_B.setZero();
_state.wind_vel.setZero();
_state.quat_nominal.setZero();
_state.quat_nominal(0) = 1.0f;
_output_new.vel.setZero();
_output_new.pos.setZero();
_output_new.quat_nominal = matrix::Quaternion<float>();
_delta_angle_corr.setZero();
_imu_down_sampled.delta_ang.setZero();
_imu_down_sampled.delta_vel.setZero();
_imu_down_sampled.delta_ang_dt = 0.0f;
_imu_down_sampled.delta_vel_dt = 0.0f;
_imu_down_sampled.time_us = timestamp;
_q_down_sampled(0) = 1.0f;
_q_down_sampled(1) = 0.0f;
_q_down_sampled(2) = 0.0f;
_q_down_sampled(3) = 0.0f;
_imu_updated = false;
_NED_origin_initialised = false;
_gps_speed_valid = false;
_mag_healthy = false;
_filter_initialised = false;
_terrain_initialised = false;
_control_status.value = 0;
_control_status_prev.value = 0;
_dt_ekf_avg = 0.001f * (float)(FILTER_UPDATE_PERRIOD_MS);
return ret;
}
bool Ekf::update()
{
if (!_filter_initialised) {
_filter_initialised = initialiseFilter();
if (!_filter_initialised) {
return false;
}
}
// Only run the filter if IMU data in the buffer has been updated
if (_imu_updated) {
// perform state and covariance prediction for the main filter
predictState();
predictCovariance();
// perform state and variance prediction for the terrain estimator
if (!_terrain_initialised) {
_terrain_initialised = initHagl();
} else {
predictHagl();
}
// control logic
controlFusionModes();
// measurement updates
// Fuse magnetometer data using the selected fuson method and only if angular alignment is complete
if (_mag_buffer.pop_first_older_than(_imu_sample_delayed.time_us, &_mag_sample_delayed)) {
if (_control_status.flags.mag_3D && _control_status.flags.yaw_align) {
fuseMag();
if (_control_status.flags.mag_dec) {
fuseDeclination();
}
} else if (_control_status.flags.mag_hdg && _control_status.flags.yaw_align) {
// fusion of a Euler yaw angle from either a 321 or 312 rotation sequence
fuseHeading();
} else {
// do no fusion at all
}
}
// determine if range finder data has fallen behind the fusin time horizon fuse it if we are
// not tilted too much to use it
if (_range_buffer.pop_first_older_than(_imu_sample_delayed.time_us, &_range_sample_delayed)
&& (_R_to_earth(2, 2) > 0.7071f)) {
// correct the range data for position offset relative to the IMU
Vector3f pos_offset_body = _params.rng_pos_body - _params.imu_pos_body;
Vector3f pos_offset_earth = _R_to_earth * pos_offset_body;
_range_sample_delayed.rng += pos_offset_earth(2) / _R_to_earth(2, 2);
// if we have range data we always try to estimate terrain height
_fuse_hagl_data = true;
// only use range finder as a height observation in the main filter if specifically enabled
if (_control_status.flags.rng_hgt) {
_fuse_height = true;
}
} else if ((_time_last_imu - _time_last_hgt_fuse) > 2 * RNG_MAX_INTERVAL && _control_status.flags.rng_hgt) {
// If we are supposed to be using range finder data as the primary height sensor, have missed or rejected measurements
// and are on the ground, then synthesise a measurement at the expected on ground value
if (!_control_status.flags.in_air) {
_range_sample_delayed.rng = _params.rng_gnd_clearance;
_range_sample_delayed.time_us = _imu_sample_delayed.time_us;
}
_fuse_height = true;
}
// determine if baro data has fallen behind the fuson time horizon and fuse it in the main filter if enabled
uint64_t last_baro_time_us = _baro_sample_delayed.time_us;
if (_baro_buffer.pop_first_older_than(_imu_sample_delayed.time_us, &_baro_sample_delayed)) {
if (_control_status.flags.baro_hgt) {
_fuse_height = true;
} else {
// calculate a filtered offset between the baro origin and local NED origin if we are not using the baro as a height reference
float local_time_step = 1e-6f*(float)(_baro_sample_delayed.time_us - last_baro_time_us);
local_time_step = math::constrain(local_time_step,0.0f,1.0f);
last_baro_time_us = _baro_sample_delayed.time_us;
float offset_rate_correction = 0.1f * (_baro_sample_delayed.hgt - _hgt_sensor_offset) + _state.pos(2) - _baro_hgt_offset;
_baro_hgt_offset += local_time_step * math::constrain(offset_rate_correction, -0.1f, 0.1f);
}
}
// If we are using GPS aiding and data has fallen behind the fusion time horizon then fuse it
if (_gps_buffer.pop_first_older_than(_imu_sample_delayed.time_us, &_gps_sample_delayed)) {
// Only use GPS data for position and velocity aiding if enabled
if (_control_status.flags.gps) {
_fuse_pos = true;
_fuse_vert_vel = true;
_fuse_hor_vel = true;
// correct velocity for offset relative to IMU
Vector3f ang_rate = _imu_sample_delayed.delta_ang * (1.0f/_imu_sample_delayed.delta_ang_dt);
Vector3f pos_offset_body = _params.gps_pos_body - _params.imu_pos_body;
Vector3f vel_offset_body = cross_product(ang_rate,pos_offset_body);
Vector3f vel_offset_earth = _R_to_earth * vel_offset_body;
_gps_sample_delayed.vel -= vel_offset_earth;
// correct position and height for offset relative to IMU
Vector3f pos_offset_earth = _R_to_earth * pos_offset_body;
_gps_sample_delayed.pos(0) -= pos_offset_earth(0);
_gps_sample_delayed.pos(1) -= pos_offset_earth(1);
_gps_sample_delayed.hgt += pos_offset_earth(2);
}
// only use gps height observation in the main filter if specifically enabled
if (_control_status.flags.gps_hgt) {
_fuse_height = true;
}
}
// If we are using external vision aiding and data has fallen behind the fusion time horizon then fuse it
if (_ext_vision_buffer.pop_first_older_than(_imu_sample_delayed.time_us, &_ev_sample_delayed)) {
// use external vision posiiton and height observations
if (_control_status.flags.ev_pos) {
_fuse_pos = true;
_fuse_height = true;
// correct position and height for offset relative to IMU
Vector3f pos_offset_body = _params.ev_pos_body - _params.imu_pos_body;
Vector3f pos_offset_earth = _R_to_earth * pos_offset_body;
_ev_sample_delayed.posNED(0) -= pos_offset_earth(0);
_ev_sample_delayed.posNED(1) -= pos_offset_earth(1);
_ev_sample_delayed.posNED(2) -= pos_offset_earth(2);
}
// use external vision yaw observation
if (_control_status.flags.ev_yaw) {
fuseHeading();
}
}
// If we are using optical flow aiding and data has fallen behind the fusion time horizon, then fuse it
if (_flow_buffer.pop_first_older_than(_imu_sample_delayed.time_us, &_flow_sample_delayed)
&& _control_status.flags.opt_flow && (_time_last_imu - _time_last_optflow) < 2e5
&& (_R_to_earth(2, 2) > 0.7071f)) {
_fuse_flow = true;
}
// if we aren't doing any aiding, fake GPS measurements at the last known position to constrain drift
// Coincide fake measurements with baro data for efficiency with a minimum fusion rate of 5Hz
if (!_control_status.flags.gps && !_control_status.flags.opt_flow
&& ((_time_last_imu - _time_last_fake_gps > 2e5) || _fuse_height)) {
_fuse_pos = true;
_time_last_fake_gps = _time_last_imu;
}
// fuse available range finder data into a terrain height estimator if it has been initialised
if (_fuse_hagl_data && _terrain_initialised) {
fuseHagl();
_fuse_hagl_data = false;
}
// Fuse available NED velocity and position data into the main filter
if (_fuse_height || _fuse_pos || _fuse_hor_vel || _fuse_vert_vel) {
fuseVelPosHeight();
_fuse_hor_vel = _fuse_vert_vel = _fuse_pos = _fuse_height = false;
}
// Update optical flow bias estimates
calcOptFlowBias();
// Fuse optical flow LOS rate observations into the main filter
if (_fuse_flow) {
fuseOptFlow();
_last_known_posNE(0) = _state.pos(0);
_last_known_posNE(1) = _state.pos(1);
_fuse_flow = false;
}
// TODO This is just to get the logic inside but we will only start fusion once we tested this again
//if (_airspeed_buffer.pop_first_older_than(_imu_sample_delayed.time_us, &_airspeed_sample_delayed)) {
if (false) {
fuseAirspeed();
}
}
// the output observer always runs
calculateOutputStates();
// check for NaN or inf on attitude states
if (!ISFINITE(_state.quat_nominal(0)) || !ISFINITE(_output_new.quat_nominal(0))) {
return false;
}
// We don't have valid data to output until tilt and yaw alignment is complete
if (_control_status.flags.tilt_align && _control_status.flags.yaw_align) {
return true;
} else {
return false;
}
}
bool Ekf::initialiseFilter(void)
{
// Keep accumulating measurements until we have a minimum of 10 samples for the baro and magnetoemter
// Sum the IMU delta angle measurements
imuSample imu_init = _imu_buffer.get_newest();
_delVel_sum += imu_init.delta_vel;
// Sum the magnetometer measurements
if (_mag_buffer.pop_first_older_than(_imu_sample_delayed.time_us, &_mag_sample_delayed)) {
if (_mag_counter == 0 && _mag_sample_delayed.time_us !=0) {
// initialise the filter states and counter when we start getting valid data from the buffer
_mag_filt_state = _mag_sample_delayed.mag;
_mag_counter = 1;
} else if (_mag_counter != 0) {
// increment the sample count and apply a LPF to the measurement
_mag_counter ++;
_mag_filt_state = _mag_filt_state * 0.9f + _mag_sample_delayed.mag * 0.1f;
}
}
// set the default height source from the adjustable parameter
if (_hgt_counter == 0) {
if (_params.fusion_mode & MASK_USE_EVPOS) {
_primary_hgt_source = VDIST_SENSOR_EV;
} else {
_primary_hgt_source = _params.vdist_sensor_type;
}
}
if (_primary_hgt_source == VDIST_SENSOR_RANGE) {
if (_range_buffer.pop_first_older_than(_imu_sample_delayed.time_us, &_range_sample_delayed)) {
if (_hgt_counter == 0 && _range_sample_delayed.time_us != 0) {
// initialise the filter states and counter when we start getting valid data from the buffer
_control_status.flags.baro_hgt = false;
_control_status.flags.gps_hgt = false;
_control_status.flags.rng_hgt = true;
_rng_filt_state = _range_sample_delayed.rng;
_hgt_counter = 1;
} else if (_hgt_counter != 0) {
// increment the sample count and apply a LPF to the measurement
_hgt_counter ++;
_rng_filt_state = 0.9f * _rng_filt_state + 0.1f * _range_sample_delayed.rng;
}
}
} else if (_primary_hgt_source == VDIST_SENSOR_BARO || _primary_hgt_source == VDIST_SENSOR_GPS || _primary_hgt_source == VDIST_SENSOR_EV) {
// if the user parameter specifies use of GPS for height we use baro height initially and switch to GPS
// later when it passes checks.
if (_baro_buffer.pop_first_older_than(_imu_sample_delayed.time_us, &_baro_sample_delayed)) {
if (_hgt_counter == 0 && _baro_sample_delayed.time_us != 0) {
// initialise the filter states and counter when we start getting valid data from the buffer
_control_status.flags.baro_hgt = true;
_control_status.flags.gps_hgt = false;
_control_status.flags.rng_hgt = false;
_baro_hgt_offset = _baro_sample_delayed.hgt;
_hgt_counter = 1;
} else if (_hgt_counter != 0) {
// increment the sample count and apply a LPF to the measurement
_hgt_counter ++;
_baro_hgt_offset = 0.9f * _baro_hgt_offset + 0.1f * _baro_sample_delayed.hgt;
}
}
} else {
return false;
}
// check to see if we have enough measurements and return false if not
if (_hgt_counter <= 10 || _mag_counter <= 10) {
return false;
} else {
// reset variables that are shared with post alignment GPS checks
_gps_drift_velD = 0.0f;
_gps_alt_ref = 0.0f;
// Zero all of the states
_state.vel.setZero();
_state.pos.setZero();
_state.gyro_bias.setZero();
_state.accel_bias.setZero();
_state.mag_I.setZero();
_state.mag_B.setZero();
_state.wind_vel.setZero();
// get initial roll and pitch estimate from delta velocity vector, assuming vehicle is static
float pitch = 0.0f;
float roll = 0.0f;
if (_delVel_sum.norm() > 0.001f) {
_delVel_sum.normalize();
pitch = asinf(_delVel_sum(0));
roll = atan2f(-_delVel_sum(1), -_delVel_sum(2));
} else {
return false;
}
// calculate initial tilt alignment
matrix::Euler<float> euler_init(roll, pitch, 0.0f);
_state.quat_nominal = Quaternion(euler_init);
_output_new.quat_nominal = _state.quat_nominal;
// update transformation matrix from body to world frame
_R_to_earth = quat_to_invrotmat(_state.quat_nominal);
// calculate the averaged magnetometer reading
Vector3f mag_init = _mag_filt_state;
// calculate the initial magnetic field and yaw alignment
resetMagHeading(mag_init);
// if we are using the range finder as the primary source, then calculate the baro height at origin so we can use baro as a backup
// so it can be used as a backup ad set the initial height using the range finder
if (_control_status.flags.rng_hgt) {
baroSample baro_newest = _baro_buffer.get_newest();
_baro_hgt_offset = baro_newest.hgt;
_state.pos(2) = -math::max(_rng_filt_state * _R_to_earth(2, 2),_params.rng_gnd_clearance);
}
// initialise the state covariance matrix
initialiseCovariance();
// initialise the terrain estimator
initHagl();
// reset the essential fusion timeout counters
_time_last_hgt_fuse = _time_last_imu;
_time_last_pos_fuse = _time_last_imu;
_time_last_vel_fuse = _time_last_imu;
_time_last_hagl_fuse = _time_last_imu;
_time_last_of_fuse = _time_last_imu;
return true;
}
}
void Ekf::predictState()
{
if (!_earth_rate_initialised) {
if (_NED_origin_initialised) {
calcEarthRateNED(_earth_rate_NED, _pos_ref.lat_rad);
_earth_rate_initialised = true;
}
}
// apply imu bias corrections
Vector3f corrected_delta_ang = _imu_sample_delayed.delta_ang - _state.gyro_bias;
Vector3f corrected_delta_vel = _imu_sample_delayed.delta_vel - _state.accel_bias;
// correct delta angles for earth rotation rate
corrected_delta_ang -= -_R_to_earth.transpose() * _earth_rate_NED * _imu_sample_delayed.delta_ang_dt;
// convert the delta angle to a delta quaternion
Quaternion dq;
dq.from_axis_angle(corrected_delta_ang);
// rotate the previous quaternion by the delta quaternion using a quaternion multiplication
_state.quat_nominal = dq * _state.quat_nominal;
// quaternions must be normalised whenever they are modified
_state.quat_nominal.normalize();
// save the previous value of velocity so we can use trapzoidal integration
Vector3f vel_last = _state.vel;
// update the rotation matrix and calculate the increment in velocity using the current orientation
_R_to_earth = quat_to_invrotmat(_state.quat_nominal);
_state.vel += _R_to_earth * corrected_delta_vel;
// compensate for acceleration due to gravity
_state.vel(2) += _gravity_mss * _imu_sample_delayed.delta_vel_dt;
// predict position states via trapezoidal integration of velocity
_state.pos += (vel_last + _state.vel) * _imu_sample_delayed.delta_vel_dt * 0.5f;
// update transformation matrix from body to world frame
_R_to_earth = quat_to_invrotmat(_state.quat_nominal);
constrainStates();
// calculate an average filter update time
float input = 0.5f*(_imu_sample_delayed.delta_vel_dt + _imu_sample_delayed.delta_ang_dt);
// filter and limit input between -50% and +100% of nominal value
input = math::constrain(input,0.0005f * (float)(FILTER_UPDATE_PERRIOD_MS),0.002f * (float)(FILTER_UPDATE_PERRIOD_MS));
_dt_ekf_avg = 0.99f*_dt_ekf_avg + 0.005f*(_imu_sample_delayed.delta_vel_dt + _imu_sample_delayed.delta_ang_dt);
}
bool Ekf::collect_imu(imuSample &imu)
{
// accumulate and downsample IMU data across a period FILTER_UPDATE_PERRIOD_MS long
// copy imu data to local variables
_imu_sample_new.delta_ang = imu.delta_ang;
_imu_sample_new.delta_vel = imu.delta_vel;
_imu_sample_new.delta_ang_dt = imu.delta_ang_dt;
_imu_sample_new.delta_vel_dt = imu.delta_vel_dt;
_imu_sample_new.time_us = imu.time_us;
// accumulate the time deltas
_imu_down_sampled.delta_ang_dt += imu.delta_ang_dt;
_imu_down_sampled.delta_vel_dt += imu.delta_vel_dt;
// use a quaternion to accumulate delta angle data
// this quaternion represents the rotation from the start to end of the accumulation period
Quaternion delta_q;
delta_q.rotate(imu.delta_ang);
_q_down_sampled = _q_down_sampled * delta_q;
_q_down_sampled.normalize();
// rotate the accumulated delta velocity data forward each time so it is always in the updated rotation frame
matrix::Dcm<float> delta_R(delta_q.inversed());
_imu_down_sampled.delta_vel = delta_R * _imu_down_sampled.delta_vel;
// accumulate the most recent delta velocity data at the updated rotation frame
// assume effective sample time is halfway between the previous and current rotation frame
_imu_down_sampled.delta_vel += (_imu_sample_new.delta_vel + delta_R * _imu_sample_new.delta_vel) * 0.5f;
// if the target time delta between filter prediction steps has been exceeded
// write the accumulated IMU data to the ring buffer
float target_dt = (float)(FILTER_UPDATE_PERRIOD_MS) / 1000;
if (_imu_down_sampled.delta_ang_dt >= target_dt - _last_dt_overrun) {
// store the amount we have over-run the target update rate by
_last_dt_overrun = _imu_down_sampled.delta_ang_dt - target_dt;
imu.delta_ang = _q_down_sampled.to_axis_angle();
imu.delta_vel = _imu_down_sampled.delta_vel;
imu.delta_ang_dt = _imu_down_sampled.delta_ang_dt;
imu.delta_vel_dt = _imu_down_sampled.delta_vel_dt;
imu.time_us = imu.time_us;
_imu_down_sampled.delta_ang.setZero();
_imu_down_sampled.delta_vel.setZero();
_imu_down_sampled.delta_ang_dt = 0.0f;
_imu_down_sampled.delta_vel_dt = 0.0f;
_q_down_sampled(0) = 1.0f;
_q_down_sampled(1) = _q_down_sampled(2) = _q_down_sampled(3) = 0.0f;
return true;
}
return false;
}
/*
* Implement a strapdown INS algorithm using the latest IMU data at the current time horizon.
* Buffer the INS states and calculate the difference with the EKF states at the delayed fusion time horizon.
* Calculate delta angle, delta velocity and velocity corrections from the differences and apply them at the
* current time horizon so that the INS states track the EKF states at the delayed fusion time horizon.
* The inspiration for using a complementary filter to correct for time delays in the EKF
* is based on the work by A Khosravian:
* “Recursive Attitude Estimation in the Presence of Multi-rate and Multi-delay Vector Measurements”
* A Khosravian, J Trumpf, R Mahony, T Hamel, Australian National University
*/
void Ekf::calculateOutputStates()
{
// use latest IMU data
imuSample imu_new = _imu_sample_new;
// correct delta angles for bias offsets and scale factors
Vector3f delta_angle;
float dt_scale_correction = _dt_imu_avg/_dt_ekf_avg;
delta_angle(0) = _imu_sample_new.delta_ang(0) - _state.gyro_bias(0)*dt_scale_correction;
delta_angle(1) = _imu_sample_new.delta_ang(1) - _state.gyro_bias(1)*dt_scale_correction;
delta_angle(2) = _imu_sample_new.delta_ang(2) - _state.gyro_bias(2)*dt_scale_correction;
// correct delta velocity for bias offsets
Vector3f delta_vel = _imu_sample_new.delta_vel - _state.accel_bias*dt_scale_correction;
// Apply corrections to the delta angle required to track the quaternion states at the EKF fusion time horizon
delta_angle += _delta_angle_corr;
// convert the delta angle to an equivalent delta quaternions
Quaternion dq;
dq.from_axis_angle(delta_angle);
// rotate the previous INS quaternion by the delta quaternions
_output_new.time_us = imu_new.time_us;
_output_new.quat_nominal = dq * _output_new.quat_nominal;
// the quaternions must always be normalised afer modification
_output_new.quat_nominal.normalize();
// calculate the rotation matrix from body to earth frame
_R_to_earth_now = quat_to_invrotmat(_output_new.quat_nominal);
// rotate the delta velocity to earth frame
Vector3f delta_vel_NED = _R_to_earth_now * delta_vel;
// corrrect for measured accceleration due to gravity
delta_vel_NED(2) += _gravity_mss * imu_new.delta_vel_dt;
// save the previous velocity so we can use trapezidal integration
Vector3f vel_last = _output_new.vel;
// increment the INS velocity states by the measurement plus corrections
_output_new.vel += delta_vel_NED;
// use trapezoidal integration to calculate the INS position states
_output_new.pos += (_output_new.vel + vel_last) * (imu_new.delta_vel_dt * 0.5f);
// store INS states in a ring buffer that with the same length and time coordinates as the IMU data buffer
if (_imu_updated) {
_output_buffer.push(_output_new);
_imu_updated = false;
// get the oldest INS state data from the ring buffer
// this data will be at the EKF fusion time horizon
_output_sample_delayed = _output_buffer.get_oldest();
// calculate the quaternion delta between the INS and EKF quaternions at the EKF fusion time horizon
Quaternion quat_inv = _state.quat_nominal.inversed();
Quaternion q_error = _output_sample_delayed.quat_nominal * quat_inv;
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);
// calculate a gain that provides tight tracking of the estimator attitude states and
// adjust for changes in time delay to mantain consistent damping ratio of ~0.7
float time_delay = 1e-6f * (float)(_imu_sample_new.time_us - _imu_sample_delayed.time_us);
time_delay = fmaxf(time_delay, _dt_imu_avg);
float att_gain = 0.5f * _dt_imu_avg / time_delay;
// calculate a corrrection to the delta angle
// that will cause the INS to track the EKF quaternions
_delta_angle_corr = delta_ang_error * att_gain;
// calculate gains that will be used to make the INS states converge on the EKF states
float vel_gain = _dt_ekf_avg / math::constrain(_params.vel_Tau, _dt_ekf_avg, 10.0f);
float pos_gain = _dt_ekf_avg / math::constrain(_params.pos_Tau, _dt_ekf_avg, 10.0f);
// calculate velocity and position corrections at the EKF fusion time horizon
Vector3f vel_delta = (_state.vel - _output_sample_delayed.vel) * vel_gain;
Vector3f pos_delta = (_state.pos - _output_sample_delayed.pos) * pos_gain;
// loop through the output filter state history and apply the corrections to the translational states
// this method is too expensive to use for the attitude states due to the quaternion operations required
// but does not introudce a time dela in the 'correction loop' and allows smaller trackin gtime constants
// to be used
outputSample output_states;
unsigned output_length = _output_buffer.get_length();
for (unsigned i=0; i < output_length; i++) {
output_states = _output_buffer.get_from_index(i);
output_states.vel += vel_delta;
output_states.pos += pos_delta;
_output_buffer.push_to_index(i,output_states);
}
// update output state to corrected values
_output_new = _output_buffer.get_newest();
}
}
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