/**************************************************************************** * * 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 * @author Paul Riseborough */ #include "ekf.h" #include "mathlib.h" #ifndef __PX4_QURT #if defined(__cplusplus) && !defined(__PX4_NUTTX) #include #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(); 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(); _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; } } // 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 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 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(); } }