px4_autopilot/EKF/ekf.h

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/**
 * @file ekf.h
 * Class for core functions for ekf attitude and position estimator.
 *
 * @author Roman Bast <bapstroman@gmail.com>
 * @author Paul Riseborough <p_riseborough@live.com.au>
 *
 */

#pragma once

#include "estimator_interface.h"

#include "EKFGSF_yaw.h"

class Ekf final : public EstimatorInterface
{
public:
	static constexpr uint8_t _k_num_states{24};		///< number of EKF states
	typedef matrix::Vector<float, _k_num_states> Vector24f;
	typedef matrix::SquareMatrix<float, _k_num_states> SquareMatrix24f;
	typedef matrix::SquareMatrix<float, 2> Matrix2f;
	typedef matrix::Vector<float, 4> Vector4f;
	template<int ... Idxs>
	using SparseVector24f = matrix::SparseVectorf<24, Idxs...>;

	Ekf() = default;
	virtual ~Ekf() = default;

	// initialise variables to sane values (also interface class)
	bool init(uint64_t timestamp) override;

	// should be called every time new data is pushed into the filter
	bool update();

	void getGpsVelPosInnov(float hvel[2], float &vvel, float hpos[2], float &vpos) const;
	void getGpsVelPosInnovVar(float hvel[2], float &vvel, float hpos[2], float &vpos) const;
	void getGpsVelPosInnovRatio(float &hvel, float &vvel, float &hpos, float &vpos) const;

	void getEvVelPosInnov(float hvel[2], float &vvel, float hpos[2], float &vpos) const;
	void getEvVelPosInnovVar(float hvel[2], float &vvel, float hpos[2], float &vpos) const;
	void getEvVelPosInnovRatio(float &hvel, float &vvel, float &hpos, float &vpos) const;

	void getBaroHgtInnov(float &baro_hgt_innov) const { baro_hgt_innov = _baro_hgt_innov(2); }
	void getBaroHgtInnovVar(float &baro_hgt_innov_var) const { baro_hgt_innov_var = _baro_hgt_innov_var(2); }
	void getBaroHgtInnovRatio(float &baro_hgt_innov_ratio) const { baro_hgt_innov_ratio = _baro_hgt_test_ratio(1); }

	void getRngHgtInnov(float &rng_hgt_innov) const { rng_hgt_innov = _rng_hgt_innov(2); }
	void getRngHgtInnovVar(float &rng_hgt_innov_var) const { rng_hgt_innov_var = _rng_hgt_innov_var(2); }
	void getRngHgtInnovRatio(float &rng_hgt_innov_ratio) const { rng_hgt_innov_ratio = _rng_hgt_test_ratio(1); }

	void getAuxVelInnov(float aux_vel_innov[2]) const;
	void getAuxVelInnovVar(float aux_vel_innov[2]) const;
	void getAuxVelInnovRatio(float &aux_vel_innov_ratio) const { aux_vel_innov_ratio = _aux_vel_test_ratio(0); }

	void getFlowInnov(float flow_innov[2]) const { _flow_innov.copyTo(flow_innov); }
	void getFlowInnovVar(float flow_innov_var[2]) const { _flow_innov_var.copyTo(flow_innov_var); }
	void getFlowInnovRatio(float &flow_innov_ratio) const { flow_innov_ratio = _optflow_test_ratio; }
	const Vector2f &getFlowVelBody() const { return _flow_vel_body; }
	const Vector2f &getFlowVelNE() const { return _flow_vel_ne; }
	const Vector2f &getFlowCompensated() const { return _flow_compensated_XY_rad; }
	const Vector2f &getFlowUncompensated() const { return _flow_sample_delayed.flow_xy_rad; }
	const Vector3f &getFlowGyro() const { return _flow_sample_delayed.gyro_xyz; }

	void getHeadingInnov(float &heading_innov) const { heading_innov = _heading_innov; }
	void getHeadingInnovVar(float &heading_innov_var) const { heading_innov_var = _heading_innov_var; }

	void getHeadingInnovRatio(float &heading_innov_ratio) const { heading_innov_ratio = _yaw_test_ratio; }
	void getMagInnov(float mag_innov[3]) const { _mag_innov.copyTo(mag_innov); }
	void getMagInnovVar(float mag_innov_var[3]) const { _mag_innov_var.copyTo(mag_innov_var); }
	void getMagInnovRatio(float &mag_innov_ratio) const { mag_innov_ratio = _mag_test_ratio.max(); }

	void getDragInnov(float drag_innov[2]) const { _drag_innov.copyTo(drag_innov); }
	void getDragInnovVar(float drag_innov_var[2]) const { _drag_innov_var.copyTo(drag_innov_var); }
	void getDragInnovRatio(float drag_innov_ratio[2]) const { _drag_test_ratio.copyTo(drag_innov_ratio); }

	void getAirspeedInnov(float &airspeed_innov) const { airspeed_innov = _airspeed_innov; }
	void getAirspeedInnovVar(float &airspeed_innov_var) const { airspeed_innov_var = _airspeed_innov_var; }
	void getAirspeedInnovRatio(float &airspeed_innov_ratio) const { airspeed_innov_ratio = _tas_test_ratio; }

	void getBetaInnov(float &beta_innov) const { beta_innov = _beta_innov; }
	void getBetaInnovVar(float &beta_innov_var) const { beta_innov_var = _beta_innov_var; }
	void getBetaInnovRatio(float &beta_innov_ratio) const { beta_innov_ratio = _beta_test_ratio; }

	void getHaglInnov(float &hagl_innov) const { hagl_innov = _hagl_innov; }
	void getHaglInnovVar(float &hagl_innov_var) const { hagl_innov_var = _hagl_innov_var; }
	void getHaglInnovRatio(float &hagl_innov_ratio) const { hagl_innov_ratio = _hagl_test_ratio; }

	// get the state vector at the delayed time horizon
	matrix::Vector<float, 24> getStateAtFusionHorizonAsVector() const;

	// get the wind velocity in m/s
	const Vector2f &getWindVelocity() const { return _state.wind_vel; };

	// get the wind velocity var
	Vector2f getWindVelocityVariance() const { return P.slice<2, 2>(22, 22).diag(); }

	// get the true airspeed in m/s
	void get_true_airspeed(float *tas) const;

	// get the full covariance matrix
	const matrix::SquareMatrix<float, 24> &covariances() const { return P; }

	// get the diagonal elements of the covariance matrix
	matrix::Vector<float, 24> covariances_diagonal() const { return P.diag(); }

	// get the orientation (quaterion) covariances
	matrix::SquareMatrix<float, 4> orientation_covariances() const { return P.slice<4, 4>(0, 0); }

	// get the linear velocity covariances
	matrix::SquareMatrix<float, 3> velocity_covariances() const { return P.slice<3, 3>(4, 4); }

	// get the position covariances
	matrix::SquareMatrix<float, 3> position_covariances() const { return P.slice<3, 3>(7, 7); }

	// ask estimator for sensor data collection decision and do any preprocessing if required, returns true if not defined
	bool collect_gps(const gps_message &gps) override;

	// get the ekf WGS-84 origin position and height and the system time it was last set
	// return true if the origin is valid
	bool getEkfGlobalOrigin(uint64_t &origin_time, double &latitude, double &longitude, float &origin_alt) const;
	bool setEkfGlobalOrigin(const double latitude, const double longitude, const float altitude);

	float getEkfGlobalOriginAltitude() const { return _gps_alt_ref; }
	bool setEkfGlobalOriginAltitude(const float altitude);


	// get the 1-sigma horizontal and vertical position uncertainty of the ekf WGS-84 position
	void get_ekf_gpos_accuracy(float *ekf_eph, float *ekf_epv) const;

	// get the 1-sigma horizontal and vertical position uncertainty of the ekf local position
	void get_ekf_lpos_accuracy(float *ekf_eph, float *ekf_epv) const;

	// get the 1-sigma horizontal and vertical velocity uncertainty
	void get_ekf_vel_accuracy(float *ekf_evh, float *ekf_evv) const;

	// get the vehicle control limits required by the estimator to keep within sensor limitations
	void get_ekf_ctrl_limits(float *vxy_max, float *vz_max, float *hagl_min, float *hagl_max) const;

	// Reset all IMU bias states and covariances to initial alignment values.
	void resetImuBias();
	void resetGyroBias();
	void resetAccelBias();

	// Reset all magnetometer bias states and covariances to initial alignment values.
	void resetMagBias();

	Vector3f getVelocityVariance() const { return P.slice<3, 3>(4, 4).diag(); };

	Vector3f getPositionVariance() const { return P.slice<3, 3>(7, 7).diag(); }

	// return an array containing the output predictor angular, velocity and position tracking
	// error magnitudes (rad), (m/sec), (m)
	const Vector3f &getOutputTrackingError() const { return _output_tracking_error; }

	/*
	First argument returns GPS drift  metrics in the following array locations
	0 : Horizontal position drift rate (m/s)
	1 : Vertical position drift rate (m/s)
	2 : Filtered horizontal velocity (m/s)
	Second argument returns true when IMU movement is blocking the drift calculation
	Function returns true if the metrics have been updated and not returned previously by this function
	*/
	bool get_gps_drift_metrics(float drift[3], bool *blocked);

	// return true if the global position estimate is valid
	// return true if the origin is set we are not doing unconstrained free inertial navigation
	// and have not started using synthetic position observations to constrain drift
	bool global_position_is_valid() const
	{
		return (_NED_origin_initialised && local_position_is_valid());
	}

	// return true if the local position estimate is valid
	bool local_position_is_valid() const
	{
		return (!_deadreckon_time_exceeded && !_using_synthetic_position);
	}

	bool isTerrainEstimateValid() const { return _hagl_valid; };

	uint8_t getTerrainEstimateSensorBitfield() const { return _hagl_sensor_status.value; }

	// get the estimated terrain vertical position relative to the NED origin
	float getTerrainVertPos() const { return _terrain_vpos; };

	// get the terrain variance
	float get_terrain_var() const { return _terrain_var; }

	Vector3f getGyroBias() const { return _state.delta_ang_bias / _dt_ekf_avg; } // get the gyroscope bias in rad/s
	Vector3f getAccelBias() const { return _state.delta_vel_bias / _dt_ekf_avg; } // get the accelerometer bias in m/s**2
	const Vector3f &getMagBias() const { return _state.mag_B; }

	Vector3f getGyroBiasVariance() const { return Vector3f{P(10, 10), P(11, 11), P(12, 12)} / _dt_ekf_avg; } // get the gyroscope bias variance in rad/s
	Vector3f getAccelBiasVariance() const { return Vector3f{P(13, 13), P(14, 14), P(15, 15)} / _dt_ekf_avg; } // get the accelerometer bias variance in m/s**2
	Vector3f getMagBiasVariance() const { return Vector3f{P(19, 19), P(20, 20), P(21, 21)}; }

	// get GPS check status
	void get_gps_check_status(uint16_t *val) const { *val = _gps_check_fail_status.value; }

	const auto &state_reset_status() const { return _state_reset_status; }

	// return the amount the local vertical position changed in the last reset and the number of reset events
	void get_posD_reset(float *delta, uint8_t *counter) const
	{
		*delta = _state_reset_status.posD_change;
		*counter = _state_reset_status.posD_counter;
	}

	// return the amount the local vertical velocity changed in the last reset and the number of reset events
	void get_velD_reset(float *delta, uint8_t *counter) const
	{
		*delta = _state_reset_status.velD_change;
		*counter = _state_reset_status.velD_counter;
	}

	// return the amount the local horizontal position changed in the last reset and the number of reset events
	void get_posNE_reset(float delta[2], uint8_t *counter) const
	{
		_state_reset_status.posNE_change.copyTo(delta);
		*counter = _state_reset_status.posNE_counter;
	}

	// return the amount the local horizontal velocity changed in the last reset and the number of reset events
	void get_velNE_reset(float delta[2], uint8_t *counter) const
	{
		_state_reset_status.velNE_change.copyTo(delta);
		*counter = _state_reset_status.velNE_counter;
	}

	// return the amount the quaternion has changed in the last reset and the number of reset events
	void get_quat_reset(float delta_quat[4], uint8_t *counter) const
	{
		_state_reset_status.quat_change.copyTo(delta_quat);
		*counter = _state_reset_status.quat_counter;
	}

	// get EKF innovation consistency check status information comprising of:
	// status - a bitmask integer containing the pass/fail status for each EKF measurement innovation consistency check
	// Innovation Test Ratios - these are the ratio of the innovation to the acceptance threshold.
	// A value > 1 indicates that the sensor measurement has exceeded the maximum acceptable level and has been rejected by the EKF
	// Where a measurement type is a vector quantity, eg magnetometer, GPS position, etc, the maximum value is returned.
	void get_innovation_test_status(uint16_t &status, float &mag, float &vel, float &pos, float &hgt, float &tas,
					float &hagl, float &beta) const;

	// return a bitmask integer that describes which state estimates can be used for flight control
	void get_ekf_soln_status(uint16_t *status) const;

	// return the quaternion defining the rotation from the External Vision to the EKF reference frame
	matrix::Quatf getVisionAlignmentQuaternion() const { return Quatf(_R_ev_to_ekf); };

	// use the latest IMU data at the current time horizon.
	Quatf calculate_quaternion() const;

	// set minimum continuous period without GPS fail required to mark a healthy GPS status
	void set_min_required_gps_health_time(uint32_t time_us) { _min_gps_health_time_us = time_us; }

	// get solution data from the EKF-GSF emergency yaw estimator
	// returns false when data is not available
	bool getDataEKFGSF(float *yaw_composite, float *yaw_variance, float yaw[N_MODELS_EKFGSF],
			   float innov_VN[N_MODELS_EKFGSF], float innov_VE[N_MODELS_EKFGSF], float weight[N_MODELS_EKFGSF]);

private:

	// set the internal states and status to their default value
	void reset();

	bool initialiseTilt();

	// Request the EKF reset the yaw to the estimate from the internal EKF-GSF filter
	// and reset the velocity and position states to the GPS. This will cause the EKF
	// to ignore the magnetometer for the remainder of flight.
	// This should only be used as a last resort before activating a loss of navigation failsafe
	void requestEmergencyNavReset() { _do_ekfgsf_yaw_reset = true; }

	// check if the EKF is dead reckoning horizontal velocity using inertial data only
	void update_deadreckoning_status();

	void updateTerrainValidity();

	struct {
		uint8_t velNE_counter;	///< number of horizontal position reset events (allow to wrap if count exceeds 255)
		uint8_t velD_counter;	///< number of vertical velocity reset events (allow to wrap if count exceeds 255)
		uint8_t posNE_counter;	///< number of horizontal position reset events (allow to wrap if count exceeds 255)
		uint8_t posD_counter;	///< number of vertical position reset events (allow to wrap if count exceeds 255)
		uint8_t quat_counter;	///< number of quaternion reset events (allow to wrap if count exceeds 255)
		Vector2f velNE_change;  ///< North East velocity change due to last reset (m)
		float velD_change;	///< Down velocity change due to last reset (m/sec)
		Vector2f posNE_change;	///< North, East position change due to last reset (m)
		float posD_change;	///< Down position change due to last reset (m)
		Quatf quat_change;	///< quaternion delta due to last reset - multiply pre-reset quaternion by this to get post-reset quaternion
	} _state_reset_status{};	///< reset event monitoring structure containing velocity, position, height and yaw reset information

	float _dt_ekf_avg{FILTER_UPDATE_PERIOD_S}; ///< average update rate of the ekf

	Vector3f _ang_rate_delayed_raw;	///< uncorrected angular rate vector at fusion time horizon (rad/sec)

	stateSample _state{};		///< state struct of the ekf running at the delayed time horizon

	bool _filter_initialised{false};	///< true when the EKF sttes and covariances been initialised

	// variables used when position data is being fused using a relative position odometry model
	bool _fuse_hpos_as_odom{false};		///< true when the NE position data is being fused using an odometry assumption
	Vector3f _pos_meas_prev;		///< previous value of NED position measurement fused using odometry assumption (m)
	Vector2f _hpos_pred_prev;		///< previous value of NE position state used by odometry fusion (m)
	bool _hpos_prev_available{false};	///< true when previous values of the estimate and measurement are available for use
	Dcmf _R_ev_to_ekf;			///< transformation matrix that rotates observations from the EV to the EKF navigation frame, initialized with Identity

	// booleans true when fresh sensor data is available at the fusion time horizon
	bool _gps_data_ready{false};	///< true when new GPS data has fallen behind the fusion time horizon and is available to be fused
	bool _mag_data_ready{false};	///< true when new magnetometer data has fallen behind the fusion time horizon and is available to be fused
	bool _baro_data_ready{false};	///< true when new baro height data has fallen behind the fusion time horizon and is available to be fused
	bool _flow_data_ready{false};	///< true when the leading edge of the optical flow integration period has fallen behind the fusion time horizon
	bool _ev_data_ready{false};	///< true when new external vision system data has fallen behind the fusion time horizon and is available to be fused
	bool _tas_data_ready{false};	///< true when new true airspeed data has fallen behind the fusion time horizon and is available to be fused
	bool _flow_for_terrain_data_ready{false}; /// same flag as "_flow_data_ready" but used for separate terrain estimator

	uint64_t _time_prev_gps_us{0};	///< time stamp of previous GPS data retrieved from the buffer (uSec)
	uint64_t _time_last_aiding{0};	///< amount of time we have been doing inertial only deadreckoning (uSec)
	bool _using_synthetic_position{false};	///< true if we are using a synthetic position to constrain drift

	uint64_t _time_last_hor_pos_fuse{0};	///< time the last fusion of horizontal position measurements was performed (uSec)
	uint64_t _time_last_hgt_fuse{0};	///< time the last fusion of vertical position measurements was performed (uSec)
	uint64_t _time_last_hor_vel_fuse{0};	///< time the last fusion of horizontal velocity measurements was performed (uSec)
	uint64_t _time_last_ver_vel_fuse{0};	///< time the last fusion of verticalvelocity measurements was performed (uSec)
	uint64_t _time_last_delpos_fuse{0};	///< time the last fusion of incremental horizontal position measurements was performed (uSec)
	uint64_t _time_last_of_fuse{0};		///< time the last fusion of optical flow measurements were performed (uSec)
	uint64_t _time_last_flow_terrain_fuse{0}; ///< time the last fusion of optical flow measurements for terrain estimation were performed (uSec)
	uint64_t _time_last_arsp_fuse{0};	///< time the last fusion of airspeed measurements were performed (uSec)
	uint64_t _time_last_beta_fuse{0};	///< time the last fusion of synthetic sideslip measurements were performed (uSec)
	uint64_t _time_last_fake_pos{0};	///< last time we faked position measurements to constrain tilt errors during operation without external aiding (uSec)

	uint64_t _time_last_gps_yaw_fuse{0};	///< time the last fusion of GPS yaw measurements were performed (uSec)

	Vector2f _last_known_posNE;		///< last known local NE position vector (m)
	float _imu_collection_time_adj{0.0f};	///< the amount of time the IMU collection needs to be advanced to meet the target set by FILTER_UPDATE_PERIOD_MS (sec)

	uint64_t _time_acc_bias_check{0};	///< last time the  accel bias check passed (uSec)
	uint64_t _delta_time_baro_us{0};	///< delta time between two consecutive delayed baro samples from the buffer (uSec)

	Vector3f _earth_rate_NED;	///< earth rotation vector (NED) in rad/s

	Dcmf _R_to_earth;	///< transformation matrix from body frame to earth frame from last EKF prediction

	// used by magnetometer fusion mode selection
	Vector2f _accel_lpf_NE;			///< Low pass filtered horizontal earth frame acceleration (m/sec**2)
	float _yaw_delta_ef{0.0f};		///< Recent change in yaw angle measured about the earth frame D axis (rad)
	float _yaw_rate_lpf_ef{0.0f};		///< Filtered angular rate about earth frame D axis (rad/sec)
	bool _mag_bias_observable{false};	///< true when there is enough rotation to make magnetometer bias errors observable
	bool _yaw_angle_observable{false};	///< true when there is enough horizontal acceleration to make yaw observable
	uint64_t _time_yaw_started{0};		///< last system time in usec that a yaw rotation manoeuvre was detected
	uint8_t _num_bad_flight_yaw_events{0};	///< number of times a bad heading has been detected in flight and required a yaw reset
	uint64_t _mag_use_not_inhibit_us{0};	///< last system time in usec before magnetometer use was inhibited
	bool _mag_inhibit_yaw_reset_req{false};	///< true when magnetometer inhibit has been active for long enough to require a yaw reset when conditions improve.
	float _last_static_yaw{0.0f};		///< last yaw angle recorded when on ground motion checks were passing (rad)
	bool _mag_yaw_reset_req{false};		///< true when a reset of the yaw using the magnetometer data has been requested
	bool _mag_decl_cov_reset{false};	///< true after the fuseDeclination() function has been used to modify the earth field covariances after a magnetic field reset event.
	bool _synthetic_mag_z_active{false};	///< true if we are generating synthetic magnetometer Z measurements
	bool _non_mag_yaw_aiding_running_prev{false};  ///< true when heading is being fused from other sources that are not the magnetometer (for example EV or GPS).

	bool _is_yaw_fusion_inhibited{false};		///< true when yaw sensor use is being inhibited

	SquareMatrix24f P;	///< state covariance matrix

	Vector3f _delta_vel_bias_var_accum;		///< kahan summation algorithm accumulator for delta velocity bias variance
	Vector3f _delta_angle_bias_var_accum;	///< kahan summation algorithm accumulator for delta angle bias variance

	Vector3f _last_vel_obs;			///< last velocity observation (m/s)
	Vector3f _last_vel_obs_var;		///< last velocity observation variance (m/s)**2
	Vector2f _last_fail_hvel_innov;		///< last failed horizontal velocity innovation (m/s)**2
	float _vert_pos_innov_ratio;		///< vertical position innovation divided by estimated standard deviation of innovation
	uint64_t _vert_pos_fuse_attempt_time_us;	///< last system time in usec vertical position measurement fuson was attempted
	float _vert_vel_innov_ratio;		///< standard deviation of vertical velocity innovation
	uint64_t _vert_vel_fuse_time_us;	///< last system time in usec time vertical velocity measurement fuson was attempted

	Vector3f _gps_vel_innov;	///< GPS velocity innovations (m/sec)
	Vector3f _gps_vel_innov_var;	///< GPS velocity innovation variances ((m/sec)**2)

	Vector3f _gps_pos_innov;	///< GPS position innovations (m)
	Vector3f _gps_pos_innov_var;	///< GPS position innovation variances (m**2)

	Vector3f _ev_vel_innov;	///< external vision velocity innovations (m/sec)
	Vector3f _ev_vel_innov_var;	///< external vision velocity innovation variances ((m/sec)**2)

	Vector3f _ev_pos_innov;	///< external vision position innovations (m)
	Vector3f _ev_pos_innov_var;	///< external vision position innovation variances (m**2)

	Vector3f _baro_hgt_innov;		///< baro hgt innovations (m)
	Vector3f _baro_hgt_innov_var;	///< baro hgt innovation variances (m**2)

	Vector3f _rng_hgt_innov;	///< range hgt innovations (m)
	Vector3f _rng_hgt_innov_var;	///< range hgt innovation variances (m**2)

	Vector3f _aux_vel_innov;	///< horizontal auxiliary velocity innovations: (m/sec)
	Vector3f _aux_vel_innov_var;	///< horizontal auxiliary velocity innovation variances: ((m/sec)**2)

	float _heading_innov{0.0f};	///< heading measurement innovation (rad)
	float _heading_innov_var{0.0f};	///< heading measurement innovation variance (rad**2)

	Vector3f _mag_innov;		///< earth magnetic field innovations (Gauss)
	Vector3f _mag_innov_var;	///< earth magnetic field innovation variance (Gauss**2)

	Vector2f _drag_innov;		///< multirotor drag measurement innovation (m/sec**2)
	Vector2f _drag_innov_var;	///< multirotor drag measurement innovation variance ((m/sec**2)**2)

	float _airspeed_innov{0.0f};		///< airspeed measurement innovation (m/sec)
	float _airspeed_innov_var{0.0f};	///< airspeed measurement innovation variance ((m/sec)**2)

	float _beta_innov{0.0f};	///< synthetic sideslip measurement innovation (rad)
	float _beta_innov_var{0.0f};	///< synthetic sideslip measurement innovation variance (rad**2)

	float _hagl_innov{0.0f};		///< innovation of the last height above terrain measurement (m)
	float _hagl_innov_var{0.0f};		///< innovation variance for the last height above terrain measurement (m**2)

	// optical flow processing
	Vector2f _flow_innov;		///< flow measurement innovation (rad/sec)
	Vector2f _flow_innov_var;	///< flow innovation variance ((rad/sec)**2)
	Vector3f _flow_gyro_bias;	///< bias errors in optical flow sensor rate gyro outputs (rad/sec)
	Vector2f _flow_vel_body;	///< velocity from corrected flow measurement (body frame)(m/s)
	Vector2f _flow_vel_ne;		///< velocity from corrected flow measurement (local frame) (m/s)
	Vector3f _imu_del_ang_of;	///< bias corrected delta angle measurements accumulated across the same time frame as the optical flow rates (rad)
	float _delta_time_of{0.0f};	///< time in sec that _imu_del_ang_of was accumulated over (sec)
	uint64_t _time_bad_motion_us{0};	///< last system time that on-ground motion exceeded limits (uSec)
	uint64_t _time_good_motion_us{0};	///< last system time that on-ground motion was within limits (uSec)
	bool _inhibit_flow_use{false};	///< true when use of optical flow and range finder is being inhibited
	Vector2f _flow_compensated_XY_rad;	///< measured delta angle of the image about the X and Y body axes after removal of body rotation (rad), RH rotation is positive

	// output predictor states
	Vector3f _delta_angle_corr;	///< delta angle correction vector (rad)
	Vector3f _vel_err_integ;	///< integral of velocity tracking error (m)
	Vector3f _pos_err_integ;	///< integral of position tracking error (m.s)
	Vector3f _output_tracking_error; ///< contains the magnitude of the angle, velocity and position track errors (rad, m/s, m)

	// variables used for the GPS quality checks
	Vector3f _gps_pos_deriv_filt;	///< GPS NED position derivative (m/sec)
	Vector2f _gps_velNE_filt;	///< filtered GPS North and East velocity (m/sec)
	float _gps_velD_diff_filt{0.0f};	///< GPS filtered Down velocity (m/sec)
	uint64_t _last_gps_fail_us{0};		///< last system time in usec that the GPS failed it's checks
	uint64_t _last_gps_pass_us{0};		///< last system time in usec that the GPS passed it's checks
	float _gps_error_norm{1.0f};		///< normalised gps error
	uint32_t _min_gps_health_time_us{10000000}; ///< GPS is marked as healthy only after this amount of time
	bool _gps_checks_passed{false};		///> true when all active GPS checks have passed

	// Variables used to publish the WGS-84 location of the EKF local NED origin
	uint64_t _last_gps_origin_time_us{0};	///< time the origin was last set (uSec)
	float _gps_alt_ref{0.0f};		///< WGS-84 height (m)

	// Variables used by the initial filter alignment
	bool _is_first_imu_sample{true};
	uint32_t _baro_counter{0};		///< number of baro samples read during initialisation
	uint32_t _mag_counter{0};		///< number of magnetometer samples read during initialisation
	AlphaFilter<Vector3f> _accel_lpf{0.1f};	///< filtered accelerometer measurement used to align tilt (m/s/s)
	AlphaFilter<Vector3f> _gyro_lpf{0.1f};	///< filtered gyro measurement used for alignment excessive movement check (rad/sec)

	// Variables used to perform in flight resets and switch between height sources
	AlphaFilter<Vector3f> _mag_lpf{0.1f};	///< filtered magnetometer measurement for instant reset (Gauss)
	float _hgt_sensor_offset{0.0f};		///< set as necessary if desired to maintain the same height after a height reset (m)
	float _baro_hgt_offset{0.0f};		///< baro height reading at the local NED origin (m)

	// Variables used to control activation of post takeoff functionality
	float _last_on_ground_posD{0.0f};	///< last vertical position when the in_air status was false (m)
	uint64_t _flt_mag_align_start_time{0};	///< time that inflight magnetic field alignment started (uSec)
	uint64_t _time_last_mov_3d_mag_suitable{0};	///< last system time that sufficient movement to use 3-axis magnetometer fusion was detected (uSec)
	float _saved_mag_bf_variance[4] {};	///< magnetic field state variances that have been saved for use at the next initialisation (Gauss**2)
	Matrix2f _saved_mag_ef_covmat;		///< NE magnetic field state covariance sub-matrix saved for use at the next initialisation (Gauss**2)
	bool _velpos_reset_request{false};	///< true when a large yaw error has been fixed and a velocity and position state reset is required

	gps_check_fail_status_u _gps_check_fail_status{};

	// variables used to inhibit accel bias learning
	bool _accel_bias_inhibit[3] {};		///< true when the accel bias learning is being inhibited for the specified axis
	Vector3f _accel_vec_filt;		///< acceleration vector after application of a low pass filter (m/sec**2)
	float _accel_magnitude_filt{0.0f};	///< acceleration magnitude after application of a decaying envelope filter (rad/sec)
	float _ang_rate_magnitude_filt{0.0f};		///< angular rate magnitude after application of a decaying envelope filter (rad/sec)
	Vector3f _prev_dvel_bias_var;		///< saved delta velocity XYZ bias variances (m/sec)**2

	// Terrain height state estimation
	float _terrain_vpos{0.0f};		///< estimated vertical position of the terrain underneath the vehicle in local NED frame (m)
	float _terrain_var{1e4f};		///< variance of terrain position estimate (m**2)
	uint64_t _time_last_hagl_fuse{0};		///< last system time that a range sample was fused by the terrain estimator
	uint64_t _time_last_fake_hagl_fuse{0};	///< last system time that a fake range sample was fused by the terrain estimator
	bool _terrain_initialised{false};	///< true when the terrain estimator has been initialized
	bool _hagl_valid{false};		///< true when the height above ground estimate is valid
	terrain_fusion_status_u _hagl_sensor_status{}; ///< Struct indicating type of sensor used to estimate height above ground

	// height sensor status
	bool _baro_hgt_faulty{false};		///< true if valid baro data is unavailable for use
	bool _gps_hgt_intermittent{false};	///< true if gps height into the buffer is intermittent
	bool _is_gps_yaw_faulty{false};		///< true if gps yaw data is rejected by the filter for too long

	// imu fault status
	uint64_t _time_bad_vert_accel{0};	///< last time a bad vertical accel was detected (uSec)
	uint64_t _time_good_vert_accel{0};	///< last time a good vertical accel was detected (uSec)
	bool _bad_vert_accel_detected{false};	///< true when bad vertical accelerometer data has been detected
	uint16_t _clip_counter{0};		///< counter that increments when clipping ad decrements when not

	// variables used to control range aid functionality
	bool _is_range_aid_suitable{false};	///< true when range finder can be used in flight as the height reference instead of the primary height sensor

	float _height_rate_lpf{0.0f};

	// update the real time complementary filter states. This includes the prediction
	// and the correction step
	void calculateOutputStates(const imuSample &imu);
	void applyCorrectionToVerticalOutputBuffer(float vert_vel_correction);
	void applyCorrectionToOutputBuffer(const Vector3f &vel_correction, const Vector3f &pos_correction);

	// initialise filter states of both the delayed ekf and the real time complementary filter
	bool initialiseFilter(void);

	// initialise ekf covariance matrix
	void initialiseCovariance();

	// predict ekf state
	void predictState();

	// predict ekf covariance
	void predictCovariance();

	// ekf sequential fusion of magnetometer measurements
	void fuseMag();

	// fuse the first euler angle from either a 321 or 312 rotation sequence as the observation (currently measures yaw using the magnetometer)
	void fuseHeading();

	// fuse the yaw angle defined as the first rotation in a 321 Tait-Bryan rotation sequence
	// yaw : angle observation defined as the first rotation in a 321 Tait-Bryan rotation sequence (rad)
	// yaw_variance : variance of the yaw angle observation (rad^2)
	// zero_innovation : Fuse data with innovation set to zero
	void fuseYaw321(const float yaw, const float yaw_variance, bool zero_innovation);

	// fuse the yaw angle defined as the first rotation in a 312 Tait-Bryan rotation sequence
	// yaw : angle observation defined as the first rotation in a 312 Tait-Bryan rotation sequence (rad)
	// yaw_variance : variance of the yaw angle observation (rad^2)
	// zero_innovation : Fuse data with innovation set to zero
	void fuseYaw312(const float yaw, const float yaw_variance, bool zero_innovation);

	// update quaternion states and covariances using an innovation, observation variance and Jacobian vector
	// innovation : prediction - measurement
	// variance : observaton variance
	// gate_sigma : innovation consistency check gate size (Sigma)
	// jacobian : 4x1 vector of partial derivatives of observation wrt each quaternion state
	void updateQuaternion(const float innovation, const float variance, const float gate_sigma,
			      const Vector4f &yaw_jacobian);

	// fuse the yaw angle obtained from a dual antenna GPS unit
	void fuseGpsYaw();

	// reset the quaternions states using the yaw angle obtained from a dual antenna GPS unit
	// return true if the reset was successful
	bool resetYawToGps();

	// fuse magnetometer declination measurement
	// argument passed in is the declination uncertainty in radians
	void fuseDeclination(float decl_sigma);

	// apply sensible limits to the declination and length of the NE mag field states estimates
	void limitDeclination();

	// fuse airspeed measurement
	void fuseAirspeed();

	// fuse synthetic zero sideslip measurement
	void fuseSideslip();

	// fuse body frame drag specific forces for multi-rotor wind estimation
	void fuseDrag();

	// fuse single velocity and position measurement
	void fuseVelPosHeight(const float innov, const float innov_var, const int obs_index);

	void resetVelocity();

	void resetVelocityToGps();

	inline void resetHorizontalVelocityToOpticalFlow();

	inline void resetVelocityToVision();

	inline void resetHorizontalVelocityToZero();

	inline void resetVelocityTo(const Vector3f &vel);

	inline void resetHorizontalVelocityTo(const Vector2f &new_horz_vel);

	inline void resetVerticalVelocityTo(float new_vert_vel);

	void resetHorizontalPosition();

	void resetHorizontalPositionToGps();

	inline void resetHorizontalPositionToVision();

	inline void resetHorizontalPositionTo(const Vector2f &new_horz_pos);

	inline void resetVerticalPositionTo(const float &new_vert_pos);

	void resetHeight();

	// fuse optical flow line of sight rate measurements
	void fuseOptFlow();

	bool fuseHorizontalVelocity(const Vector3f &innov, const Vector2f &innov_gate, const Vector3f &obs_var,
				    Vector3f &innov_var, Vector2f &test_ratio);

	bool fuseVerticalVelocity(const Vector3f &innov, const Vector2f &innov_gate, const Vector3f &obs_var,
				  Vector3f &innov_var, Vector2f &test_ratio);

	bool fuseHorizontalPosition(const Vector3f &innov, const Vector2f &innov_gate, const Vector3f &obs_var,
				    Vector3f &innov_var, Vector2f &test_ratiov, bool inhibit_gate = false);

	bool fuseVerticalPosition(const Vector3f &innov, const Vector2f &innov_gate, const Vector3f &obs_var,
				  Vector3f &innov_var, Vector2f &test_ratio);

	// calculate optical flow body angular rate compensation
	// returns false if bias corrected body rate data is unavailable
	bool calcOptFlowBodyRateComp();

	// initialise the terrain vertical position estimator
	// return true if the initialisation is successful
	bool initHagl();

	bool shouldUseRangeFinderForHagl() const { return (_params.terrain_fusion_mode & TerrainFusionMask::TerrainFuseRangeFinder); }
	bool shouldUseOpticalFlowForHagl() const { return (_params.terrain_fusion_mode & TerrainFusionMask::TerrainFuseOpticalFlow); }

	// run the terrain estimator
	void runTerrainEstimator();

	// update the terrain vertical position estimate using a height above ground measurement from the range finder
	void fuseHagl();

	// update the terrain vertical position estimate using an optical flow measurement
	void fuseFlowForTerrain();

	// reset the heading and magnetic field states using the declination and magnetometer/external vision measurements
	// return true if successful
	bool resetMagHeading(const Vector3f &mag_init, bool increase_yaw_var = true, bool update_buffer = true);

	// Do a forced re-alignment of the yaw angle to align with the horizontal velocity vector from the GPS.
	// It is used to align the yaw angle after launch or takeoff for fixed wing vehicle.
	bool realignYawGPS();

	// Return the magnetic declination in radians to be used by the alignment and fusion processing
	float getMagDeclination();

	// modify output filter to match the the EKF state at the fusion time horizon
	void alignOutputFilter();

	// update the rotation matrix which transforms EV navigation frame measurements into NED
	void calcExtVisRotMat();

	Vector3f getVisionVelocityInEkfFrame() const;

	Vector3f getVisionVelocityVarianceInEkfFrame() const;

	// matrix vector multiplication for computing K<24,1> * H<1,24> * P<24,24>
	// that is optimized by exploring the sparsity in H
	template <size_t ...Idxs>
	SquareMatrix24f computeKHP(const Vector24f &K, const SparseVector24f<Idxs...> &H) const
	{
		SquareMatrix24f KHP;
		constexpr size_t non_zeros = sizeof...(Idxs);
		float KH[non_zeros];

		for (unsigned row = 0; row < _k_num_states; row++) {
			for (unsigned i = 0; i < H.non_zeros(); i++) {
				KH[i] = K(row) * H.atCompressedIndex(i);
			}

			for (unsigned column = 0; column < _k_num_states; column++) {
				float tmp = 0.f;

				for (unsigned i = 0; i < H.non_zeros(); i++) {
					const size_t index = H.index(i);
					tmp += KH[i] * P(index, column);
				}

				KHP(row, column) = tmp;
			}
		}

		return KHP;
	}

	// measurement update with a single measurement
	// returns true if fusion is performed
	template <size_t ...Idxs>
	bool measurementUpdate(Vector24f &K, const SparseVector24f<Idxs...> &H, float innovation)
	{
		for (unsigned i = 0; i < 3; i++) {
			if (_accel_bias_inhibit[i]) {
				K(13 + i) = 0.0f;
			}
		}

		// apply covariance correction via P_new = (I -K*H)*P
		// first calculate expression for KHP
		// then calculate P - KHP
		const SquareMatrix24f KHP = computeKHP(K, H);

		const bool is_healthy = checkAndFixCovarianceUpdate(KHP);

		if (is_healthy) {
			// apply the covariance corrections
			P -= KHP;

			fixCovarianceErrors(true);

			// apply the state corrections
			fuse(K, innovation);
		}

		return is_healthy;
	}

	// if the covariance correction will result in a negative variance, then
	// the covariance matrix is unhealthy and must be corrected
	bool checkAndFixCovarianceUpdate(const SquareMatrix24f &KHP);

	// limit the diagonal of the covariance matrix
	// force symmetry when the argument is true
	void fixCovarianceErrors(bool force_symmetry);

	// constrain the ekf states
	void constrainStates();

	// generic function which will perform a fusion step given a kalman gain K
	// and a scalar innovation value
	void fuse(const Vector24f &K, float innovation);

	float compensateBaroForDynamicPressure(float baro_alt_uncompensated) const override;

	// calculate the earth rotation vector from a given latitude
	Vector3f calcEarthRateNED(float lat_rad) const;

	// return true id the GPS quality is good enough to set an origin and start aiding
	bool gps_is_good(const gps_message &gps);

	// Control the filter fusion modes
	void controlFusionModes();

	// control fusion of external vision observations
	void controlExternalVisionFusion();

	// control fusion of optical flow observations
	void controlOpticalFlowFusion();
	void updateOnGroundMotionForOpticalFlowChecks();
	void resetOnGroundMotionForOpticalFlowChecks();

	// control fusion of GPS observations
	void controlGpsFusion();
	void controlGpsYawFusion();

	// control fusion of magnetometer observations
	void controlMagFusion();

	bool noOtherYawAidingThanMag() const;
	bool otherHeadingSourcesHaveStopped();

	void checkHaglYawResetReq();
	float getTerrainVPos() const { return isTerrainEstimateValid() ? _terrain_vpos : _last_on_ground_posD; }

	void runOnGroundYawReset();
	bool isYawResetAuthorized() const { return !_is_yaw_fusion_inhibited; }
	bool canResetMagHeading() const;
	void runInAirYawReset();
	bool canRealignYawUsingGps() const { return _control_status.flags.fixed_wing; }
	void runVelPosReset();

	void selectMagAuto();
	void check3DMagFusionSuitability();
	void checkYawAngleObservability();
	void checkMagBiasObservability();
	bool isYawAngleObservable() const { return _yaw_angle_observable; }
	bool isMagBiasObservable() const { return _mag_bias_observable; }
	bool canUse3DMagFusion() const;

	void checkMagDeclRequired();
	void checkMagInhibition();
	bool shouldInhibitMag() const;
	void checkMagFieldStrength();
	bool isStrongMagneticDisturbance() const { return _control_status.flags.mag_field_disturbed; }
	bool isMeasuredMatchingGpsMagStrength() const;
	bool isMeasuredMatchingAverageMagStrength() const;
	static bool isMeasuredMatchingExpected(float measured, float expected, float gate);
	void runMagAndMagDeclFusions();
	void run3DMagAndDeclFusions();

	// control fusion of range finder observations
	void controlRangeFinderFusion();

	// control fusion of air data observations
	void controlAirDataFusion();

	// control fusion of synthetic sideslip observations
	void controlBetaFusion();

	// control fusion of multi-rotor drag specific force observations
	void controlDragFusion();

	// control fusion of pressure altitude observations
	void controlBaroFusion();

	// control fusion of fake position observations to constrain drift
	void controlFakePosFusion();

	// control fusion of auxiliary velocity observations
	void controlAuxVelFusion();

	// control for height sensor timeouts, sensor changes and state resets
	void controlHeightSensorTimeouts();

	void checkVerticalAccelerationHealth();

	// control for combined height fusion mode (implemented for switching between baro and range height)
	void controlHeightFusion();

	// determine if flight condition is suitable to use range finder instead of the primary height sensor
	void checkRangeAidSuitability();
	bool isRangeAidSuitable() const { return _is_range_aid_suitable; }

	// set control flags to use baro height
	void setControlBaroHeight();

	// set control flags to use range height
	void setControlRangeHeight();

	// set control flags to use GPS height
	void setControlGPSHeight();

	// set control flags to use external vision height
	void setControlEVHeight();

	void stopMagFusion();
	void stopMag3DFusion();
	void stopMagHdgFusion();
	void startMagHdgFusion();
	void startMag3DFusion();

	void startBaroHgtFusion();
	void startGpsHgtFusion();

	void updateBaroHgtOffset();

	// return an estimation of the GPS altitude variance
	float getGpsHeightVariance();

	// calculate the measurement variance for the optical flow sensor
	float calcOptFlowMeasVar();

	// rotate quaternion covariances into variances for an equivalent rotation vector
	Vector3f calcRotVecVariances();

	// initialise the quaternion covariances using rotation vector variances
	// do not call before quaternion states are initialised
	void initialiseQuatCovariances(Vector3f &rot_vec_var);

	// perform a limited reset of the magnetic field related state covariances
	void resetMagRelatedCovariances();

	void resetQuatCov();
	void zeroQuatCov();
	void resetMagCov();

	// perform a limited reset of the wind state covariances
	void resetWindCovariance();

	// perform a reset of the wind states
	void resetWindStates();

	// check that the range finder data is continuous
	void updateRangeDataContinuity();

	// Increase the yaw error variance of the quaternions
	// Argument is additional yaw variance in rad**2
	void increaseQuatYawErrVariance(float yaw_variance);

	// load and save mag field state covariance data for re-use
	void loadMagCovData();
	void saveMagCovData();
	void clearMagCov();
	void zeroMagCov();

	// uncorrelate quaternion states from other states
	void uncorrelateQuatFromOtherStates();

	// calculate a synthetic value for the magnetometer Z component, given the 3D magnetomter
	// sensor measurement
	float calculate_synthetic_mag_z_measurement(const Vector3f &mag_meas, const Vector3f &mag_earth_predicted);

	bool isTimedOut(uint64_t last_sensor_timestamp, uint64_t timeout_period) const
	{
		return last_sensor_timestamp + timeout_period < _time_last_imu;
	}

	bool isRecent(uint64_t sensor_timestamp, uint64_t acceptance_interval) const
	{
		return sensor_timestamp + acceptance_interval > _time_last_imu;
	}

	void startGpsFusion();
	void stopGpsFusion();
	void stopGpsPosFusion();
	void stopGpsVelFusion();

	void startGpsYawFusion();
	void stopGpsYawFusion();

	void startEvPosFusion();
	void startEvVelFusion();
	void startEvYawFusion();

	void stopEvFusion();
	void stopEvPosFusion();
	void stopEvVelFusion();
	void stopEvYawFusion();

	void stopAuxVelFusion();

	void stopFlowFusion();

	void setVelPosFaultStatus(const int index, const bool status);

	// reset the quaternion states and covariances to the new yaw value, preserving the roll and pitch
	// yaw : Euler yaw angle (rad)
	// yaw_variance : yaw error variance (rad^2)
	// update_buffer : true if the state change should be also applied to the output observer buffer
	void resetQuatStateYaw(float yaw, float yaw_variance, bool update_buffer);

	// Declarations used to control use of the EKF-GSF yaw estimator

	// yaw estimator instance
	EKFGSF_yaw _yawEstimator;

	int64_t _ekfgsf_yaw_reset_time{0};	///< timestamp of last emergency yaw reset (uSec)
	bool _do_ekfgsf_yaw_reset{false};	// true when an emergency yaw reset has been requested
	uint8_t _ekfgsf_yaw_reset_count{0};	// number of times the yaw has been reset to the EKF-GSF estimate

	// Call once per _imu_sample_delayed update after all main EKF data fusion oeprations have been completed
	void runYawEKFGSF();

	// Resets the main Nav EKf yaw to the estimator from the EKF-GSF yaw estimator
	// Resets the horizontal velocity and position to the default navigation sensor
	// Returns true if the reset was successful
	bool resetYawToEKFGSF();

	void resetGpsDriftCheckFilters();
};