PX4-Autopilot/EKF/EKFGSF_yaw.cpp

#include "EKFGSF_yaw.h"
#include <cstdlib>

EKFGSF_yaw::EKFGSF_yaw()
{
	// this flag must be false when we start
	_ahrs_ekf_gsf_tilt_aligned = false;

	// these objects are initialised in initialise() before being used internally, but can be reported for logging before then
	memset(&_ahrs_ekf_gsf, 0, sizeof(_ahrs_ekf_gsf));
	memset(&_ekf_gsf, 0, sizeof(_ekf_gsf));
	_gsf_yaw = 0.0f;
	_ahrs_accel.zero();
}

void EKFGSF_yaw::update(const imuSample& imu_sample,
			bool run_EKF,			// set to true when flying or movement is suitable for yaw estimation
			float airspeed,			// true airspeed used for centripetal accel compensation - set to 0 when not required.
			const Vector3f &imu_gyro_bias)  // estimated rate gyro bias (rad/sec)
{
	// copy to class variables
	_delta_ang = imu_sample.delta_ang;
	_delta_vel = imu_sample.delta_vel;
	_delta_ang_dt = imu_sample.delta_ang_dt;
	_delta_vel_dt = imu_sample.delta_vel_dt;
	_run_ekf_gsf = run_EKF;
	_true_airspeed = airspeed;

	// to reduce effect of vibration, filter using an LPF whose time constant is 1/10 of the AHRS tilt correction time constant
	const float filter_coef = fminf(10.0f * _delta_vel_dt * _tilt_gain, 1.0f);
	const Vector3f accel = _delta_vel / fmaxf(_delta_vel_dt, 0.001f);
	_ahrs_accel = _ahrs_accel * (1.0f - filter_coef) + accel * filter_coef;

	// Initialise states first time
	if (!_ahrs_ekf_gsf_tilt_aligned) {
		// check for excessive acceleration to reduce likelihood of large initial roll/pitch errors
		// due to vehicle movement
		const float accel_norm_sq = accel.norm_squared();
		const float upper_accel_limit = CONSTANTS_ONE_G * 1.1f;
		const float lower_accel_limit = CONSTANTS_ONE_G * 0.9f;
		const bool ok_to_align = (accel_norm_sq > sq(lower_accel_limit)) && (accel_norm_sq < sq(upper_accel_limit));
		if (ok_to_align) {
			initialiseEKFGSF();
			ahrsAlignTilt();
			_ahrs_ekf_gsf_tilt_aligned = true;
		}
		return;
	}

	// calculate common values used by the AHRS complementary filter models
	_ahrs_accel_norm = _ahrs_accel.norm();

	// AHRS prediction cycle for each model - this always runs
	_ahrs_accel_fusion_gain = ahrsCalcAccelGain();
	for (uint8_t model_index = 0; model_index < N_MODELS_EKFGSF; model_index ++) {
		predictEKF(model_index);
	}

	// The 3-state EKF models only run when flying to avoid corrupted estimates due to operator handling and GPS interference
	if (_run_ekf_gsf && _vel_data_updated) {
		if (!_ekf_gsf_vel_fuse_started) {
			initialiseEKFGSF();
			ahrsAlignYaw();
			// Initialise to gyro bias estimate from main filter because there could be a large
			// uncorrected rate gyro bias error about the gravity vector
			for (uint8_t model_index = 0; model_index < N_MODELS_EKFGSF; model_index ++) {
				_ahrs_ekf_gsf[model_index].gyro_bias = imu_gyro_bias;
			}
			_ekf_gsf_vel_fuse_started = true;
		} else {
			bool bad_update = false;
			for (uint8_t model_index = 0; model_index < N_MODELS_EKFGSF; model_index ++) {
				// subsequent measurements are fused as direct state observations
				if (!updateEKF(model_index)) {
					bad_update = true;
				}
			}

			if (!bad_update) {
				float total_weight = 0.0f;
				// calculate weighting for each model assuming a normal distribution
				const float min_weight = 1e-5f;
				uint8_t n_weight_clips = 0;
				for (uint8_t model_index = 0; model_index < N_MODELS_EKFGSF; model_index ++) {
					_model_weights(model_index) = gaussianDensity(model_index) * _model_weights(model_index);
					if (_model_weights(model_index) < min_weight) {
						n_weight_clips++;
						_model_weights(model_index) = min_weight;
					}
					total_weight += _model_weights(model_index);
				}

				// normalise the weighting function
				if (n_weight_clips < N_MODELS_EKFGSF) {
					_model_weights /= total_weight;
				} else {
					// all weights have collapsed due to excessive innovation variances so reset filters
					initialiseEKFGSF();
				}
			}
		}
	} else if (_ekf_gsf_vel_fuse_started && !_run_ekf_gsf) {
		// wait to fly again
		_ekf_gsf_vel_fuse_started = false;
	}

	// Calculate a composite yaw vector as a weighted average of the states for each model.
	// To avoid issues with angle wrapping, the yaw state is converted to a vector with length
	// equal to the weighting value before it is summed.
	Vector2f yaw_vector;
	for (uint8_t model_index = 0; model_index < N_MODELS_EKFGSF; model_index ++) {
		yaw_vector(0) += _model_weights(model_index) * cosf(_ekf_gsf[model_index].X(2));
		yaw_vector(1) += _model_weights(model_index) * sinf(_ekf_gsf[model_index].X(2));
	}
	_gsf_yaw = atan2f(yaw_vector(1),yaw_vector(0));

	// calculate a composite variance for the yaw state from a weighted average of the variance for each model
	// models with larger innovations are weighted less
	_gsf_yaw_variance = 0.0f;
	for (uint8_t model_index = 0; model_index < N_MODELS_EKFGSF; model_index ++) {
		const float yaw_delta = wrap_pi(_ekf_gsf[model_index].X(2) - _gsf_yaw);
		_gsf_yaw_variance += _model_weights(model_index) * (_ekf_gsf[model_index].P(2,2) + yaw_delta * yaw_delta);
	}

	// prevent the same velocity data being used more than once
	_vel_data_updated = false;
}

void EKFGSF_yaw::ahrsPredict(const uint8_t model_index)
{
	// generate attitude solution using simple complementary filter for the selected model

	const Vector3f ang_rate = _delta_ang / fmaxf(_delta_ang_dt, 0.001f) - _ahrs_ekf_gsf[model_index].gyro_bias;

	const Dcmf R_to_body = _ahrs_ekf_gsf[model_index].R.transpose();
	const Vector3f gravity_direction_bf = R_to_body.col(2);

	// Perform angular rate correction using accel data and reduce correction as accel magnitude moves away from 1 g (reduces drift when vehicle picked up and moved).
	// During fixed wing flight, compensate for centripetal acceleration assuming coordinated turns and X axis forward
	Vector3f tilt_correction;
	if (_ahrs_accel_fusion_gain > 0.0f) {

		Vector3f accel = _ahrs_accel;

		if (_true_airspeed > FLT_EPSILON) {
			// Calculate body frame centripetal acceleration with assumption X axis is aligned with the airspeed vector
			// Use cross product of body rate and body frame airspeed vector
			const Vector3f centripetal_accel_bf = Vector3f(0.0f, _true_airspeed * ang_rate(2), - _true_airspeed * ang_rate(1));

			// correct measured accel for centripetal acceleration
			accel -= centripetal_accel_bf;
		}

		tilt_correction = (gravity_direction_bf % accel) * _ahrs_accel_fusion_gain / _ahrs_accel_norm;

	}

	// Gyro bias estimation
	constexpr float gyro_bias_limit = 0.05f;
	const float spinRate = ang_rate.length();
	if (spinRate < 0.175f) {
		_ahrs_ekf_gsf[model_index].gyro_bias -= tilt_correction * (_gyro_bias_gain * _delta_ang_dt);
		_ahrs_ekf_gsf[model_index].gyro_bias = matrix::constrain(_ahrs_ekf_gsf[model_index].gyro_bias, -gyro_bias_limit, gyro_bias_limit);
	}

	// delta angle from previous to current frame
	const Vector3f delta_angle_corrected = _delta_ang + (tilt_correction - _ahrs_ekf_gsf[model_index].gyro_bias) * _delta_ang_dt;

	// Apply delta angle to rotation matrix
	_ahrs_ekf_gsf[model_index].R = ahrsPredictRotMat(_ahrs_ekf_gsf[model_index].R, delta_angle_corrected);

}

void EKFGSF_yaw::ahrsAlignTilt()
{
	// Rotation matrix is constructed directly from acceleration measurement and will be the same for
	// all models so only need to calculate it once. Assumptions are:
	// 1) Yaw angle is zero - yaw is aligned later for each model when velocity fusion commences.
	// 2) The vehicle is not accelerating so all of the measured acceleration is due to gravity.

	// Calculate earth frame Down axis unit vector rotated into body frame
	const Vector3f down_in_bf = -_delta_vel.normalized();

	// Calculate earth frame North axis unit vector rotated into body frame, orthogonal to 'down_in_bf'
	const Vector3f i_vec_bf(1.0f,0.0f,0.0f);
	Vector3f north_in_bf = i_vec_bf - down_in_bf * (i_vec_bf.dot(down_in_bf));
	north_in_bf.normalize();

	// Calculate earth frame East axis unit vector rotated into body frame, orthogonal to 'down_in_bf' and 'north_in_bf'
	const Vector3f east_in_bf = down_in_bf % north_in_bf;

	// Each column in a rotation matrix from earth frame to body frame represents the projection of the
	// corresponding earth frame unit vector rotated into the body frame, eg 'north_in_bf' would be the first column.
	// We need the rotation matrix from body frame to earth frame so the earth frame unit vectors rotated into body
	// frame are copied into corresponding rows instead.
	Dcmf R;
	R.setRow(0, north_in_bf);
	R.setRow(1, east_in_bf);
	R.setRow(2, down_in_bf);

	for (uint8_t model_index = 0; model_index < N_MODELS_EKFGSF; model_index++) {
		_ahrs_ekf_gsf[model_index].R = R;
	}
}

void EKFGSF_yaw::ahrsAlignYaw()
{
	// Align yaw angle for each model
	for (uint8_t model_index = 0; model_index < N_MODELS_EKFGSF; model_index++) {
		Dcmf& R = _ahrs_ekf_gsf[model_index].R;
		const float yaw = wrap_pi(_ekf_gsf[model_index].X(2));
		R = updateYawInRotMat(yaw, R);

		_ahrs_ekf_gsf[model_index].aligned = true;
	}
}

void EKFGSF_yaw::predictEKF(const uint8_t model_index)
{
	// generate an attitude reference using IMU data
	ahrsPredict(model_index);

	// we don't start running the EKF part of the algorithm until there are regular velocity observations
	if (!_ekf_gsf_vel_fuse_started) {
		return;
	}

	// Calculate the yaw state using a projection onto the horizontal that avoids gimbal lock
	const Dcmf& R = _ahrs_ekf_gsf[model_index].R;
	_ekf_gsf[model_index].X(2) = shouldUse321RotationSequence(R) ?
					getEuler321Yaw(R) :
					getEuler312Yaw(R);

	// calculate delta velocity in a horizontal front-right frame
	const Vector3f del_vel_NED = _ahrs_ekf_gsf[model_index].R * _delta_vel;
	const float cos_yaw = cosf(_ekf_gsf[model_index].X(2));
	const float sin_yaw = sinf(_ekf_gsf[model_index].X(2));
	const float dvx =   del_vel_NED(0) * cos_yaw + del_vel_NED(1) * sin_yaw;
	const float dvy = - del_vel_NED(0) * sin_yaw + del_vel_NED(1) * cos_yaw;

	// sum delta velocities in earth frame:
	_ekf_gsf[model_index].X(0) += del_vel_NED(0);
	_ekf_gsf[model_index].X(1) += del_vel_NED(1);

	// predict covariance - equations generated using EKF/python/gsf_ekf_yaw_estimator/main.py

	// Local short variable name copies required for readability
	const float &P00 = _ekf_gsf[model_index].P(0,0);
	const float &P01 = _ekf_gsf[model_index].P(0,1);
	const float &P02 = _ekf_gsf[model_index].P(0,2);
	const float &P11 = _ekf_gsf[model_index].P(1,1);
	const float &P12 = _ekf_gsf[model_index].P(1,2);
	const float &P22 = _ekf_gsf[model_index].P(2,2);
	const float &psi = _ekf_gsf[model_index].X(2);

	// Use fixed values for delta velocity and delta angle process noise variances
	const float dvxVar = sq(_accel_noise * _delta_vel_dt); // variance of forward delta velocity - (m/s)^2
	const float dvyVar = dvxVar; // variance of right delta velocity - (m/s)^2
	const float dazVar = sq(_gyro_noise * _delta_ang_dt); // variance of yaw delta angle - rad^2

	// optimized auto generated code from SymPy script src/lib/ecl/EKF/python/ekf_derivation/main.py
	const float S0 = cosf(psi);
	const float S1 = ecl::powf(S0, 2);
	const float S2 = sinf(psi);
	const float S3 = ecl::powf(S2, 2);
	const float S4 = S0*dvy + S2*dvx;
	const float S5 = P02 - P22*S4;
	const float S6 = S0*dvx - S2*dvy;
	const float S7 = S0*S2;
	const float S8 = P01 + S7*dvxVar - S7*dvyVar;
	const float S9 = P12 + P22*S6;

	_ekf_gsf[model_index].P(0,0) = P00 - P02*S4 + S1*dvxVar + S3*dvyVar - S4*S5;
	_ekf_gsf[model_index].P(0,1) = -P12*S4 + S5*S6 + S8;
	_ekf_gsf[model_index].P(1,1) = P11 + P12*S6 + S1*dvyVar + S3*dvxVar + S6*S9;
	_ekf_gsf[model_index].P(0,2) = S5;
	_ekf_gsf[model_index].P(1,2) = S9;
	_ekf_gsf[model_index].P(2,2) = P22 + dazVar;

	// covariance matrix is symmetrical, so copy upper half to lower half
	_ekf_gsf[model_index].P(1,0) = _ekf_gsf[model_index].P(0,1);
	_ekf_gsf[model_index].P(2,0) = _ekf_gsf[model_index].P(0,2);
	_ekf_gsf[model_index].P(2,1) = _ekf_gsf[model_index].P(1,2);

	// constrain variances
	const float min_var = 1e-6f;
	for (unsigned index = 0; index < 3; index++) {
		_ekf_gsf[model_index].P(index,index) = fmaxf(_ekf_gsf[model_index].P(index,index),min_var);
	}
}

// Update EKF states and covariance for specified model index using velocity measurement
bool EKFGSF_yaw::updateEKF(const uint8_t model_index)
{
	// set observation variance from accuracy estimate supplied by GPS and apply a sanity check minimum
	const float velObsVar = sq(fmaxf(_vel_accuracy, 0.01f));

	// calculate velocity observation innovations
	_ekf_gsf[model_index].innov(0) = _ekf_gsf[model_index].X(0) - _vel_NE(0);
	_ekf_gsf[model_index].innov(1) = _ekf_gsf[model_index].X(1) - _vel_NE(1);

	// Use temporary variables for covariance elements to reduce verbosity of auto-code expressions
	const float &P00 = _ekf_gsf[model_index].P(0,0);
	const float &P01 = _ekf_gsf[model_index].P(0,1);
	const float &P02 = _ekf_gsf[model_index].P(0,2);
	const float &P11 = _ekf_gsf[model_index].P(1,1);
	const float &P12 = _ekf_gsf[model_index].P(1,2);
	const float &P22 = _ekf_gsf[model_index].P(2,2);

	// optimized auto generated code from SymPy script src/lib/ecl/EKF/python/ekf_derivation/main.py
	const float t0 = ecl::powf(P01, 2);
	const float t1 = -t0;
	const float t2 = P00*P11 + P00*velObsVar + P11*velObsVar + t1 + ecl::powf(velObsVar, 2);
	if (fabsf(t2) < 1e-6f) {
		return false;
	}
	const float t3 = 1.0F/t2;
	const float t4 = P11 + velObsVar;
	const float t5 = P01*t3;
	const float t6 = -t5;
	const float t7 = P00 + velObsVar;
	const float t8 = P00*t4 + t1;
	const float t9 = t5*velObsVar;
	const float t10 = P11*t7;
	const float t11 = t1 + t10;
	const float t12 = P01*P12;
	const float t13 = P02*t4;
	const float t14 = P01*P02;
	const float t15 = P12*t7;
	const float t16 = t0*velObsVar;
	const float t17 = ecl::powf(t2, -2);
	const float t18 = t4*velObsVar + t8;
	const float t19 = t17*t18;
	const float t20 = t17*(t16 + t7*t8);
	const float t21 = t0 - t10;
	const float t22 = t17*t21;
	const float t23 = t14 - t15;
	const float t24 = P01*t23;
	const float t25 = t12 - t13;
	const float t26 = t16 - t21*t4;
	const float t27 = t17*t26;
	const float t28 = t11 + t7*velObsVar;
	const float t30 = t17*t28;
	const float t31 = P01*t25;
	const float t32 = t23*t4 + t31;
	const float t33 = t17*t32;
	const float t35 = t24 + t25*t7;
	const float t36 = t17*t35;

	_ekf_gsf[model_index].S_det_inverse = t3;

	_ekf_gsf[model_index].S_inverse(0,0) = t3*t4;
	_ekf_gsf[model_index].S_inverse(0,1) = t6;
	_ekf_gsf[model_index].S_inverse(1,1) = t3*t7;
	_ekf_gsf[model_index].S_inverse(1,0) = _ekf_gsf[model_index].S_inverse(0,1);

	matrix::Matrix<float, 3, 2> K;
	K(0,0) = t3*t8;
	K(1,0) = t9;
	K(2,0) = t3*(-t12 + t13);
	K(0,1) = t9;
	K(1,1) = t11*t3;
	K(2,1) = t3*(-t14 + t15);

	_ekf_gsf[model_index].P(0,0) = P00 - t16*t19 - t20*t8;
	_ekf_gsf[model_index].P(0,1) = P01*(t18*t22 - t20*velObsVar + 1);
	_ekf_gsf[model_index].P(1,1) = P11 - t16*t30 + t22*t26;
	_ekf_gsf[model_index].P(0,2) = P02 + t19*t24 + t20*t25;
	_ekf_gsf[model_index].P(1,2) = P12 + t23*t27 + t30*t31;
	_ekf_gsf[model_index].P(2,2) = P22 - t23*t33 - t25*t36;
	_ekf_gsf[model_index].P(1,0) = _ekf_gsf[model_index].P(0,1);
	_ekf_gsf[model_index].P(2,0) = _ekf_gsf[model_index].P(0,2);
	_ekf_gsf[model_index].P(2,1) = _ekf_gsf[model_index].P(1,2);

	// constrain variances
	const float min_var = 1e-6f;
	for (unsigned index = 0; index < 3; index++) {
		_ekf_gsf[model_index].P(index,index) = fmaxf(_ekf_gsf[model_index].P(index,index),min_var);
	}

	// test ratio = transpose(innovation) * inverse(innovation variance) * innovation = [1x2] * [2,2] * [2,1] = [1,1]
	const float test_ratio = _ekf_gsf[model_index].innov * (_ekf_gsf[model_index].S_inverse * _ekf_gsf[model_index].innov);

	// Perform a chi-square innovation consistency test and calculate a compression scale factor
	// that limits the magnitude of innovations to 5-sigma
	// If the test ratio is greater than 25 (5 Sigma) then reduce the length of the innovation vector to clip it at 5-Sigma
	// This protects from large measurement spikes
	const float innov_comp_scale_factor = test_ratio > 25.f ? sqrtf(25.0f / test_ratio) : 1.f;

	// Correct the state vector and capture the change in yaw angle
	const float oldYaw = _ekf_gsf[model_index].X(2);

	_ekf_gsf[model_index].X -= (K * _ekf_gsf[model_index].innov) * innov_comp_scale_factor;

	const float yawDelta = _ekf_gsf[model_index].X(2) - oldYaw;

	// apply the change in yaw angle to the AHRS
	// take advantage of sparseness in the yaw rotation matrix
	const float cosYaw = cosf(yawDelta);
	const float sinYaw = sinf(yawDelta);
	const float R_prev00 = _ahrs_ekf_gsf[model_index].R(0, 0);
	const float R_prev01 = _ahrs_ekf_gsf[model_index].R(0, 1);
	const float R_prev02 = _ahrs_ekf_gsf[model_index].R(0, 2);

	_ahrs_ekf_gsf[model_index].R(0, 0) = R_prev00 * cosYaw - _ahrs_ekf_gsf[model_index].R(1, 0) * sinYaw;
	_ahrs_ekf_gsf[model_index].R(0, 1) = R_prev01 * cosYaw - _ahrs_ekf_gsf[model_index].R(1, 1) * sinYaw;
	_ahrs_ekf_gsf[model_index].R(0, 2) = R_prev02 * cosYaw - _ahrs_ekf_gsf[model_index].R(1, 2) * sinYaw;
	_ahrs_ekf_gsf[model_index].R(1, 0) = R_prev00 * sinYaw + _ahrs_ekf_gsf[model_index].R(1, 0) * cosYaw;
	_ahrs_ekf_gsf[model_index].R(1, 1) = R_prev01 * sinYaw + _ahrs_ekf_gsf[model_index].R(1, 1) * cosYaw;
	_ahrs_ekf_gsf[model_index].R(1, 2) = R_prev02 * sinYaw + _ahrs_ekf_gsf[model_index].R(1, 2) * cosYaw;

	return true;
}

void EKFGSF_yaw::initialiseEKFGSF()
{
	_gsf_yaw = 0.0f;
	_ekf_gsf_vel_fuse_started = false;
	_gsf_yaw_variance = _m_pi2 * _m_pi2;
	_model_weights.setAll(1.0f / (float)N_MODELS_EKFGSF);  // All filter models start with the same weight

	memset(&_ekf_gsf, 0, sizeof(_ekf_gsf));
	const float yaw_increment = 2.0f * _m_pi / (float)N_MODELS_EKFGSF;
	for (uint8_t model_index = 0; model_index < N_MODELS_EKFGSF; model_index++) {
		// evenly space initial yaw estimates in the region between +-Pi
		_ekf_gsf[model_index].X(2) = -_m_pi + (0.5f * yaw_increment) + ((float)model_index * yaw_increment);

		// take velocity states and corresponding variance from last measurement
		_ekf_gsf[model_index].X(0) = _vel_NE(0);
		_ekf_gsf[model_index].X(1) = _vel_NE(1);
		_ekf_gsf[model_index].P(0,0) = sq(_vel_accuracy);
		_ekf_gsf[model_index].P(1,1) = _ekf_gsf[model_index].P(0,0);

		// use half yaw interval for yaw uncertainty
		_ekf_gsf[model_index].P(2,2) = sq(0.5f * yaw_increment);
	}
}

float EKFGSF_yaw::gaussianDensity(const uint8_t model_index) const
{
	// calculate transpose(innovation) * inv(S) * innovation
	const float normDist = _ekf_gsf[model_index].innov.dot(_ekf_gsf[model_index].S_inverse * _ekf_gsf[model_index].innov);

	return _m_2pi_inv * sqrtf(_ekf_gsf[model_index].S_det_inverse) * expf(-0.5f * normDist);
}

bool EKFGSF_yaw::getLogData(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]) const
{
	if (_ekf_gsf_vel_fuse_started) {
		*yaw_composite = _gsf_yaw;
		*yaw_variance = _gsf_yaw_variance;
		for (uint8_t model_index = 0; model_index < N_MODELS_EKFGSF; model_index++) {
			yaw[model_index] = _ekf_gsf[model_index].X(2);
			innov_VN[model_index] = _ekf_gsf[model_index].innov(0);
			innov_VE[model_index] = _ekf_gsf[model_index].innov(1);
			weight[model_index] = _model_weights(model_index);
		}
		return true;
	}
	return false;
}

float EKFGSF_yaw::ahrsCalcAccelGain() const
{
	// Calculate the acceleration fusion gain using a continuous function that is unity at 1g and zero
	// at the min and max g value. Allow for more acceleration when flying as a fixed wing vehicle using centripetal
	// acceleration correction as higher and more sustained g will be experienced.
	// Use a quadratic instead of linear function to prevent vibration around 1g reducing the tilt correction effectiveness.
	// see https://www.desmos.com/calculator/dbqbxvnwfg

	float attenuation = 2.f;
	const bool centripetal_accel_compensation_enabled = (_true_airspeed > FLT_EPSILON);

	if (centripetal_accel_compensation_enabled
	    && _ahrs_accel_norm > CONSTANTS_ONE_G) {
		attenuation = 1.f;
	}

	const float delta_accel_g = (_ahrs_accel_norm - CONSTANTS_ONE_G) / CONSTANTS_ONE_G;
	return _tilt_gain * sq(1.f - math::min(attenuation * fabsf(delta_accel_g), 1.f));
}

Matrix3f EKFGSF_yaw::ahrsPredictRotMat(const Matrix3f &R, const Vector3f &g)
{
	Matrix3f ret = R;
	ret(0,0) += R(0,1) * g(2) - R(0,2) * g(1);
	ret(0,1) += R(0,2) * g(0) - R(0,0) * g(2);
	ret(0,2) += R(0,0) * g(1) - R(0,1) * g(0);
	ret(1,0) += R(1,1) * g(2) - R(1,2) * g(1);
	ret(1,1) += R(1,2) * g(0) - R(1,0) * g(2);
	ret(1,2) += R(1,0) * g(1) - R(1,1) * g(0);
	ret(2,0) += R(2,1) * g(2) - R(2,2) * g(1);
	ret(2,1) += R(2,2) * g(0) - R(2,0) * g(2);
	ret(2,2) += R(2,0) * g(1) - R(2,1) * g(0);

	// Renormalise rows
	for (uint8_t r = 0; r < 3; r++) {
		const float rowLengthSq = ret.row(r).norm_squared();
		if (rowLengthSq > FLT_EPSILON) {
			// Use linear approximation for inverse sqrt taking advantage of the row length being close to 1.0
			const float rowLengthInv = 1.5f - 0.5f * rowLengthSq;
			ret.row(r) *=  rowLengthInv;
		}
        }

	return ret;
}

bool EKFGSF_yaw::getYawData(float *yaw, float *yaw_variance) const
{
	if(_ekf_gsf_vel_fuse_started) {
		*yaw = _gsf_yaw;
		*yaw_variance = _gsf_yaw_variance;
		return true;
	}
	return false;
}

void EKFGSF_yaw::setVelocity(const Vector2f &velocity, float accuracy)
{
	_vel_NE = velocity;
	_vel_accuracy = accuracy;
	_vel_data_updated = true;
}