EKF: Convert magnetic field observation methods to use SymPy generated code (#879)

* EKF: Add comparison test for mag field fusion generated code

* EKF: convert mag field fusion to use SymPy generated code

* EKF: Add test comparison program for yaw fusion equations

* Stop setting 0 to 0

* Reduce if/else statement to only if

* EKF: more accurate implementation for sequential fusion of magnetometer data

* test: update change indicator

* Use matrix::SparseVector<float, 24, ...> for observation jacobian

* Adapt the auto code generation to allow for different bracket styles

* Add auto generated code for mag fusion

* Add generic computation of KHP

* Apply generic computation of KHP to mag fusion

* tests: update change indicator

* tests: update change indicator

Co-authored-by: kamilritz <kritz@ethz.ch>

EKF/ekf.h

@@ -52,6 +52,8 @@ public:
 	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;
@@ -664,6 +666,29 @@ private:
 
 	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;
+		float KH[H.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;
+	}
+
 	// 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);

EKF/mag_fusion.cpp

@@ -34,6 +34,7 @@
 /**
  * @file heading_fusion.cpp
  * Magnetometer fusion methods.
+ * Equations generated using EKF/python/ekf_derivation/main.py
  *
  * @author Roman Bast <bapstroman@gmail.com>
  * @author Paul Riseborough <p_riseborough@live.com.au>
@@ -47,29 +48,112 @@
 void Ekf::fuseMag()
 {
 	// assign intermediate variables
-	const float q0 = _state.quat_nominal(0);
-	const float q1 = _state.quat_nominal(1);
-	const float q2 = _state.quat_nominal(2);
-	const float q3 = _state.quat_nominal(3);
+	const float &q0 = _state.quat_nominal(0);
+	const float &q1 = _state.quat_nominal(1);
+	const float &q2 = _state.quat_nominal(2);
+	const float &q3 = _state.quat_nominal(3);
 
-	const float magN = _state.mag_I(0);
-	const float magE = _state.mag_I(1);
-	const float magD = _state.mag_I(2);
+	const float &magN = _state.mag_I(0);
+	const float &magE = _state.mag_I(1);
+	const float &magD = _state.mag_I(2);
 
 	// XYZ Measurement uncertainty. Need to consider timing errors for fast rotations
 	const float R_MAG = sq(fmaxf(_params.mag_noise, 0.0f));
 
-	// intermediate variables from algebraic optimisation
-	float SH_MAG[9];
-	SH_MAG[0] = 2.0f*magD*q3 + 2.0f*magE*q2 + 2.0f*magN*q1;
-	SH_MAG[1] = 2.0f*magD*q0 - 2.0f*magE*q1 + 2.0f*magN*q2;
-	SH_MAG[2] = 2.0f*magD*q1 + 2.0f*magE*q0 - 2.0f*magN*q3;
-	SH_MAG[3] = sq(q3);
-	SH_MAG[4] = sq(q2);
-	SH_MAG[5] = sq(q1);
-	SH_MAG[6] = sq(q0);
-	SH_MAG[7] = 2.0f*magN*q0;
-	SH_MAG[8] = 2.0f*magE*q3;
+	// calculate intermediate variables used for X axis innovation variance, observation Jacobians and Kalman gains
+	const char* numerical_error_covariance_reset_string = "numerical error - covariance reset";
+	const float HKX0 = -magD*q2 + magE*q3 + magN*q0;
+	const float HKX1 = magD*q3 + magE*q2 + magN*q1;
+	const float HKX2 = magE*q1;
+	const float HKX3 = magD*q0;
+	const float HKX4 = magN*q2;
+	const float HKX5 = magD*q1 + magE*q0 - magN*q3;
+	const float HKX6 = powf(q0, 2) + powf(q1, 2) - powf(q2, 2) - powf(q3, 2);
+	const float HKX7 = q0*q3 + q1*q2;
+	const float HKX8 = q1*q3;
+	const float HKX9 = q0*q2;
+	const float HKX10 = 2*HKX7;
+	const float HKX11 = -2*HKX8 + 2*HKX9;
+	const float HKX12 = 2*HKX1;
+	const float HKX13 = 2*HKX0;
+	const float HKX14 = -2*HKX2 + 2*HKX3 + 2*HKX4;
+	const float HKX15 = 2*HKX5;
+	const float HKX16 = HKX10*P(0,17) - HKX11*P(0,18) + HKX12*P(0,1) + HKX13*P(0,0) - HKX14*P(0,2) + HKX15*P(0,3) + HKX6*P(0,16) + P(0,19);
+	const float HKX17 = HKX10*P(16,17) - HKX11*P(16,18) + HKX12*P(1,16) + HKX13*P(0,16) - HKX14*P(2,16) + HKX15*P(3,16) + HKX6*P(16,16) + P(16,19);
+	const float HKX18 = HKX10*P(17,18) - HKX11*P(18,18) + HKX12*P(1,18) + HKX13*P(0,18) - HKX14*P(2,18) + HKX15*P(3,18) + HKX6*P(16,18) + P(18,19);
+	const float HKX19 = HKX10*P(2,17) - HKX11*P(2,18) + HKX12*P(1,2) + HKX13*P(0,2) - HKX14*P(2,2) + HKX15*P(2,3) + HKX6*P(2,16) + P(2,19);
+	const float HKX20 = HKX10*P(17,17) - HKX11*P(17,18) + HKX12*P(1,17) + HKX13*P(0,17) - HKX14*P(2,17) + HKX15*P(3,17) + HKX6*P(16,17) + P(17,19);
+	const float HKX21 = HKX10*P(3,17) - HKX11*P(3,18) + HKX12*P(1,3) + HKX13*P(0,3) - HKX14*P(2,3) + HKX15*P(3,3) + HKX6*P(3,16) + P(3,19);
+	const float HKX22 = HKX10*P(1,17) - HKX11*P(1,18) + HKX12*P(1,1) + HKX13*P(0,1) - HKX14*P(1,2) + HKX15*P(1,3) + HKX6*P(1,16) + P(1,19);
+	const float HKX23 = HKX10*P(17,19) - HKX11*P(18,19) + HKX12*P(1,19) + HKX13*P(0,19) - HKX14*P(2,19) + HKX15*P(3,19) + HKX6*P(16,19) + P(19,19);
+
+	_mag_innov_var(0) = HKX10*HKX20 - HKX11*HKX18 + HKX12*HKX22 + HKX13*HKX16 - HKX14*HKX19 + HKX15*HKX21 + HKX17*HKX6 + HKX23 + R_MAG;
+
+	if (_mag_innov_var(0) < R_MAG) {
+		// the innovation variance contribution from the state covariances is negative which means the covariance matrix is badly conditioned
+		_fault_status.flags.bad_mag_x = true;
+
+		// we need to re-initialise covariances and abort this fusion step
+		resetMagRelatedCovariances();
+		ECL_ERR("magX %s", numerical_error_covariance_reset_string);
+		return;
+	}
+
+	_fault_status.flags.bad_mag_x = false;
+
+	const float HKX24 = 1.0F/_mag_innov_var(0);
+
+	// intermediate variables for calculation of innovations variances for Y and Z axes
+	// don't calculate all terms needed for observation jacobians and Kalman gains because
+	// these will have to be recalculated when the X and Y axes are fused
+	const float IV0 = q0*q1;
+	const float IV1 = q2*q3;
+	const float IV2 = 2*IV0 + 2*IV1;
+	const float IV3 = 2*q0*q3 - 2*q1*q2;
+	const float IV4 = 2*magD*q3 + 2*magE*q2 + 2*magN*q1;
+	const float IV5 = 2*magD*q1 + 2*magE*q0 - 2*magN*q3;
+	const float IV6 = 2*magD*q0 - 2*magE*q1 + 2*magN*q2;
+	const float IV7 = -2*magD*q2 + 2*magE*q3 + 2*magN*q0;
+	const float IV8 = powf(q2, 2);
+	const float IV9 = powf(q3, 2);
+	const float IV10 = powf(q0, 2) - powf(q1, 2);
+	const float IV11 = IV10 + IV8 - IV9;
+	const float IV12 = IV7*P(2,3);
+	const float IV13 = IV5*P(0,1);
+	const float IV14 = IV6*P(0,1);
+	const float IV15 = IV4*P(2,3);
+	const float IV16 = 2*q0*q2 + 2*q1*q3;
+	const float IV17 = 2*IV0 - 2*IV1;
+	const float IV18 = IV10 - IV8 + IV9;
+
+	_mag_innov_var(1) = IV11*P(17,20) + IV11*(IV11*P(17,17) + IV2*P(17,18) - IV3*P(16,17) + IV4*P(2,17) + IV5*P(0,17) + IV6*P(1,17) - IV7*P(3,17) + P(17,20)) + IV2*P(18,20) + IV2*(IV11*P(17,18) + IV2*P(18,18) - IV3*P(16,18) + IV4*P(2,18) + IV5*P(0,18) + IV6*P(1,18) - IV7*P(3,18) + P(18,20)) - IV3*P(16,20) - IV3*(IV11*P(16,17) + IV2*P(16,18) - IV3*P(16,16) + IV4*P(2,16) + IV5*P(0,16) + IV6*P(1,16) - IV7*P(3,16) + P(16,20)) + IV4*P(2,20) + IV4*(IV11*P(2,17) - IV12 + IV2*P(2,18) - IV3*P(2,16) + IV4*P(2,2) + IV5*P(0,2) + IV6*P(1,2) + P(2,20)) + IV5*P(0,20) + IV5*(IV11*P(0,17) + IV14 + IV2*P(0,18) - IV3*P(0,16) + IV4*P(0,2) + IV5*P(0,0) - IV7*P(0,3) + P(0,20)) + IV6*P(1,20) + IV6*(IV11*P(1,17) + IV13 + IV2*P(1,18) - IV3*P(1,16) + IV4*P(1,2) + IV6*P(1,1) - IV7*P(1,3) + P(1,20)) - IV7*P(3,20) - IV7*(IV11*P(3,17) + IV15 + IV2*P(3,18) - IV3*P(3,16) + IV5*P(0,3) + IV6*P(1,3) - IV7*P(3,3) + P(3,20)) + P(20,20) + R_MAG;
+	_mag_innov_var(2) = IV16*P(16,21) + IV16*(IV16*P(16,16) - IV17*P(16,17) + IV18*P(16,18) + IV4*P(3,16) - IV5*P(1,16) + IV6*P(0,16) + IV7*P(2,16) + P(16,21)) - IV17*P(17,21) - IV17*(IV16*P(16,17) - IV17*P(17,17) + IV18*P(17,18) + IV4*P(3,17) - IV5*P(1,17) + IV6*P(0,17) + IV7*P(2,17) + P(17,21)) + IV18*P(18,21) + IV18*(IV16*P(16,18) - IV17*P(17,18) + IV18*P(18,18) + IV4*P(3,18) - IV5*P(1,18) + IV6*P(0,18) + IV7*P(2,18) + P(18,21)) + IV4*P(3,21) + IV4*(IV12 + IV16*P(3,16) - IV17*P(3,17) + IV18*P(3,18) + IV4*P(3,3) - IV5*P(1,3) + IV6*P(0,3) + P(3,21)) - IV5*P(1,21) - IV5*(IV14 + IV16*P(1,16) - IV17*P(1,17) + IV18*P(1,18) + IV4*P(1,3) - IV5*P(1,1) + IV7*P(1,2) + P(1,21)) + IV6*P(0,21) + IV6*(-IV13 + IV16*P(0,16) - IV17*P(0,17) + IV18*P(0,18) + IV4*P(0,3) + IV6*P(0,0) + IV7*P(0,2) + P(0,21)) + IV7*P(2,21) + IV7*(IV15 + IV16*P(2,16) - IV17*P(2,17) + IV18*P(2,18) - IV5*P(1,2) + IV6*P(0,2) + IV7*P(2,2) + P(2,21)) + P(21,21) + R_MAG;
+
+	// chedk innovation variances for being badly conditioned
+
+	if (_mag_innov_var(1) < R_MAG) {
+		// the innovation variance contribution from the state covariances is negtive which means the covariance matrix is badly conditioned
+		_fault_status.flags.bad_mag_y = true;
+
+		// we need to re-initialise covariances and abort this fusion step
+		resetMagRelatedCovariances();
+		ECL_ERR("magY %s", numerical_error_covariance_reset_string);
+		return;
+	}
+
+	_fault_status.flags.bad_mag_y = false;
+
+	if (_mag_innov_var(2) < R_MAG) {
+		// the innovation variance contribution from the state covariances is negative which means the covariance matrix is badly conditioned
+		_fault_status.flags.bad_mag_z = true;
+
+		// we need to re-initialise covariances and abort this fusion step
+		resetMagRelatedCovariances();
+		ECL_ERR("magZ %s", numerical_error_covariance_reset_string);
+		return;
+	}
+
+	_fault_status.flags.bad_mag_z = false;
 
 	// rotate magnetometer earth field state into body frame
 	const Dcmf R_to_body = quatToInverseRotMat(_state.quat_nominal);
@@ -84,64 +168,6 @@ void Ekf::fuseMag()
 		_mag_innov(2) = 0.0f;
 	}
 
-	// X axis innovation variance
-	_mag_innov_var(0) = (P(19,19) + R_MAG + P(1,19)*SH_MAG[0] - P(2,19)*SH_MAG[1] + P(3,19)*SH_MAG[2] - P(16,19)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + (2.0f*q0*q3 + 2.0f*q1*q2)*(P(19,17) + P(1,17)*SH_MAG[0] - P(2,17)*SH_MAG[1] + P(3,17)*SH_MAG[2] - P(16,17)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P(17,17)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,17)*(2.0f*q0*q2 - 2.0f*q1*q3) + P(0,17)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - (2.0f*q0*q2 - 2.0f*q1*q3)*(P(19,18) + P(1,18)*SH_MAG[0] - P(2,18)*SH_MAG[1] + P(3,18)*SH_MAG[2] - P(16,18)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P(17,18)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,18)*(2.0f*q0*q2 - 2.0f*q1*q3) + P(0,18)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + (SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)*(P(19,0) + P(1,0)*SH_MAG[0] - P(2,0)*SH_MAG[1] + P(3,0)*SH_MAG[2] - P(16,0)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P(17,0)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,0)*(2.0f*q0*q2 - 2.0f*q1*q3) + P(0,0)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + P(17,19)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,19)*(2.0f*q0*q2 - 2.0f*q1*q3) + SH_MAG[0]*(P(19,1) + P(1,1)*SH_MAG[0] - P(2,1)*SH_MAG[1] + P(3,1)*SH_MAG[2] - P(16,1)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P(17,1)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,1)*(2.0f*q0*q2 - 2.0f*q1*q3) + P(0,1)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - SH_MAG[1]*(P(19,2) + P(1,2)*SH_MAG[0] - P(2,2)*SH_MAG[1] + P(3,2)*SH_MAG[2] - P(16,2)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P(17,2)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,2)*(2.0f*q0*q2 - 2.0f*q1*q3) + P(0,2)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + SH_MAG[2]*(P(19,3) + P(1,3)*SH_MAG[0] - P(2,3)*SH_MAG[1] + P(3,3)*SH_MAG[2] - P(16,3)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P(17,3)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,3)*(2.0f*q0*q2 - 2.0f*q1*q3) + P(0,3)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - (SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6])*(P(19,16) + P(1,16)*SH_MAG[0] - P(2,16)*SH_MAG[1] + P(3,16)*SH_MAG[2] - P(16,16)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P(17,16)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,16)*(2.0f*q0*q2 - 2.0f*q1*q3) + P(0,16)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + P(0,19)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2));
-	// check for a badly conditioned covariance matrix
-	const char* numerical_error_covariance_reset_string = "numerical error - covariance reset";
-
-	if (_mag_innov_var(0) >= R_MAG) {
-		// the innovation variance contribution from the state covariances is non-negative - no fault
-		_fault_status.flags.bad_mag_x = false;
-
-	} else {
-		// the innovation variance contribution from the state covariances is negative which means the covariance matrix is badly conditioned
-		_fault_status.flags.bad_mag_x = true;
-
-		// we need to re-initialise covariances and abort this fusion step
-		resetMagRelatedCovariances();
-		ECL_ERR("magX %s", numerical_error_covariance_reset_string);
-		return;
-
-	}
-
-	// Y axis innovation variance
-	_mag_innov_var(1) = (P(20,20) + R_MAG + P(0,20)*SH_MAG[2] + P(1,20)*SH_MAG[1] + P(2,20)*SH_MAG[0] - P(17,20)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - (2.0f*q0*q3 - 2.0f*q1*q2)*(P(20,16) + P(0,16)*SH_MAG[2] + P(1,16)*SH_MAG[1] + P(2,16)*SH_MAG[0] - P(17,16)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P(16,16)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,16)*(2.0f*q0*q1 + 2.0f*q2*q3) - P(3,16)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + (2.0f*q0*q1 + 2.0f*q2*q3)*(P(20,18) + P(0,18)*SH_MAG[2] + P(1,18)*SH_MAG[1] + P(2,18)*SH_MAG[0] - P(17,18)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P(16,18)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,18)*(2.0f*q0*q1 + 2.0f*q2*q3) - P(3,18)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - (SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)*(P(20,3) + P(0,3)*SH_MAG[2] + P(1,3)*SH_MAG[1] + P(2,3)*SH_MAG[0] - P(17,3)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P(16,3)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,3)*(2.0f*q0*q1 + 2.0f*q2*q3) - P(3,3)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - P(16,20)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,20)*(2.0f*q0*q1 + 2.0f*q2*q3) + SH_MAG[2]*(P(20,0) + P(0,0)*SH_MAG[2] + P(1,0)*SH_MAG[1] + P(2,0)*SH_MAG[0] - P(17,0)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P(16,0)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,0)*(2.0f*q0*q1 + 2.0f*q2*q3) - P(3,0)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + SH_MAG[1]*(P(20,1) + P(0,1)*SH_MAG[2] + P(1,1)*SH_MAG[1] + P(2,1)*SH_MAG[0] - P(17,1)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P(16,1)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,1)*(2.0f*q0*q1 + 2.0f*q2*q3) - P(3,1)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + SH_MAG[0]*(P(20,2) + P(0,2)*SH_MAG[2] + P(1,2)*SH_MAG[1] + P(2,2)*SH_MAG[0] - P(17,2)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P(16,2)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,2)*(2.0f*q0*q1 + 2.0f*q2*q3) - P(3,2)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - (SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6])*(P(20,17) + P(0,17)*SH_MAG[2] + P(1,17)*SH_MAG[1] + P(2,17)*SH_MAG[0] - P(17,17)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P(16,17)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,17)*(2.0f*q0*q1 + 2.0f*q2*q3) - P(3,17)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - P(3,20)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2));
-
-	// check for a badly conditioned covariance matrix
-	if (_mag_innov_var(1) >= R_MAG) {
-		// the innovation variance contribution from the state covariances is non-negative - no fault
-		_fault_status.flags.bad_mag_y = false;
-
-	} else {
-		// the innovation variance contribution from the state covariances is negtive which means the covariance matrix is badly conditioned
-		_fault_status.flags.bad_mag_y = true;
-
-		// we need to re-initialise covariances and abort this fusion step
-		resetMagRelatedCovariances();
-		ECL_ERR("magY %s", numerical_error_covariance_reset_string);
-		return;
-
-	}
-
-	// Z axis innovation variance
-	_mag_innov_var(2) = (P(21,21) + R_MAG + P(0,21)*SH_MAG[1] - P(1,21)*SH_MAG[2] + P(3,21)*SH_MAG[0] + P(18,21)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + (2.0f*q0*q2 + 2.0f*q1*q3)*(P(21,16) + P(0,16)*SH_MAG[1] - P(1,16)*SH_MAG[2] + P(3,16)*SH_MAG[0] + P(18,16)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P(16,16)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,16)*(2.0f*q0*q1 - 2.0f*q2*q3) + P(2,16)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - (2.0f*q0*q1 - 2.0f*q2*q3)*(P(21,17) + P(0,17)*SH_MAG[1] - P(1,17)*SH_MAG[2] + P(3,17)*SH_MAG[0] + P(18,17)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P(16,17)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,17)*(2.0f*q0*q1 - 2.0f*q2*q3) + P(2,17)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + (SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)*(P(21,2) + P(0,2)*SH_MAG[1] - P(1,2)*SH_MAG[2] + P(3,2)*SH_MAG[0] + P(18,2)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P(16,2)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,2)*(2.0f*q0*q1 - 2.0f*q2*q3) + P(2,2)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + P(16,21)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,21)*(2.0f*q0*q1 - 2.0f*q2*q3) + SH_MAG[1]*(P(21,0) + P(0,0)*SH_MAG[1] - P(1,0)*SH_MAG[2] + P(3,0)*SH_MAG[0] + P(18,0)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P(16,0)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,0)*(2.0f*q0*q1 - 2.0f*q2*q3) + P(2,0)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - SH_MAG[2]*(P(21,1) + P(0,1)*SH_MAG[1] - P(1,1)*SH_MAG[2] + P(3,1)*SH_MAG[0] + P(18,1)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P(16,1)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,1)*(2.0f*q0*q1 - 2.0f*q2*q3) + P(2,1)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + SH_MAG[0]*(P(21,3) + P(0,3)*SH_MAG[1] - P(1,3)*SH_MAG[2] + P(3,3)*SH_MAG[0] + P(18,3)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P(16,3)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,3)*(2.0f*q0*q1 - 2.0f*q2*q3) + P(2,3)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + (SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6])*(P(21,18) + P(0,18)*SH_MAG[1] - P(1,18)*SH_MAG[2] + P(3,18)*SH_MAG[0] + P(18,18)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P(16,18)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,18)*(2.0f*q0*q1 - 2.0f*q2*q3) + P(2,18)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + P(2,21)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2));
-
-	// check for a badly conditioned covariance matrix
-	if (_mag_innov_var(2) >= R_MAG) {
-		// the innovation variance contribution from the state covariances is non-negative - no fault
-		_fault_status.flags.bad_mag_z = false;
-
-	} else {
-		// the innovation variance contribution from the state covariances is negative which means the covariance matrix is badly conditioned
-		_fault_status.flags.bad_mag_z = true;
-
-		// we need to re-initialise covariances and abort this fusion step
-		resetMagRelatedCovariances();
-		ECL_ERR("magZ %s", numerical_error_covariance_reset_string);
-		return;
-
-	}
-
 	// Perform an innovation consistency check and report the result
 	bool all_innovation_checks_passed = true;
 
@@ -170,7 +196,7 @@ void Ekf::fuseMag()
 	const bool update_all_states = ((_imu_sample_delayed.time_us - _flt_mag_align_start_time) > (uint64_t)5e6);
 
 	// Observation jacobian and Kalman gain vectors
-	Vector24f H_MAG;
+	SparseVector24f<0,1,2,3,16,17,18,19,20,21> Hfusion;
 	Vector24f Kfusion;
 
 	// update the states and covariance using sequential fusion of the magnetometer components
@@ -179,99 +205,114 @@ void Ekf::fuseMag()
 		// Calculate Kalman gains and observation jacobians
 		if (index == 0) {
 			// Calculate X axis observation jacobians
-			H_MAG.setZero();
-			H_MAG(0) = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
-			H_MAG(1) = SH_MAG[0];
-			H_MAG(2) = -SH_MAG[1];
-			H_MAG(3) = SH_MAG[2];
-			H_MAG(16) = SH_MAG[5] - SH_MAG[4] - SH_MAG[3] + SH_MAG[6];
-			H_MAG(17) = 2.0f*q0*q3 + 2.0f*q1*q2;
-			H_MAG(18) = 2.0f*q1*q3 - 2.0f*q0*q2;
-			H_MAG(19) = 1.0f;
+			Hfusion.at<0>() = 2*HKX0;
+			Hfusion.at<1>() = 2*HKX1;
+			Hfusion.at<2>() = 2*HKX2 - 2*HKX3 - 2*HKX4;
+			Hfusion.at<3>() = 2*HKX5;
+			Hfusion.at<16>() = HKX6;
+			Hfusion.at<17>() = 2*HKX7;
+			Hfusion.at<18>() = 2*HKX8 - 2*HKX9;
+			Hfusion.at<19>() = 1;
 
 			// Calculate X axis Kalman gains
-			float SK_MX[5];
-			SK_MX[0] = 1.0f / _mag_innov_var(0);
-			SK_MX[1] = SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6];
-			SK_MX[2] = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
-			SK_MX[3] = 2.0f*q0*q2 - 2.0f*q1*q3;
-			SK_MX[4] = 2.0f*q0*q3 + 2.0f*q1*q2;
-
 			if (update_all_states) {
-				Kfusion(0) = SK_MX[0]*(P(0,19) + P(0,1)*SH_MAG[0] - P(0,2)*SH_MAG[1] + P(0,3)*SH_MAG[2] + P(0,0)*SK_MX[2] - P(0,16)*SK_MX[1] + P(0,17)*SK_MX[4] - P(0,18)*SK_MX[3]);
-				Kfusion(1) = SK_MX[0]*(P(1,19) + P(1,1)*SH_MAG[0] - P(1,2)*SH_MAG[1] + P(1,3)*SH_MAG[2] + P(1,0)*SK_MX[2] - P(1,16)*SK_MX[1] + P(1,17)*SK_MX[4] - P(1,18)*SK_MX[3]);
-				Kfusion(2) = SK_MX[0]*(P(2,19) + P(2,1)*SH_MAG[0] - P(2,2)*SH_MAG[1] + P(2,3)*SH_MAG[2] + P(2,0)*SK_MX[2] - P(2,16)*SK_MX[1] + P(2,17)*SK_MX[4] - P(2,18)*SK_MX[3]);
-				Kfusion(3) = SK_MX[0]*(P(3,19) + P(3,1)*SH_MAG[0] - P(3,2)*SH_MAG[1] + P(3,3)*SH_MAG[2] + P(3,0)*SK_MX[2] - P(3,16)*SK_MX[1] + P(3,17)*SK_MX[4] - P(3,18)*SK_MX[3]);
-				Kfusion(4) = SK_MX[0]*(P(4,19) + P(4,1)*SH_MAG[0] - P(4,2)*SH_MAG[1] + P(4,3)*SH_MAG[2] + P(4,0)*SK_MX[2] - P(4,16)*SK_MX[1] + P(4,17)*SK_MX[4] - P(4,18)*SK_MX[3]);
-				Kfusion(5) = SK_MX[0]*(P(5,19) + P(5,1)*SH_MAG[0] - P(5,2)*SH_MAG[1] + P(5,3)*SH_MAG[2] + P(5,0)*SK_MX[2] - P(5,16)*SK_MX[1] + P(5,17)*SK_MX[4] - P(5,18)*SK_MX[3]);
-				Kfusion(6) = SK_MX[0]*(P(6,19) + P(6,1)*SH_MAG[0] - P(6,2)*SH_MAG[1] + P(6,3)*SH_MAG[2] + P(6,0)*SK_MX[2] - P(6,16)*SK_MX[1] + P(6,17)*SK_MX[4] - P(6,18)*SK_MX[3]);
-				Kfusion(7) = SK_MX[0]*(P(7,19) + P(7,1)*SH_MAG[0] - P(7,2)*SH_MAG[1] + P(7,3)*SH_MAG[2] + P(7,0)*SK_MX[2] - P(7,16)*SK_MX[1] + P(7,17)*SK_MX[4] - P(7,18)*SK_MX[3]);
-				Kfusion(8) = SK_MX[0]*(P(8,19) + P(8,1)*SH_MAG[0] - P(8,2)*SH_MAG[1] + P(8,3)*SH_MAG[2] + P(8,0)*SK_MX[2] - P(8,16)*SK_MX[1] + P(8,17)*SK_MX[4] - P(8,18)*SK_MX[3]);
-				Kfusion(9) = SK_MX[0]*(P(9,19) + P(9,1)*SH_MAG[0] - P(9,2)*SH_MAG[1] + P(9,3)*SH_MAG[2] + P(9,0)*SK_MX[2] - P(9,16)*SK_MX[1] + P(9,17)*SK_MX[4] - P(9,18)*SK_MX[3]);
-				Kfusion(10) = SK_MX[0]*(P(10,19) + P(10,1)*SH_MAG[0] - P(10,2)*SH_MAG[1] + P(10,3)*SH_MAG[2] + P(10,0)*SK_MX[2] - P(10,16)*SK_MX[1] + P(10,17)*SK_MX[4] - P(10,18)*SK_MX[3]);
-				Kfusion(11) = SK_MX[0]*(P(11,19) + P(11,1)*SH_MAG[0] - P(11,2)*SH_MAG[1] + P(11,3)*SH_MAG[2] + P(11,0)*SK_MX[2] - P(11,16)*SK_MX[1] + P(11,17)*SK_MX[4] - P(11,18)*SK_MX[3]);
-				Kfusion(12) = SK_MX[0]*(P(12,19) + P(12,1)*SH_MAG[0] - P(12,2)*SH_MAG[1] + P(12,3)*SH_MAG[2] + P(12,0)*SK_MX[2] - P(12,16)*SK_MX[1] + P(12,17)*SK_MX[4] - P(12,18)*SK_MX[3]);
-				Kfusion(13) = SK_MX[0]*(P(13,19) + P(13,1)*SH_MAG[0] - P(13,2)*SH_MAG[1] + P(13,3)*SH_MAG[2] + P(13,0)*SK_MX[2] - P(13,16)*SK_MX[1] + P(13,17)*SK_MX[4] - P(13,18)*SK_MX[3]);
-				Kfusion(14) = SK_MX[0]*(P(14,19) + P(14,1)*SH_MAG[0] - P(14,2)*SH_MAG[1] + P(14,3)*SH_MAG[2] + P(14,0)*SK_MX[2] - P(14,16)*SK_MX[1] + P(14,17)*SK_MX[4] - P(14,18)*SK_MX[3]);
-				Kfusion(15) = SK_MX[0]*(P(15,19) + P(15,1)*SH_MAG[0] - P(15,2)*SH_MAG[1] + P(15,3)*SH_MAG[2] + P(15,0)*SK_MX[2] - P(15,16)*SK_MX[1] + P(15,17)*SK_MX[4] - P(15,18)*SK_MX[3]);
-				Kfusion(22) = SK_MX[0]*(P(22,19) + P(22,1)*SH_MAG[0] - P(22,2)*SH_MAG[1] + P(22,3)*SH_MAG[2] + P(22,0)*SK_MX[2] - P(22,16)*SK_MX[1] + P(22,17)*SK_MX[4] - P(22,18)*SK_MX[3]);
-				Kfusion(23) = SK_MX[0]*(P(23,19) + P(23,1)*SH_MAG[0] - P(23,2)*SH_MAG[1] + P(23,3)*SH_MAG[2] + P(23,0)*SK_MX[2] - P(23,16)*SK_MX[1] + P(23,17)*SK_MX[4] - P(23,18)*SK_MX[3]);
+				Kfusion(0) = HKX16*HKX24;
+				Kfusion(1) = HKX22*HKX24;
+				Kfusion(2) = HKX19*HKX24;
+				Kfusion(3) = HKX21*HKX24;
+
+				for (unsigned row = 4; row <= 15; row++) {
+					Kfusion(row) = HKX24*(HKX10*P(row,17) - HKX11*P(row,18) + HKX12*P(1,row) + HKX13*P(0,row) - HKX14*P(2,row) + HKX15*P(3,row) + HKX6*P(row,16) + P(row,19));
+				}
+
+				for (unsigned row = 22; row <= 23; row++) {
+					Kfusion(row) = HKX24*(HKX10*P(17,row) - HKX11*P(18,row) + HKX12*P(1,row) + HKX13*P(0,row) - HKX14*P(2,row) + HKX15*P(3,row) + HKX6*P(16,row) + P(19,row));
+				}
 			}
 
-			Kfusion(16) = SK_MX[0]*(P(16,19) + P(16,1)*SH_MAG[0] - P(16,2)*SH_MAG[1] + P(16,3)*SH_MAG[2] + P(16,0)*SK_MX[2] - P(16,16)*SK_MX[1] + P(16,17)*SK_MX[4] - P(16,18)*SK_MX[3]);
-			Kfusion(17) = SK_MX[0]*(P(17,19) + P(17,1)*SH_MAG[0] - P(17,2)*SH_MAG[1] + P(17,3)*SH_MAG[2] + P(17,0)*SK_MX[2] - P(17,16)*SK_MX[1] + P(17,17)*SK_MX[4] - P(17,18)*SK_MX[3]);
-			Kfusion(18) = SK_MX[0]*(P(18,19) + P(18,1)*SH_MAG[0] - P(18,2)*SH_MAG[1] + P(18,3)*SH_MAG[2] + P(18,0)*SK_MX[2] - P(18,16)*SK_MX[1] + P(18,17)*SK_MX[4] - P(18,18)*SK_MX[3]);
-			Kfusion(19) = SK_MX[0]*(P(19,19) + P(19,1)*SH_MAG[0] - P(19,2)*SH_MAG[1] + P(19,3)*SH_MAG[2] + P(19,0)*SK_MX[2] - P(19,16)*SK_MX[1] + P(19,17)*SK_MX[4] - P(19,18)*SK_MX[3]);
-			Kfusion(20) = SK_MX[0]*(P(20,19) + P(20,1)*SH_MAG[0] - P(20,2)*SH_MAG[1] + P(20,3)*SH_MAG[2] + P(20,0)*SK_MX[2] - P(20,16)*SK_MX[1] + P(20,17)*SK_MX[4] - P(20,18)*SK_MX[3]);
-			Kfusion(21) = SK_MX[0]*(P(21,19) + P(21,1)*SH_MAG[0] - P(21,2)*SH_MAG[1] + P(21,3)*SH_MAG[2] + P(21,0)*SK_MX[2] - P(21,16)*SK_MX[1] + P(21,17)*SK_MX[4] - P(21,18)*SK_MX[3]);
+			Kfusion(16) = HKX17*HKX24;
+			Kfusion(17) = HKX20*HKX24;
+			Kfusion(18) = HKX18*HKX24;
+			Kfusion(19) = HKX23*HKX24;
+
+			for (unsigned row = 20; row <= 21; row++) {
+				Kfusion(row) = HKX24*(HKX10*P(17,row) - HKX11*P(18,row) + HKX12*P(1,row) + HKX13*P(0,row) - HKX14*P(2,row) + HKX15*P(3,row) + HKX6*P(16,row) + P(19,row));
+			}
 
 		} else if (index == 1) {
+
+			// recalculate innovation variance becasue states and covariances have changed due to previous fusion
+			const float HKY0 = magD*q1 + magE*q0 - magN*q3;
+			const float HKY1 = magD*q0 - magE*q1 + magN*q2;
+			const float HKY2 = magD*q3 + magE*q2 + magN*q1;
+			const float HKY3 = magD*q2;
+			const float HKY4 = magE*q3;
+			const float HKY5 = magN*q0;
+			const float HKY6 = q1*q2;
+			const float HKY7 = q0*q3;
+			const float HKY8 = powf(q0, 2) - powf(q1, 2) + powf(q2, 2) - powf(q3, 2);
+			const float HKY9 = q0*q1 + q2*q3;
+			const float HKY10 = 2*HKY9;
+			const float HKY11 = -2*HKY6 + 2*HKY7;
+			const float HKY12 = 2*HKY2;
+			const float HKY13 = 2*HKY0;
+			const float HKY14 = 2*HKY1;
+			const float HKY15 = -2*HKY3 + 2*HKY4 + 2*HKY5;
+			const float HKY16 = HKY10*P(0,18) - HKY11*P(0,16) + HKY12*P(0,2) + HKY13*P(0,0) + HKY14*P(0,1) - HKY15*P(0,3) + HKY8*P(0,17) + P(0,20);
+			const float HKY17 = HKY10*P(17,18) - HKY11*P(16,17) + HKY12*P(2,17) + HKY13*P(0,17) + HKY14*P(1,17) - HKY15*P(3,17) + HKY8*P(17,17) + P(17,20);
+			const float HKY18 = HKY10*P(16,18) - HKY11*P(16,16) + HKY12*P(2,16) + HKY13*P(0,16) + HKY14*P(1,16) - HKY15*P(3,16) + HKY8*P(16,17) + P(16,20);
+			const float HKY19 = HKY10*P(3,18) - HKY11*P(3,16) + HKY12*P(2,3) + HKY13*P(0,3) + HKY14*P(1,3) - HKY15*P(3,3) + HKY8*P(3,17) + P(3,20);
+			const float HKY20 = HKY10*P(18,18) - HKY11*P(16,18) + HKY12*P(2,18) + HKY13*P(0,18) + HKY14*P(1,18) - HKY15*P(3,18) + HKY8*P(17,18) + P(18,20);
+			const float HKY21 = HKY10*P(1,18) - HKY11*P(1,16) + HKY12*P(1,2) + HKY13*P(0,1) + HKY14*P(1,1) - HKY15*P(1,3) + HKY8*P(1,17) + P(1,20);
+			const float HKY22 = HKY10*P(2,18) - HKY11*P(2,16) + HKY12*P(2,2) + HKY13*P(0,2) + HKY14*P(1,2) - HKY15*P(2,3) + HKY8*P(2,17) + P(2,20);
+			const float HKY23 = HKY10*P(18,20) - HKY11*P(16,20) + HKY12*P(2,20) + HKY13*P(0,20) + HKY14*P(1,20) - HKY15*P(3,20) + HKY8*P(17,20) + P(20,20);
+
+			_mag_innov_var(1) = (HKY10*HKY20 - HKY11*HKY18 + HKY12*HKY22 + HKY13*HKY16 + HKY14*HKY21 - HKY15*HKY19 + HKY17*HKY8 + HKY23 + R_MAG);
+
+			if (_mag_innov_var(1) < R_MAG) {
+				// the innovation variance contribution from the state covariances is negative which means the covariance matrix is badly conditioned
+				_fault_status.flags.bad_mag_y = true;
+
+				// we need to re-initialise covariances and abort this fusion step
+				resetMagRelatedCovariances();
+				ECL_ERR("magY %s", numerical_error_covariance_reset_string);
+				return;
+			}
+			const float HKY24 = 1.0F/_mag_innov_var(1);
+
 			// Calculate Y axis observation jacobians
-			H_MAG.setZero();
-			H_MAG(0) = SH_MAG[2];
-			H_MAG(1) = SH_MAG[1];
-			H_MAG(2) = SH_MAG[0];
-			H_MAG(3) = 2.0f*magD*q2 - SH_MAG[8] - SH_MAG[7];
-			H_MAG(16) = 2.0f*q1*q2 - 2.0f*q0*q3;
-			H_MAG(17) = SH_MAG[4] - SH_MAG[3] - SH_MAG[5] + SH_MAG[6];
-			H_MAG(18) = 2.0f*q0*q1 + 2.0f*q2*q3;
-			H_MAG(20) = 1.0f;
+			Hfusion.setZero();
+			Hfusion.at<0>() = 2*HKY0;
+			Hfusion.at<1>() = 2*HKY1;
+			Hfusion.at<2>() = 2*HKY2;
+			Hfusion.at<3>() = 2*HKY3 - 2*HKY4 - 2*HKY5;
+			Hfusion.at<16>() = 2*HKY6 - 2*HKY7;
+			Hfusion.at<17>() = HKY8;
+			Hfusion.at<18>() = 2*HKY9;
+			Hfusion.at<20>() = 1;
 
 			// Calculate Y axis Kalman gains
-			float SK_MY[5];
-			SK_MY[0] = 1.0f / _mag_innov_var(1);
-			SK_MY[1] = SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6];
-			SK_MY[2] = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
-			SK_MY[3] = 2.0f*q0*q3 - 2.0f*q1*q2;
-			SK_MY[4] = 2.0f*q0*q1 + 2.0f*q2*q3;
-
 			if (update_all_states) {
-				Kfusion(0) = SK_MY[0]*(P(0,20) + P(0,0)*SH_MAG[2] + P(0,1)*SH_MAG[1] + P(0,2)*SH_MAG[0] - P(0,3)*SK_MY[2] - P(0,17)*SK_MY[1] - P(0,16)*SK_MY[3] + P(0,18)*SK_MY[4]);
-				Kfusion(1) = SK_MY[0]*(P(1,20) + P(1,0)*SH_MAG[2] + P(1,1)*SH_MAG[1] + P(1,2)*SH_MAG[0] - P(1,3)*SK_MY[2] - P(1,17)*SK_MY[1] - P(1,16)*SK_MY[3] + P(1,18)*SK_MY[4]);
-				Kfusion(2) = SK_MY[0]*(P(2,20) + P(2,0)*SH_MAG[2] + P(2,1)*SH_MAG[1] + P(2,2)*SH_MAG[0] - P(2,3)*SK_MY[2] - P(2,17)*SK_MY[1] - P(2,16)*SK_MY[3] + P(2,18)*SK_MY[4]);
-				Kfusion(3) = SK_MY[0]*(P(3,20) + P(3,0)*SH_MAG[2] + P(3,1)*SH_MAG[1] + P(3,2)*SH_MAG[0] - P(3,3)*SK_MY[2] - P(3,17)*SK_MY[1] - P(3,16)*SK_MY[3] + P(3,18)*SK_MY[4]);
-				Kfusion(4) = SK_MY[0]*(P(4,20) + P(4,0)*SH_MAG[2] + P(4,1)*SH_MAG[1] + P(4,2)*SH_MAG[0] - P(4,3)*SK_MY[2] - P(4,17)*SK_MY[1] - P(4,16)*SK_MY[3] + P(4,18)*SK_MY[4]);
-				Kfusion(5) = SK_MY[0]*(P(5,20) + P(5,0)*SH_MAG[2] + P(5,1)*SH_MAG[1] + P(5,2)*SH_MAG[0] - P(5,3)*SK_MY[2] - P(5,17)*SK_MY[1] - P(5,16)*SK_MY[3] + P(5,18)*SK_MY[4]);
-				Kfusion(6) = SK_MY[0]*(P(6,20) + P(6,0)*SH_MAG[2] + P(6,1)*SH_MAG[1] + P(6,2)*SH_MAG[0] - P(6,3)*SK_MY[2] - P(6,17)*SK_MY[1] - P(6,16)*SK_MY[3] + P(6,18)*SK_MY[4]);
-				Kfusion(7) = SK_MY[0]*(P(7,20) + P(7,0)*SH_MAG[2] + P(7,1)*SH_MAG[1] + P(7,2)*SH_MAG[0] - P(7,3)*SK_MY[2] - P(7,17)*SK_MY[1] - P(7,16)*SK_MY[3] + P(7,18)*SK_MY[4]);
-				Kfusion(8) = SK_MY[0]*(P(8,20) + P(8,0)*SH_MAG[2] + P(8,1)*SH_MAG[1] + P(8,2)*SH_MAG[0] - P(8,3)*SK_MY[2] - P(8,17)*SK_MY[1] - P(8,16)*SK_MY[3] + P(8,18)*SK_MY[4]);
-				Kfusion(9) = SK_MY[0]*(P(9,20) + P(9,0)*SH_MAG[2] + P(9,1)*SH_MAG[1] + P(9,2)*SH_MAG[0] - P(9,3)*SK_MY[2] - P(9,17)*SK_MY[1] - P(9,16)*SK_MY[3] + P(9,18)*SK_MY[4]);
-				Kfusion(10) = SK_MY[0]*(P(10,20) + P(10,0)*SH_MAG[2] + P(10,1)*SH_MAG[1] + P(10,2)*SH_MAG[0] - P(10,3)*SK_MY[2] - P(10,17)*SK_MY[1] - P(10,16)*SK_MY[3] + P(10,18)*SK_MY[4]);
-				Kfusion(11) = SK_MY[0]*(P(11,20) + P(11,0)*SH_MAG[2] + P(11,1)*SH_MAG[1] + P(11,2)*SH_MAG[0] - P(11,3)*SK_MY[2] - P(11,17)*SK_MY[1] - P(11,16)*SK_MY[3] + P(11,18)*SK_MY[4]);
-				Kfusion(12) = SK_MY[0]*(P(12,20) + P(12,0)*SH_MAG[2] + P(12,1)*SH_MAG[1] + P(12,2)*SH_MAG[0] - P(12,3)*SK_MY[2] - P(12,17)*SK_MY[1] - P(12,16)*SK_MY[3] + P(12,18)*SK_MY[4]);
-				Kfusion(13) = SK_MY[0]*(P(13,20) + P(13,0)*SH_MAG[2] + P(13,1)*SH_MAG[1] + P(13,2)*SH_MAG[0] - P(13,3)*SK_MY[2] - P(13,17)*SK_MY[1] - P(13,16)*SK_MY[3] + P(13,18)*SK_MY[4]);
-				Kfusion(14) = SK_MY[0]*(P(14,20) + P(14,0)*SH_MAG[2] + P(14,1)*SH_MAG[1] + P(14,2)*SH_MAG[0] - P(14,3)*SK_MY[2] - P(14,17)*SK_MY[1] - P(14,16)*SK_MY[3] + P(14,18)*SK_MY[4]);
-				Kfusion(15) = SK_MY[0]*(P(15,20) + P(15,0)*SH_MAG[2] + P(15,1)*SH_MAG[1] + P(15,2)*SH_MAG[0] - P(15,3)*SK_MY[2] - P(15,17)*SK_MY[1] - P(15,16)*SK_MY[3] + P(15,18)*SK_MY[4]);
-				Kfusion(22) = SK_MY[0]*(P(22,20) + P(22,0)*SH_MAG[2] + P(22,1)*SH_MAG[1] + P(22,2)*SH_MAG[0] - P(22,3)*SK_MY[2] - P(22,17)*SK_MY[1] - P(22,16)*SK_MY[3] + P(22,18)*SK_MY[4]);
-				Kfusion(23) = SK_MY[0]*(P(23,20) + P(23,0)*SH_MAG[2] + P(23,1)*SH_MAG[1] + P(23,2)*SH_MAG[0] - P(23,3)*SK_MY[2] - P(23,17)*SK_MY[1] - P(23,16)*SK_MY[3] + P(23,18)*SK_MY[4]);
+				Kfusion(0) = HKY16*HKY24;
+				Kfusion(1) = HKY21*HKY24;
+				Kfusion(2) = HKY22*HKY24;
+				Kfusion(3) = HKY19*HKY24;
+
+				for (unsigned row = 4; row <= 15; row++) {
+					Kfusion(row) = HKY24*(HKY10*P(row,18) - HKY11*P(row,16) + HKY12*P(2,row) + HKY13*P(0,row) + HKY14*P(1,row) - HKY15*P(3,row) + HKY8*P(row,17) + P(row,20));
+				}
+
+				for (unsigned row = 22; row <= 23; row++) {
+					Kfusion(row) = HKY24*(HKY10*P(18,row) - HKY11*P(16,row) + HKY12*P(2,row) + HKY13*P(0,row) + HKY14*P(1,row) - HKY15*P(3,row) + HKY8*P(17,row) + P(20,row));
+				}
 			}
 
-			Kfusion(16) = SK_MY[0]*(P(16,20) + P(16,0)*SH_MAG[2] + P(16,1)*SH_MAG[1] + P(16,2)*SH_MAG[0] - P(16,3)*SK_MY[2] - P(16,17)*SK_MY[1] - P(16,16)*SK_MY[3] + P(16,18)*SK_MY[4]);
-			Kfusion(17) = SK_MY[0]*(P(17,20) + P(17,0)*SH_MAG[2] + P(17,1)*SH_MAG[1] + P(17,2)*SH_MAG[0] - P(17,3)*SK_MY[2] - P(17,17)*SK_MY[1] - P(17,16)*SK_MY[3] + P(17,18)*SK_MY[4]);
-			Kfusion(18) = SK_MY[0]*(P(18,20) + P(18,0)*SH_MAG[2] + P(18,1)*SH_MAG[1] + P(18,2)*SH_MAG[0] - P(18,3)*SK_MY[2] - P(18,17)*SK_MY[1] - P(18,16)*SK_MY[3] + P(18,18)*SK_MY[4]);
-			Kfusion(19) = SK_MY[0]*(P(19,20) + P(19,0)*SH_MAG[2] + P(19,1)*SH_MAG[1] + P(19,2)*SH_MAG[0] - P(19,3)*SK_MY[2] - P(19,17)*SK_MY[1] - P(19,16)*SK_MY[3] + P(19,18)*SK_MY[4]);
-			Kfusion(20) = SK_MY[0]*(P(20,20) + P(20,0)*SH_MAG[2] + P(20,1)*SH_MAG[1] + P(20,2)*SH_MAG[0] - P(20,3)*SK_MY[2] - P(20,17)*SK_MY[1] - P(20,16)*SK_MY[3] + P(20,18)*SK_MY[4]);
-			Kfusion(21) = SK_MY[0]*(P(21,20) + P(21,0)*SH_MAG[2] + P(21,1)*SH_MAG[1] + P(21,2)*SH_MAG[0] - P(21,3)*SK_MY[2] - P(21,17)*SK_MY[1] - P(21,16)*SK_MY[3] + P(21,18)*SK_MY[4]);
+			Kfusion(16) = HKY18*HKY24;
+			Kfusion(17) = HKY17*HKY24;
+			Kfusion(18) = HKY20*HKY24;
+			Kfusion(19) = HKY24*(HKY10*P(18,19) - HKY11*P(16,19) + HKY12*P(2,19) + HKY13*P(0,19) + HKY14*P(1,19) - HKY15*P(3,19) + HKY8*P(17,19) + P(19,20));
+			Kfusion(20) = HKY23*HKY24;
+			Kfusion(21) = HKY24*(HKY10*P(18,21) - HKY11*P(16,21) + HKY12*P(2,21) + HKY13*P(0,21) + HKY14*P(1,21) - HKY15*P(3,21) + HKY8*P(17,21) + P(20,21));
 
 		} else if (index == 2) {
 
@@ -280,88 +321,88 @@ void Ekf::fuseMag()
 				continue;
 			}
 
-			// calculate Z axis observation jacobians
-			H_MAG.setZero();
-			H_MAG(0) = SH_MAG[1];
-			H_MAG(1) = -SH_MAG[2];
-			H_MAG(2) = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
-			H_MAG(3) = SH_MAG[0];
-			H_MAG(16) = 2.0f*q0*q2 + 2.0f*q1*q3;
-			H_MAG(17) = 2.0f*q2*q3 - 2.0f*q0*q1;
-			H_MAG(18) = SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6];
-			H_MAG(21) = 1.0f;
+			// recalculate innovation variance becasue states and covariances have changed due to previous fusion
+			const float HKZ0 = magD*q0 - magE*q1 + magN*q2;
+			const float HKZ1 = magN*q3;
+			const float HKZ2 = magD*q1;
+			const float HKZ3 = magE*q0;
+			const float HKZ4 = -magD*q2 + magE*q3 + magN*q0;
+			const float HKZ5 = magD*q3 + magE*q2 + magN*q1;
+			const float HKZ6 = q0*q2 + q1*q3;
+			const float HKZ7 = q2*q3;
+			const float HKZ8 = q0*q1;
+			const float HKZ9 = powf(q0, 2) - powf(q1, 2) - powf(q2, 2) + powf(q3, 2);
+			const float HKZ10 = 2*HKZ6;
+			const float HKZ11 = -2*HKZ7 + 2*HKZ8;
+			const float HKZ12 = 2*HKZ5;
+			const float HKZ13 = 2*HKZ0;
+			const float HKZ14 = -2*HKZ1 + 2*HKZ2 + 2*HKZ3;
+			const float HKZ15 = 2*HKZ4;
+			const float HKZ16 = HKZ10*P(0,16) - HKZ11*P(0,17) + HKZ12*P(0,3) + HKZ13*P(0,0) - HKZ14*P(0,1) + HKZ15*P(0,2) + HKZ9*P(0,18) + P(0,21);
+			const float HKZ17 = HKZ10*P(16,18) - HKZ11*P(17,18) + HKZ12*P(3,18) + HKZ13*P(0,18) - HKZ14*P(1,18) + HKZ15*P(2,18) + HKZ9*P(18,18) + P(18,21);
+			const float HKZ18 = HKZ10*P(16,17) - HKZ11*P(17,17) + HKZ12*P(3,17) + HKZ13*P(0,17) - HKZ14*P(1,17) + HKZ15*P(2,17) + HKZ9*P(17,18) + P(17,21);
+			const float HKZ19 = HKZ10*P(1,16) - HKZ11*P(1,17) + HKZ12*P(1,3) + HKZ13*P(0,1) - HKZ14*P(1,1) + HKZ15*P(1,2) + HKZ9*P(1,18) + P(1,21);
+			const float HKZ20 = HKZ10*P(16,16) - HKZ11*P(16,17) + HKZ12*P(3,16) + HKZ13*P(0,16) - HKZ14*P(1,16) + HKZ15*P(2,16) + HKZ9*P(16,18) + P(16,21);
+			const float HKZ21 = HKZ10*P(3,16) - HKZ11*P(3,17) + HKZ12*P(3,3) + HKZ13*P(0,3) - HKZ14*P(1,3) + HKZ15*P(2,3) + HKZ9*P(3,18) + P(3,21);
+			const float HKZ22 = HKZ10*P(2,16) - HKZ11*P(2,17) + HKZ12*P(2,3) + HKZ13*P(0,2) - HKZ14*P(1,2) + HKZ15*P(2,2) + HKZ9*P(2,18) + P(2,21);
+			const float HKZ23 = HKZ10*P(16,21) - HKZ11*P(17,21) + HKZ12*P(3,21) + HKZ13*P(0,21) - HKZ14*P(1,21) + HKZ15*P(2,21) + HKZ9*P(18,21) + P(21,21);
 
-			// Calculate Z axis Kalman gains
-			float SK_MZ[5];
-			SK_MZ[0] = 1.0f / _mag_innov_var(2);
-			SK_MZ[1] = SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6];
-			SK_MZ[2] = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
-			SK_MZ[3] = 2.0f*q0*q1 - 2.0f*q2*q3;
-			SK_MZ[4] = 2.0f*q0*q2 + 2.0f*q1*q3;
+			_mag_innov_var(2) = (HKZ10*HKZ20 - HKZ11*HKZ18 + HKZ12*HKZ21 + HKZ13*HKZ16 - HKZ14*HKZ19 + HKZ15*HKZ22 + HKZ17*HKZ9 + HKZ23 + R_MAG);
 
-			if (update_all_states) {
-				Kfusion(0) = SK_MZ[0]*(P(0,21) + P(0,0)*SH_MAG[1] - P(0,1)*SH_MAG[2] + P(0,3)*SH_MAG[0] + P(0,2)*SK_MZ[2] + P(0,18)*SK_MZ[1] + P(0,16)*SK_MZ[4] - P(0,17)*SK_MZ[3]);
-				Kfusion(1) = SK_MZ[0]*(P(1,21) + P(1,0)*SH_MAG[1] - P(1,1)*SH_MAG[2] + P(1,3)*SH_MAG[0] + P(1,2)*SK_MZ[2] + P(1,18)*SK_MZ[1] + P(1,16)*SK_MZ[4] - P(1,17)*SK_MZ[3]);
-				Kfusion(2) = SK_MZ[0]*(P(2,21) + P(2,0)*SH_MAG[1] - P(2,1)*SH_MAG[2] + P(2,3)*SH_MAG[0] + P(2,2)*SK_MZ[2] + P(2,18)*SK_MZ[1] + P(2,16)*SK_MZ[4] - P(2,17)*SK_MZ[3]);
-				Kfusion(3) = SK_MZ[0]*(P(3,21) + P(3,0)*SH_MAG[1] - P(3,1)*SH_MAG[2] + P(3,3)*SH_MAG[0] + P(3,2)*SK_MZ[2] + P(3,18)*SK_MZ[1] + P(3,16)*SK_MZ[4] - P(3,17)*SK_MZ[3]);
-				Kfusion(4) = SK_MZ[0]*(P(4,21) + P(4,0)*SH_MAG[1] - P(4,1)*SH_MAG[2] + P(4,3)*SH_MAG[0] + P(4,2)*SK_MZ[2] + P(4,18)*SK_MZ[1] + P(4,16)*SK_MZ[4] - P(4,17)*SK_MZ[3]);
-				Kfusion(5) = SK_MZ[0]*(P(5,21) + P(5,0)*SH_MAG[1] - P(5,1)*SH_MAG[2] + P(5,3)*SH_MAG[0] + P(5,2)*SK_MZ[2] + P(5,18)*SK_MZ[1] + P(5,16)*SK_MZ[4] - P(5,17)*SK_MZ[3]);
-				Kfusion(6) = SK_MZ[0]*(P(6,21) + P(6,0)*SH_MAG[1] - P(6,1)*SH_MAG[2] + P(6,3)*SH_MAG[0] + P(6,2)*SK_MZ[2] + P(6,18)*SK_MZ[1] + P(6,16)*SK_MZ[4] - P(6,17)*SK_MZ[3]);
-				Kfusion(7) = SK_MZ[0]*(P(7,21) + P(7,0)*SH_MAG[1] - P(7,1)*SH_MAG[2] + P(7,3)*SH_MAG[0] + P(7,2)*SK_MZ[2] + P(7,18)*SK_MZ[1] + P(7,16)*SK_MZ[4] - P(7,17)*SK_MZ[3]);
-				Kfusion(8) = SK_MZ[0]*(P(8,21) + P(8,0)*SH_MAG[1] - P(8,1)*SH_MAG[2] + P(8,3)*SH_MAG[0] + P(8,2)*SK_MZ[2] + P(8,18)*SK_MZ[1] + P(8,16)*SK_MZ[4] - P(8,17)*SK_MZ[3]);
-				Kfusion(9) = SK_MZ[0]*(P(9,21) + P(9,0)*SH_MAG[1] - P(9,1)*SH_MAG[2] + P(9,3)*SH_MAG[0] + P(9,2)*SK_MZ[2] + P(9,18)*SK_MZ[1] + P(9,16)*SK_MZ[4] - P(9,17)*SK_MZ[3]);
-				Kfusion(10) = SK_MZ[0]*(P(10,21) + P(10,0)*SH_MAG[1] - P(10,1)*SH_MAG[2] + P(10,3)*SH_MAG[0] + P(10,2)*SK_MZ[2] + P(10,18)*SK_MZ[1] + P(10,16)*SK_MZ[4] - P(10,17)*SK_MZ[3]);
-				Kfusion(11) = SK_MZ[0]*(P(11,21) + P(11,0)*SH_MAG[1] - P(11,1)*SH_MAG[2] + P(11,3)*SH_MAG[0] + P(11,2)*SK_MZ[2] + P(11,18)*SK_MZ[1] + P(11,16)*SK_MZ[4] - P(11,17)*SK_MZ[3]);
-				Kfusion(12) = SK_MZ[0]*(P(12,21) + P(12,0)*SH_MAG[1] - P(12,1)*SH_MAG[2] + P(12,3)*SH_MAG[0] + P(12,2)*SK_MZ[2] + P(12,18)*SK_MZ[1] + P(12,16)*SK_MZ[4] - P(12,17)*SK_MZ[3]);
-				Kfusion(13) = SK_MZ[0]*(P(13,21) + P(13,0)*SH_MAG[1] - P(13,1)*SH_MAG[2] + P(13,3)*SH_MAG[0] + P(13,2)*SK_MZ[2] + P(13,18)*SK_MZ[1] + P(13,16)*SK_MZ[4] - P(13,17)*SK_MZ[3]);
-				Kfusion(14) = SK_MZ[0]*(P(14,21) + P(14,0)*SH_MAG[1] - P(14,1)*SH_MAG[2] + P(14,3)*SH_MAG[0] + P(14,2)*SK_MZ[2] + P(14,18)*SK_MZ[1] + P(14,16)*SK_MZ[4] - P(14,17)*SK_MZ[3]);
-				Kfusion(15) = SK_MZ[0]*(P(15,21) + P(15,0)*SH_MAG[1] - P(15,1)*SH_MAG[2] + P(15,3)*SH_MAG[0] + P(15,2)*SK_MZ[2] + P(15,18)*SK_MZ[1] + P(15,16)*SK_MZ[4] - P(15,17)*SK_MZ[3]);
-				Kfusion(22) = SK_MZ[0]*(P(22,21) + P(22,0)*SH_MAG[1] - P(22,1)*SH_MAG[2] + P(22,3)*SH_MAG[0] + P(22,2)*SK_MZ[2] + P(22,18)*SK_MZ[1] + P(22,16)*SK_MZ[4] - P(22,17)*SK_MZ[3]);
-				Kfusion(23) = SK_MZ[0]*(P(23,21) + P(23,0)*SH_MAG[1] - P(23,1)*SH_MAG[2] + P(23,3)*SH_MAG[0] + P(23,2)*SK_MZ[2] + P(23,18)*SK_MZ[1] + P(23,16)*SK_MZ[4] - P(23,17)*SK_MZ[3]);
+			if (_mag_innov_var(2) < R_MAG) {
+				// the innovation variance contribution from the state covariances is negative which means the covariance matrix is badly conditioned
+				_fault_status.flags.bad_mag_z = true;
+
+				// we need to re-initialise covariances and abort this fusion step
+				resetMagRelatedCovariances();
+				ECL_ERR("magZ %s", numerical_error_covariance_reset_string);
+				return;
 			}
 
-			Kfusion(16) = SK_MZ[0]*(P(16,21) + P(16,0)*SH_MAG[1] - P(16,1)*SH_MAG[2] + P(16,3)*SH_MAG[0] + P(16,2)*SK_MZ[2] + P(16,18)*SK_MZ[1] + P(16,16)*SK_MZ[4] - P(16,17)*SK_MZ[3]);
-			Kfusion(17) = SK_MZ[0]*(P(17,21) + P(17,0)*SH_MAG[1] - P(17,1)*SH_MAG[2] + P(17,3)*SH_MAG[0] + P(17,2)*SK_MZ[2] + P(17,18)*SK_MZ[1] + P(17,16)*SK_MZ[4] - P(17,17)*SK_MZ[3]);
-			Kfusion(18) = SK_MZ[0]*(P(18,21) + P(18,0)*SH_MAG[1] - P(18,1)*SH_MAG[2] + P(18,3)*SH_MAG[0] + P(18,2)*SK_MZ[2] + P(18,18)*SK_MZ[1] + P(18,16)*SK_MZ[4] - P(18,17)*SK_MZ[3]);
-			Kfusion(19) = SK_MZ[0]*(P(19,21) + P(19,0)*SH_MAG[1] - P(19,1)*SH_MAG[2] + P(19,3)*SH_MAG[0] + P(19,2)*SK_MZ[2] + P(19,18)*SK_MZ[1] + P(19,16)*SK_MZ[4] - P(19,17)*SK_MZ[3]);
-			Kfusion(20) = SK_MZ[0]*(P(20,21) + P(20,0)*SH_MAG[1] - P(20,1)*SH_MAG[2] + P(20,3)*SH_MAG[0] + P(20,2)*SK_MZ[2] + P(20,18)*SK_MZ[1] + P(20,16)*SK_MZ[4] - P(20,17)*SK_MZ[3]);
-			Kfusion(21) = SK_MZ[0]*(P(21,21) + P(21,0)*SH_MAG[1] - P(21,1)*SH_MAG[2] + P(21,3)*SH_MAG[0] + P(21,2)*SK_MZ[2] + P(21,18)*SK_MZ[1] + P(21,16)*SK_MZ[4] - P(21,17)*SK_MZ[3]);
+			const float HKZ24 = 1.0F/_mag_innov_var(2);
 
+			// calculate Z axis observation jacobians
+			Hfusion.setZero();
+			Hfusion.at<0>() = 2*HKZ0;
+			Hfusion.at<1>() = 2*HKZ1 - 2*HKZ2 - 2*HKZ3;
+			Hfusion.at<2>() = 2*HKZ4;
+			Hfusion.at<3>() = 2*HKZ5;
+			Hfusion.at<16>() = 2*HKZ6;
+			Hfusion.at<17>() = 2*HKZ7 - 2*HKZ8;
+			Hfusion.at<18>() = HKZ9;
+			Hfusion.at<21>() = 1;
+
+			// Calculate Z axis Kalman gains
+			if (update_all_states) {
+				Kfusion(0) = HKZ16*HKZ24;
+				Kfusion(1) = HKZ19*HKZ24;
+				Kfusion(2) = HKZ22*HKZ24;
+				Kfusion(3) = HKZ21*HKZ24;
+
+				for (unsigned row = 4; row <= 15; row++) {
+					Kfusion(row) = HKZ24*(HKZ10*P(row,16) - HKZ11*P(row,17) + HKZ12*P(3,row) + HKZ13*P(0,row) - HKZ14*P(1,row) + HKZ15*P(2,row) + HKZ9*P(row,18) + P(row,21));
+				}
+
+				for (unsigned row = 22; row <= 23; row++) {
+					Kfusion(row) = HKZ24*(HKZ10*P(16,row) - HKZ11*P(17,row) + HKZ12*P(3,row) + HKZ13*P(0,row) - HKZ14*P(1,row) + HKZ15*P(2,row) + HKZ9*P(18,row) + P(21,row));
+				}
+			}
+
+			Kfusion(16) = HKZ20*HKZ24;
+			Kfusion(17) = HKZ18*HKZ24;
+			Kfusion(18) = HKZ17*HKZ24;
+
+			for (unsigned row = 19; row <= 20; row++) {
+				Kfusion(row) = HKZ24*(HKZ10*P(16,row) - HKZ11*P(17,row) + HKZ12*P(3,row) + HKZ13*P(0,row) - HKZ14*P(1,row) + HKZ15*P(2,row) + HKZ9*P(18,row) + P(row,21));
+			}
+
+			Kfusion(21) = HKZ23*HKZ24;
 		}
 
 		// apply covariance correction via P_new = (I -K*H)*P
 		// first calculate expression for KHP
 		// then calculate P - KHP
-		SquareMatrix24f KHP;
-		float KH[10];
-
-		for (unsigned row = 0; row < _k_num_states; row++) {
-
-			KH[0] = Kfusion(row) * H_MAG(0);
-			KH[1] = Kfusion(row) * H_MAG(1);
-			KH[2] = Kfusion(row) * H_MAG(2);
-			KH[3] = Kfusion(row) * H_MAG(3);
-			KH[4] = Kfusion(row) * H_MAG(16);
-			KH[5] = Kfusion(row) * H_MAG(17);
-			KH[6] = Kfusion(row) * H_MAG(18);
-			KH[7] = Kfusion(row) * H_MAG(19);
-			KH[8] = Kfusion(row) * H_MAG(20);
-			KH[9] = Kfusion(row) * H_MAG(21);
-
-			for (unsigned column = 0; column < _k_num_states; column++) {
-				float tmp = KH[0] * P(0,column);
-				tmp += KH[1] * P(1,column);
-				tmp += KH[2] * P(2,column);
-				tmp += KH[3] * P(3,column);
-				tmp += KH[4] * P(16,column);
-				tmp += KH[5] * P(17,column);
-				tmp += KH[6] * P(18,column);
-				tmp += KH[7] * P(19,column);
-				tmp += KH[8] * P(20,column);
-				tmp += KH[9] * P(21,column);
-				KHP(row,column) = tmp;
-			}
-		}
+		const SquareMatrix24f KHP = computeKHP(Kfusion, Hfusion);
 
 		const bool healthy = checkAndFixCovarianceUpdate(KHP);
 
@@ -393,81 +434,66 @@ void Ekf::fuseMag()
 void Ekf::fuseYaw321(float yaw, float yaw_variance, bool zero_innovation)
 {
 	// assign intermediate state variables
-	const float q0 = _state.quat_nominal(0);
-	const float q1 = _state.quat_nominal(1);
-	const float q2 = _state.quat_nominal(2);
-	const float q3 = _state.quat_nominal(3);
+	const float &q0 = _state.quat_nominal(0);
+	const float &q1 = _state.quat_nominal(1);
+	const float &q2 = _state.quat_nominal(2);
+	const float &q3 = _state.quat_nominal(3);
 
 	const float R_YAW = fmaxf(yaw_variance, 1.0e-4f);
 	const float measurement = wrap_pi(yaw);
 
-	// calculate observation jacobian when we are observing the first rotation in a 321 sequence
-	float t9 = q0*q3;
-	float t10 = q1*q2;
-	float t2 = t9+t10;
-	float t3 = q0*q0;
-	float t4 = q1*q1;
-	float t5 = q2*q2;
-	float t6 = q3*q3;
-	float t7 = t3+t4-t5-t6;
+	// calculate 321 yaw observation matrix
+	// choose A or B computational paths to avoid singularity in derivation at +-90 degrees yaw
+	bool canUseA = false;
+	const float SA0 = 2*q3;
+	const float SA1 = 2*q2;
+	const float SA2 = SA0*q0 + SA1*q1;
+	const float SA3 = sq(q0) + sq(q1) - sq(q2) - sq(q3);
+	float SA4, SA5_inv;
+	if (sq(SA3) > 1E-6f) {
+		SA4 = 1.0F/sq(SA3);
+		SA5_inv = sq(SA2)*SA4 + 1;
+		canUseA = fabsf(SA5_inv) > 1E-6f;
+	}
 
-	float t16 = q3*t3;
-	float t17 = q3*t5;
-	float t18 = q0*q1*q2*2.0f;
-	float t19 = t16+t17+t18-q3*t4+q3*t6;
-
-	float t24 = q2*t4;
-	float t25 = q2*t6;
-	float t26 = q0*q1*q3*2.0f;
-	float t27 = t24+t25+t26-q2*t3+q2*t5;
-	float t28 = q1*t3;
-	float t29 = q1*t5;
-	float t30 = q0*q2*q3*2.0f;
-	float t31 = t28+t29+t30+q1*t4-q1*t6;
-	float t32 = q0*t4;
-	float t33 = q0*t6;
-	float t34 = q1*q2*q3*2.0f;
-	float t35 = t32+t33+t34+q0*t3-q0*t5;
+	bool canUseB = false;
+	const float SB0 = 2*q0;
+	const float SB1 = 2*q1;
+	const float SB2 = SB0*q3 + SB1*q2;
+	const float SB4 = sq(q0) + sq(q1) - sq(q2) - sq(q3);
+	float SB3, SB5_inv;
+	if (sq(SB2) > 1E-6f) {
+		SB3 = 1.0F/sq(SB2);
+		SB5_inv = SB3*sq(SB4) + 1;
+		canUseB = fabsf(SB5_inv) > 1E-6f;
+	}
 
 	Vector4f H_YAW;
-	// two computational paths are provided to work around singularities in calculation of the Jacobians
-	float t8 = t7*t7;
-	float t15 = t2*t2;
-	if (t8 > t15 && t8 > 1E-6f) {
-		// this path has a singularities at yaw = +-90 degrees
-		t8 = 1.0f/t8;
-		float t11 = t2*t2;
-		float t12 = t8*t11*4.0f;
-		float t13 = t12+1.0f;
-		float t14 = 1.0f/t13;
 
-		H_YAW(0) = t8*t14*t19*(-2.0f);
-		H_YAW(1) = t8*t14*t27*(-2.0f);
-		H_YAW(2) = t8*t14*t31*2.0f;
-		H_YAW(3) = t8*t14*t35*2.0f;
+	if (canUseA && (!canUseB || fabsf(SA5_inv) >= fabsf(SB5_inv))) {
+		const float SA5 = 1.0F/SA5_inv;
+		const float SA6 = 1.0F/SA3;
+		const float SA7 = SA2*SA4;
+		const float SA8 = 2*SA7;
+		const float SA9 = 2*SA6;
 
-	} else if (t15 > 1E-6f) {
-		// this path has singularities at yaw = 0 and +-180 deg
-		t15 = 1.0f/t15;
-		float t20 = t7*t7;
-		float t21 = t15*t20*0.25f;
-		float t22 = t21+1.0f;
+		H_YAW(0) = SA5*(SA0*SA6 - SA8*q0);
+		H_YAW(1) = SA5*(SA1*SA6 - SA8*q1);
+		H_YAW(2) = SA5*(SA1*SA7 + SA9*q1);
+		H_YAW(3) = SA5*(SA0*SA7 + SA9*q0);
+	} else if (canUseB && (!canUseA || fabsf(SB5_inv) > fabsf(SA5_inv))) {
+		const float SB5 = 1.0F/SB5_inv;
+		const float SB6 = 1.0F/SB2;
+		const float SB7 = SB3*SB4;
+		const float SB8 = 2*SB7;
+		const float SB9 = 2*SB6;
 
-		if (fabsf(t22) > 1E-6f) {
-			float t23 = 1.0f/t22;
-
-			H_YAW(0) = t15*t19*t23*(-0.5f);
-			H_YAW(1) = t15*t23*t27*(-0.5f);
-			H_YAW(2) = t15*t23*t31*0.5f;
-			H_YAW(3) = t15*t23*t35*0.5f;
-
-		} else {
-			return;
-
-		}
+		H_YAW(0) = -SB5*(SB0*SB6 - SB8*q3);
+		H_YAW(1) = -SB5*(SB1*SB6 - SB8*q2);
+		H_YAW(2) = -SB5*(-SB1*SB7 - SB9*q2);
+		H_YAW(3) = -SB5*(-SB0*SB7 - SB9*q3);
 	} else {
 		return;
-
 	}
 
 	// calculate the yaw innovation and wrap to the interval between +-pi
@@ -496,69 +522,58 @@ void Ekf::fuseYaw312(float yaw, float yaw_variance, bool zero_innovation)
 	const float R_YAW = fmaxf(yaw_variance, 1.0e-4f);
 	const float measurement = wrap_pi(yaw);
 
-	// calculate observation jacobian when we are observing a rotation in a 312 sequence
-	float t9 = q0*q3;
-	float t10 = q1*q2;
-	float t2 = t9-t10;
-	float t3 = q0*q0;
-	float t4 = q1*q1;
-	float t5 = q2*q2;
-	float t6 = q3*q3;
-	float t7 = t3-t4+t5-t6;
+	// calculate 312 yaw observation matrix
+	// choose A or B computational paths to avoid singularity in derivation at +-90 degrees yaw
+	bool canUseA = false;
+	const float SA0 = 2*q3;
+	const float SA1 = 2*q2;
+	const float SA2 = SA0*q0 - SA1*q1;
+	const float SA3 = sq(q0) - sq(q1) + sq(q2) - sq(q3);
+	float SA4, SA5_inv;
+	if (sq(SA3) > 1E-6f) {
+		SA4 = 1.0F/sq(SA3);
+		SA5_inv = sq(SA2)*SA4 + 1;
+		canUseA = fabsf(SA5_inv) > 1E-6f;
+	}
 
-	float t16 = q3*t3;
-	float t17 = q3*t4;
-	float t18 = t16+t17-q3*t5+q3*t6-q0*q1*q2*2.0f;
-	float t23 = q2*t3;
-	float t24 = q2*t4;
-	float t25 = t23+t24+q2*t5-q2*t6-q0*q1*q3*2.0f;
-	float t26 = q1*t5;
-	float t27 = q1*t6;
-	float t28 = t26+t27-q1*t3+q1*t4-q0*q2*q3*2.0f;
-	float t29 = q0*t5;
-	float t30 = q0*t6;
-	float t31 = t29+t30+q0*t3-q0*t4-q1*q2*q3*2.0f;
+	bool canUseB = false;
+	const float SB0 = 2*q0;
+	const float SB1 = 2*q1;
+	const float SB2 = -SB0*q3 + SB1*q2;
+	const float SB4 = -sq(q0) + sq(q1) - sq(q2) + sq(q3);
+	float SB3, SB5_inv;
+	if (sq(SB2) > 1E-6f) {
+		SB3 = 1.0F/sq(SB2);
+		SB5_inv = SB3*sq(SB4) + 1;
+		canUseB = fabsf(SB5_inv) > 1E-6f;
+	}
 
 	Vector4f H_YAW;
-	// two computational paths are provided to work around singularities in calculation of the Jacobians
-	float t8 = t7*t7;
-	float t15 = t2*t2;
-	if (t8 > t15 && t8 > 1E-6f) {
-		// this path has a singularities at yaw = +-90 degrees
-		t8 = 1.0f/t8;
-		float t11 = t2*t2;
-		float t12 = t8*t11*4.0f;
-		float t13 = t12+1.0f;
-		float t14 = 1.0f/t13;
 
-		H_YAW(0) = t8*t14*t18*(-2.0f);
-		H_YAW(1) = t8*t14*t25*(-2.0f);
-		H_YAW(2) = t8*t14*t28*2.0f;
-		H_YAW(3) = t8*t14*t31*2.0f;
+	if (canUseA && (!canUseB || fabsf(SA5_inv) >= fabsf(SB5_inv))) {
+		const float SA5 = 1.0F/SA5_inv;
+		const float SA6 = 1.0F/SA3;
+		const float SA7 = SA2*SA4;
+		const float SA8 = 2*SA7;
+		const float SA9 = 2*SA6;
 
-	} else if (t15 > 1E-6f) {
-		// this path has singularities at yaw = 0 and +-180 deg
-		t15 = 1.0f/t15;
-		float t19 = t7*t7;
-		float t20 = t15*t19*0.25f;
-		float t21 = t20+1.0f;
-
-		if (fabsf(t21) > 1E-6f) {
-			float t22 = 1.0f/t21;
-
-			H_YAW(0) = t15*t18*t22*(-0.5f);
-			H_YAW(1) = t15*t22*t25*(-0.5f);
-			H_YAW(2) = t15*t22*t28*0.5f;
-			H_YAW(3) = t15*t22*t31*0.5f;
-
-		} else {
-			return;
-
-		}
+		H_YAW(0) = SA5*(SA0*SA6 - SA8*q0);
+		H_YAW(1) = SA5*(-SA1*SA6 + SA8*q1);
+		H_YAW(2) = SA5*(-SA1*SA7 - SA9*q1);
+		H_YAW(3) = SA5*(SA0*SA7 + SA9*q0);
+	} else if (canUseB && (!canUseA || fabsf(SB5_inv) > fabsf(SA5_inv))) {
+		const float SB5 = 1.0F/SB5_inv;
+		const float SB6 = 1.0F/SB2;
+		const float SB7 = SB3*SB4;
+		const float SB8 = 2*SB7;
+		const float SB9 = 2*SB6;
 
+		H_YAW(0) = -SB5*(-SB0*SB6 + SB8*q3);
+		H_YAW(1) = -SB5*(SB1*SB6 - SB8*q2);
+		H_YAW(2) = -SB5*(-SB1*SB7 - SB9*q2);
+		H_YAW(3) = -SB5*(SB0*SB7 + SB9*q3);
 	} else {
 		return;
-
 	}
 
 	float innovation;
@@ -857,81 +872,57 @@ void Ekf::fuseHeading()
 void Ekf::fuseDeclination(float decl_sigma)
 {
 	// assign intermediate state variables
-	const float magN = _state.mag_I(0);
-	const float magE = _state.mag_I(1);
+	const float &magN = _state.mag_I(0);
+	const float &magE = _state.mag_I(1);
 
-	// minimum horizontal field strength before calculation becomes badly conditioned (T)
-	constexpr float h_field_min = 0.001f;
+	// minimum North field strength before calculation becomes badly conditioned (T)
+	constexpr float N_field_min = 0.001f;
 
 	// observation variance (rad**2)
 	const float R_DECL = sq(decl_sigma);
 
 	// Calculate intermediate variables
-	float t2 = magE*magE;
-	float t3 = magN*magN;
-	float t4 = t2+t3;
-	// if the horizontal magnetic field is too small, this calculation will be badly conditioned
-	if (t4 < h_field_min*h_field_min) {
+	if (fabsf(magN) < sq(N_field_min)) {
+		// calculation is badly conditioned close to +-90 deg declination
 		return;
 	}
-	float t5 = P(16,16)*t2;
-	float t6 = P(17,17)*t3;
-	float t7 = t2*t2;
-	float t8 = R_DECL*t7;
-	float t9 = t3*t3;
-	float t10 = R_DECL*t9;
-	float t11 = R_DECL*t2*t3*2.0f;
-	float t14 = P(16,17)*magE*magN;
-	float t15 = P(17,16)*magE*magN;
-	float t12 = t5+t6+t8+t10+t11-t14-t15;
-	float t13;
-	if (fabsf(t12) > 1e-6f) {
-		t13 = 1.0f / t12;
-	} else {
-		return;
-	}
-	float t18 = magE*magE;
-	float t19 = magN*magN;
-	float t20 = t18+t19;
-	float t21;
-	if (fabsf(t20) > 1e-6f) {
-		t21 = 1.0f/t20;
+	const float HK0 = powf(magN, -2);
+	const float HK1 = HK0*powf(magE, 2) + 1.0F;
+	const float HK2 = 1.0F/HK1;
+	const float HK3 = 1.0F/magN;
+	const float HK4 = HK2*HK3;
+	const float HK5 = HK3*magE;
+	const float HK6 = HK5*P(16,17) - P(17,17);
+	const float HK7 = powf(HK1, -2);
+	const float HK8 = HK5*P(16,16) - P(16,17);
+	const float innovation_variance = -HK0*HK6*HK7 + HK7*HK8*magE/powf(magN, 3) + R_DECL;
+	float HK9;
+	if (innovation_variance > R_DECL) {
+		HK9 = HK4/innovation_variance;
 	} else {
+		// variance calculation is badly conditioned
 		return;
 	}
 
 	// Calculate the observation Jacobian
 	// Note only 2 terms are non-zero which can be used in matrix operations for calculation of Kalman gains and covariance update to significantly reduce cost
-	Vector24f H_DECL;
-	H_DECL(16) = -magE*t21;
-	H_DECL(17) = magN*t21;
+	// Note Hfusion indices do not match state indices
+	SparseVector24f<16,17> Hfusion;
+	Hfusion.at<16>() = -HK0*HK2*magE;
+	Hfusion.at<17>() = HK4;
 
 	// Calculate the Kalman gains
 	Vector24f Kfusion;
-	Kfusion(0) = -t4*t13*(P(0,16)*magE-P(0,17)*magN);
-	Kfusion(1) = -t4*t13*(P(1,16)*magE-P(1,17)*magN);
-	Kfusion(2) = -t4*t13*(P(2,16)*magE-P(2,17)*magN);
-	Kfusion(3) = -t4*t13*(P(3,16)*magE-P(3,17)*magN);
-	Kfusion(4) = -t4*t13*(P(4,16)*magE-P(4,17)*magN);
-	Kfusion(5) = -t4*t13*(P(5,16)*magE-P(5,17)*magN);
-	Kfusion(6) = -t4*t13*(P(6,16)*magE-P(6,17)*magN);
-	Kfusion(7) = -t4*t13*(P(7,16)*magE-P(7,17)*magN);
-	Kfusion(8) = -t4*t13*(P(8,16)*magE-P(8,17)*magN);
-	Kfusion(9) = -t4*t13*(P(9,16)*magE-P(9,17)*magN);
-	Kfusion(10) = -t4*t13*(P(10,16)*magE-P(10,17)*magN);
-	Kfusion(11) = -t4*t13*(P(11,16)*magE-P(11,17)*magN);
-	Kfusion(12) = -t4*t13*(P(12,16)*magE-P(12,17)*magN);
-	Kfusion(13) = -t4*t13*(P(13,16)*magE-P(13,17)*magN);
-	Kfusion(14) = -t4*t13*(P(14,16)*magE-P(14,17)*magN);
-	Kfusion(15) = -t4*t13*(P(15,16)*magE-P(15,17)*magN);
-	Kfusion(16) = -t4*t13*(P(16,16)*magE-P(16,17)*magN);
-	Kfusion(17) = -t4*t13*(P(17,16)*magE-P(17,17)*magN);
-	Kfusion(18) = -t4*t13*(P(18,16)*magE-P(18,17)*magN);
-	Kfusion(19) = -t4*t13*(P(19,16)*magE-P(19,17)*magN);
-	Kfusion(20) = -t4*t13*(P(20,16)*magE-P(20,17)*magN);
-	Kfusion(21) = -t4*t13*(P(21,16)*magE-P(21,17)*magN);
-	Kfusion(22) = -t4*t13*(P(22,16)*magE-P(22,17)*magN);
-	Kfusion(23) = -t4*t13*(P(23,16)*magE-P(23,17)*magN);
+	for (unsigned row = 0; row <= 15; row++) {
+		Kfusion(row) = -HK9*(HK5*P(row,16) - P(row,17));
+	}
+
+	Kfusion(16) = -HK8*HK9;
+	Kfusion(17) = -HK6*HK9;
+
+	for (unsigned row = 18; row <= 23; row++) {
+		Kfusion(row) = -HK9*(HK5*P(16,row) - P(17,row));
+	}
 
 	const float innovation = math::constrain(atan2f(magE, magN) - getMagDeclination(), -0.5f, 0.5f);
 
@@ -939,19 +930,7 @@ void Ekf::fuseDeclination(float decl_sigma)
 	// first calculate expression for KHP
 	// then calculate P - KHP
 	// take advantage of the empty columns in KH to reduce the number of operations
-	SquareMatrix24f KHP;
-	float KH[2];
-	for (unsigned row = 0; row < _k_num_states; row++) {
-
-		KH[0] = Kfusion(row) * H_DECL(16);
-		KH[1] = Kfusion(row) * H_DECL(17);
-
-		for (unsigned column = 0; column < _k_num_states; column++) {
-			float tmp = KH[0] * P(16,column);
-			tmp += KH[1] * P(17,column);
-			KHP(row,column) = tmp;
-		}
-	}
+	const SquareMatrix24f KHP = computeKHP(Kfusion, Hfusion);
 
 	const bool healthy = checkAndFixCovarianceUpdate(KHP);
 

EKF/python/ekf_derivation/code_gen.py

@@ -27,26 +27,20 @@ class CodeGenerator:
         write_string = write_string + "\n\n"
         self.file.write(write_string)
 
-    def write_matrix(self, matrix, identifier, is_symmetric=False):
+    def write_matrix(self, matrix, variable_name, is_symmetric=False, pre_bracket="(", post_bracket=")"):
         write_string = ""
 
         if matrix.shape[0] * matrix.shape[1] == 1:
-            write_string = write_string + identifier + " = " + self.get_ccode(matrix[0]) + ";\n"
+            write_string = write_string + variable_name + " = " + self.get_ccode(matrix[0]) + ";\n"
         elif matrix.shape[0] == 1 or matrix.shape[1] == 1:
             for i in range(0,len(matrix)):
-                if (identifier == "Kfusion"):
-                    # Vector f format used by Kfusion
-                    write_string = write_string + identifier + "(" + str(i) + ") = " + self.get_ccode(matrix[i]) + ";\n"
-                else:
-                    # legacy array format used by Hfusion
-                    write_string = write_string + identifier + "[" + str(i) + "] = " + self.get_ccode(matrix[i]) + ";\n"
+                write_string = write_string + variable_name + pre_bracket + str(i) + post_bracket + " = " + self.get_ccode(matrix[i]) + ";\n"
+
         else:
             for j in range(0, matrix.shape[1]):
                 for i in range(0, matrix.shape[0]):
                     if j >= i or not is_symmetric:
-                        write_string = write_string + identifier + "(" + str(i) + "," + str(j) + ") = " + self.get_ccode(matrix[i,j]) + ";\n"
-                        # legacy array format
-                        # write_string = write_string + identifier + "[" + str(i) + "][" + str(j) + "] = " + self.get_ccode(matrix[i,j]) + ";\n"
+                        write_string = write_string + variable_name + pre_bracket + str(i) + "," + str(j) + post_bracket + " = " + self.get_ccode(matrix[i,j]) + ";\n"
 
         write_string = write_string + "\n\n"
         self.file.write(write_string)

EKF/python/ekf_derivation/generated/3Dmag_fusion_generated_compare.cpp

@@ -0,0 +1,604 @@
+#include <math.h>
+#include <stdio.h>
+#include <cstdlib>
+#include "../../../../../matrix/matrix/math.hpp"
+
+typedef matrix::Vector<float, 24> Vector24f;
+typedef matrix::SquareMatrix<float, 24> SquareMatrix24f;
+
+float sq(float in) {
+    return in * in;
+}
+
+int main()
+{
+    // Compare calculation of observation Jacobians and Kalman gains for sympy and matlab generated equations
+
+	float Hfusion[24];
+    Vector24f H_MAG;
+    Vector24f Kfusion;
+    float mag_innov_var;
+
+    // quaternion inputs must be normalised
+    float q0 = 2.0f * ((float)rand() - 0.5f);
+    float q1 = 2.0f * ((float)rand() - 0.5f);
+    float q2 = 2.0f * ((float)rand() - 0.5f);
+    float q3 = 2.0f * ((float)rand() - 0.5f);
+    const float length = sqrtf(sq(q0) + sq(q1) + sq(q2) + sq(q3));
+    q0 /= length;
+    q1 /= length;
+    q2 /= length;
+    q3 /= length;
+
+	const float magN = 2.0f * ((float)rand() - 0.5f);
+	const float magE = 2.0f * ((float)rand() - 0.5f);
+	const float magD = 2.0f * ((float)rand() - 0.5f);
+
+	const float R_MAG = sq(0.05f);
+    const bool update_all_states = true;
+
+    // create a symmetrical positive dfinite matrix with off diagonals between -1 and 1 and diagonals between 0 and 1
+    SquareMatrix24f P;
+    for (int col=0; col<=23; col++) {
+        for (int row=0; row<=col; row++) {
+            if (row == col) {
+                P(row,col) = (float)rand();
+            } else {
+                P(col,row) = P(row,col) = 2.0f * ((float)rand() - 0.5f);
+            }
+        }
+    }
+
+    // common expressions used by sympy generated equations
+	// calculate intermediate variables used for X axis innovation variance, observation Jacobians and Kalman gainss
+	const float HKX0 = -magD*q2 + magE*q3 + magN*q0;
+    const float HKX1 = magD*q3 + magE*q2 + magN*q1;
+    const float HKX2 = magE*q1;
+    const float HKX3 = magD*q0;
+    const float HKX4 = magN*q2;
+    const float HKX5 = magD*q1 + magE*q0 - magN*q3;
+    const float HKX6 = powf(q0, 2) + powf(q1, 2) - powf(q2, 2) - powf(q3, 2);
+    const float HKX7 = q0*q3 + q1*q2;
+    const float HKX8 = q1*q3;
+    const float HKX9 = q0*q2;
+    const float HKX10 = 2*HKX7;
+    const float HKX11 = -2*HKX8 + 2*HKX9;
+    const float HKX12 = 2*HKX1;
+    const float HKX13 = 2*HKX0;
+    const float HKX14 = -2*HKX2 + 2*HKX3 + 2*HKX4;
+    const float HKX15 = 2*HKX5;
+    const float HKX16 = HKX10*P(0,17) - HKX11*P(0,18) + HKX12*P(0,1) + HKX13*P(0,0) - HKX14*P(0,2) + HKX15*P(0,3) + HKX6*P(0,16) + P(0,19);
+    const float HKX17 = HKX10*P(16,17) - HKX11*P(16,18) + HKX12*P(1,16) + HKX13*P(0,16) - HKX14*P(2,16) + HKX15*P(3,16) + HKX6*P(16,16) + P(16,19);
+    const float HKX18 = HKX10*P(17,18) - HKX11*P(18,18) + HKX12*P(1,18) + HKX13*P(0,18) - HKX14*P(2,18) + HKX15*P(3,18) + HKX6*P(16,18) + P(18,19);
+    const float HKX19 = HKX10*P(2,17) - HKX11*P(2,18) + HKX12*P(1,2) + HKX13*P(0,2) - HKX14*P(2,2) + HKX15*P(2,3) + HKX6*P(2,16) + P(2,19);
+    const float HKX20 = HKX10*P(17,17) - HKX11*P(17,18) + HKX12*P(1,17) + HKX13*P(0,17) - HKX14*P(2,17) + HKX15*P(3,17) + HKX6*P(16,17) + P(17,19);
+    const float HKX21 = HKX10*P(3,17) - HKX11*P(3,18) + HKX12*P(1,3) + HKX13*P(0,3) - HKX14*P(2,3) + HKX15*P(3,3) + HKX6*P(3,16) + P(3,19);
+    const float HKX22 = HKX10*P(1,17) - HKX11*P(1,18) + HKX12*P(1,1) + HKX13*P(0,1) - HKX14*P(1,2) + HKX15*P(1,3) + HKX6*P(1,16) + P(1,19);
+    const float HKX23 = HKX10*P(17,19) - HKX11*P(18,19) + HKX12*P(1,19) + HKX13*P(0,19) - HKX14*P(2,19) + HKX15*P(3,19) + HKX6*P(16,19) + P(19,19);
+    const float HKX24 = 1.0F/(HKX10*HKX20 - HKX11*HKX18 + HKX12*HKX22 + HKX13*HKX16 - HKX14*HKX19 + HKX15*HKX21 + HKX17*HKX6 + HKX23 + R_MAG);
+
+    // common expressions used by matlab generated equations
+	float SH_MAG[9];
+	SH_MAG[0] = 2.0f*magD*q3 + 2.0f*magE*q2 + 2.0f*magN*q1;
+	SH_MAG[1] = 2.0f*magD*q0 - 2.0f*magE*q1 + 2.0f*magN*q2;
+	SH_MAG[2] = 2.0f*magD*q1 + 2.0f*magE*q0 - 2.0f*magN*q3;
+	SH_MAG[3] = sq(q3);
+	SH_MAG[4] = sq(q2);
+	SH_MAG[5] = sq(q1);
+	SH_MAG[6] = sq(q0);
+	SH_MAG[7] = 2.0f*magN*q0;
+	SH_MAG[8] = 2.0f*magE*q3;
+
+    // Compare X axis equations
+    {
+        mag_innov_var = (HKX10*HKX20 - HKX11*HKX18 + HKX12*HKX22 + HKX13*HKX16 - HKX14*HKX19 + HKX15*HKX21 + HKX17*HKX6 + HKX23 + R_MAG);
+        float HK50 = 1.0F/mag_innov_var;
+
+        // Calculate X axis observation jacobians
+        memset(Hfusion, 0, sizeof(Hfusion));
+        Hfusion[0] = 2*HKX0;
+        Hfusion[1] = 2*HKX1;
+        Hfusion[2] = 2*HKX2 - 2*HKX3 - 2*HKX4;
+        Hfusion[3] = 2*HKX5;
+        Hfusion[16] = HKX6;
+        Hfusion[17] = 2*HKX7;
+        Hfusion[18] = 2*HKX8 - 2*HKX9;
+        Hfusion[19] = 1;
+
+        // Calculate X axis Kalman gains
+        if (update_all_states) {
+            Kfusion(0) = HKX16*HKX24;
+            Kfusion(1) = HKX22*HKX24;
+            Kfusion(2) = HKX19*HKX24;
+            Kfusion(3) = HKX21*HKX24;
+
+            for (unsigned row = 4; row <= 15; row++) {
+                Kfusion(row) = HKX24*(HKX10*P(row,17) - HKX11*P(row,18) + HKX12*P(1,row) + HKX13*P(0,row) - HKX14*P(2,row) + HKX15*P(3,row) + HKX6*P(row,16) + P(row,19));
+            }
+
+            for (unsigned row = 22; row <= 23; row++) {
+                Kfusion(row) = HKX24*(HKX10*P(17,row) - HKX11*P(18,row) + HKX12*P(1,row) + HKX13*P(0,row) - HKX14*P(2,row) + HKX15*P(3,row) + HKX6*P(16,row) + P(19,row));
+            }
+        }
+
+        Kfusion(16) = HKX17*HKX24;
+        Kfusion(17) = HKX20*HKX24;
+        Kfusion(18) = HKX18*HKX24;
+        Kfusion(19) = HKX23*HKX24;
+
+        for (unsigned row = 20; row <= 21; row++) {
+            Kfusion(row) = HKX24*(HKX10*P(17,row) - HKX11*P(18,row) + HKX12*P(1,row) + HKX13*P(0,row) - HKX14*P(2,row) + HKX15*P(3,row) + HKX6*P(16,row) + P(19,row));
+        }
+
+        // save output and repeat calculation using legacy matlab generated code
+        float Hfusion_sympy[24];
+        Vector24f Kfusion_sympy;
+        for (int row=0; row<24; row++) {
+            Hfusion_sympy[row] = Hfusion[row];
+            Kfusion_sympy(row) = Kfusion(row);
+        }
+
+        // repeat calculation using matlab generated equations
+     	// X axis innovation variance
+	    mag_innov_var = (P(19,19) + R_MAG + P(1,19)*SH_MAG[0] - P(2,19)*SH_MAG[1] + P(3,19)*SH_MAG[2] - P(16,19)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + (2.0f*q0*q3 + 2.0f*q1*q2)*(P(19,17) + P(1,17)*SH_MAG[0] - P(2,17)*SH_MAG[1] + P(3,17)*SH_MAG[2] - P(16,17)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P(17,17)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,17)*(2.0f*q0*q2 - 2.0f*q1*q3) + P(0,17)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - (2.0f*q0*q2 - 2.0f*q1*q3)*(P(19,18) + P(1,18)*SH_MAG[0] - P(2,18)*SH_MAG[1] + P(3,18)*SH_MAG[2] - P(16,18)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P(17,18)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,18)*(2.0f*q0*q2 - 2.0f*q1*q3) + P(0,18)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + (SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)*(P(19,0) + P(1,0)*SH_MAG[0] - P(2,0)*SH_MAG[1] + P(3,0)*SH_MAG[2] - P(16,0)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P(17,0)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,0)*(2.0f*q0*q2 - 2.0f*q1*q3) + P(0,0)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + P(17,19)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,19)*(2.0f*q0*q2 - 2.0f*q1*q3) + SH_MAG[0]*(P(19,1) + P(1,1)*SH_MAG[0] - P(2,1)*SH_MAG[1] + P(3,1)*SH_MAG[2] - P(16,1)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P(17,1)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,1)*(2.0f*q0*q2 - 2.0f*q1*q3) + P(0,1)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - SH_MAG[1]*(P(19,2) + P(1,2)*SH_MAG[0] - P(2,2)*SH_MAG[1] + P(3,2)*SH_MAG[2] - P(16,2)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P(17,2)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,2)*(2.0f*q0*q2 - 2.0f*q1*q3) + P(0,2)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + SH_MAG[2]*(P(19,3) + P(1,3)*SH_MAG[0] - P(2,3)*SH_MAG[1] + P(3,3)*SH_MAG[2] - P(16,3)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P(17,3)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,3)*(2.0f*q0*q2 - 2.0f*q1*q3) + P(0,3)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - (SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6])*(P(19,16) + P(1,16)*SH_MAG[0] - P(2,16)*SH_MAG[1] + P(3,16)*SH_MAG[2] - P(16,16)*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P(17,16)*(2.0f*q0*q3 + 2.0f*q1*q2) - P(18,16)*(2.0f*q0*q2 - 2.0f*q1*q3) + P(0,16)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + P(0,19)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2));
+
+        // Calculate X axis observation jacobians
+        H_MAG.setZero();
+        H_MAG(0) = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
+        H_MAG(1) = SH_MAG[0];
+        H_MAG(2) = -SH_MAG[1];
+        H_MAG(3) = SH_MAG[2];
+        H_MAG(16) = SH_MAG[5] - SH_MAG[4] - SH_MAG[3] + SH_MAG[6];
+        H_MAG(17) = 2.0f*q0*q3 + 2.0f*q1*q2;
+        H_MAG(18) = 2.0f*q1*q3 - 2.0f*q0*q2;
+        H_MAG(19) = 1.0f;
+
+        // Calculate X axis Kalman gains
+        float SK_MX[5];
+        SK_MX[0] = 1.0f / mag_innov_var;
+        SK_MX[1] = SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6];
+        SK_MX[2] = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
+        SK_MX[3] = 2.0f*q0*q2 - 2.0f*q1*q3;
+        SK_MX[4] = 2.0f*q0*q3 + 2.0f*q1*q2;
+
+        if (update_all_states) {
+            Kfusion(0) = SK_MX[0]*(P(0,19) + P(0,1)*SH_MAG[0] - P(0,2)*SH_MAG[1] + P(0,3)*SH_MAG[2] + P(0,0)*SK_MX[2] - P(0,16)*SK_MX[1] + P(0,17)*SK_MX[4] - P(0,18)*SK_MX[3]);
+            Kfusion(1) = SK_MX[0]*(P(1,19) + P(1,1)*SH_MAG[0] - P(1,2)*SH_MAG[1] + P(1,3)*SH_MAG[2] + P(1,0)*SK_MX[2] - P(1,16)*SK_MX[1] + P(1,17)*SK_MX[4] - P(1,18)*SK_MX[3]);
+            Kfusion(2) = SK_MX[0]*(P(2,19) + P(2,1)*SH_MAG[0] - P(2,2)*SH_MAG[1] + P(2,3)*SH_MAG[2] + P(2,0)*SK_MX[2] - P(2,16)*SK_MX[1] + P(2,17)*SK_MX[4] - P(2,18)*SK_MX[3]);
+            Kfusion(3) = SK_MX[0]*(P(3,19) + P(3,1)*SH_MAG[0] - P(3,2)*SH_MAG[1] + P(3,3)*SH_MAG[2] + P(3,0)*SK_MX[2] - P(3,16)*SK_MX[1] + P(3,17)*SK_MX[4] - P(3,18)*SK_MX[3]);
+            Kfusion(4) = SK_MX[0]*(P(4,19) + P(4,1)*SH_MAG[0] - P(4,2)*SH_MAG[1] + P(4,3)*SH_MAG[2] + P(4,0)*SK_MX[2] - P(4,16)*SK_MX[1] + P(4,17)*SK_MX[4] - P(4,18)*SK_MX[3]);
+            Kfusion(5) = SK_MX[0]*(P(5,19) + P(5,1)*SH_MAG[0] - P(5,2)*SH_MAG[1] + P(5,3)*SH_MAG[2] + P(5,0)*SK_MX[2] - P(5,16)*SK_MX[1] + P(5,17)*SK_MX[4] - P(5,18)*SK_MX[3]);
+            Kfusion(6) = SK_MX[0]*(P(6,19) + P(6,1)*SH_MAG[0] - P(6,2)*SH_MAG[1] + P(6,3)*SH_MAG[2] + P(6,0)*SK_MX[2] - P(6,16)*SK_MX[1] + P(6,17)*SK_MX[4] - P(6,18)*SK_MX[3]);
+            Kfusion(7) = SK_MX[0]*(P(7,19) + P(7,1)*SH_MAG[0] - P(7,2)*SH_MAG[1] + P(7,3)*SH_MAG[2] + P(7,0)*SK_MX[2] - P(7,16)*SK_MX[1] + P(7,17)*SK_MX[4] - P(7,18)*SK_MX[3]);
+            Kfusion(8) = SK_MX[0]*(P(8,19) + P(8,1)*SH_MAG[0] - P(8,2)*SH_MAG[1] + P(8,3)*SH_MAG[2] + P(8,0)*SK_MX[2] - P(8,16)*SK_MX[1] + P(8,17)*SK_MX[4] - P(8,18)*SK_MX[3]);
+            Kfusion(9) = SK_MX[0]*(P(9,19) + P(9,1)*SH_MAG[0] - P(9,2)*SH_MAG[1] + P(9,3)*SH_MAG[2] + P(9,0)*SK_MX[2] - P(9,16)*SK_MX[1] + P(9,17)*SK_MX[4] - P(9,18)*SK_MX[3]);
+            Kfusion(10) = SK_MX[0]*(P(10,19) + P(10,1)*SH_MAG[0] - P(10,2)*SH_MAG[1] + P(10,3)*SH_MAG[2] + P(10,0)*SK_MX[2] - P(10,16)*SK_MX[1] + P(10,17)*SK_MX[4] - P(10,18)*SK_MX[3]);
+            Kfusion(11) = SK_MX[0]*(P(11,19) + P(11,1)*SH_MAG[0] - P(11,2)*SH_MAG[1] + P(11,3)*SH_MAG[2] + P(11,0)*SK_MX[2] - P(11,16)*SK_MX[1] + P(11,17)*SK_MX[4] - P(11,18)*SK_MX[3]);
+            Kfusion(12) = SK_MX[0]*(P(12,19) + P(12,1)*SH_MAG[0] - P(12,2)*SH_MAG[1] + P(12,3)*SH_MAG[2] + P(12,0)*SK_MX[2] - P(12,16)*SK_MX[1] + P(12,17)*SK_MX[4] - P(12,18)*SK_MX[3]);
+            Kfusion(13) = SK_MX[0]*(P(13,19) + P(13,1)*SH_MAG[0] - P(13,2)*SH_MAG[1] + P(13,3)*SH_MAG[2] + P(13,0)*SK_MX[2] - P(13,16)*SK_MX[1] + P(13,17)*SK_MX[4] - P(13,18)*SK_MX[3]);
+            Kfusion(14) = SK_MX[0]*(P(14,19) + P(14,1)*SH_MAG[0] - P(14,2)*SH_MAG[1] + P(14,3)*SH_MAG[2] + P(14,0)*SK_MX[2] - P(14,16)*SK_MX[1] + P(14,17)*SK_MX[4] - P(14,18)*SK_MX[3]);
+            Kfusion(15) = SK_MX[0]*(P(15,19) + P(15,1)*SH_MAG[0] - P(15,2)*SH_MAG[1] + P(15,3)*SH_MAG[2] + P(15,0)*SK_MX[2] - P(15,16)*SK_MX[1] + P(15,17)*SK_MX[4] - P(15,18)*SK_MX[3]);
+            Kfusion(22) = SK_MX[0]*(P(22,19) + P(22,1)*SH_MAG[0] - P(22,2)*SH_MAG[1] + P(22,3)*SH_MAG[2] + P(22,0)*SK_MX[2] - P(22,16)*SK_MX[1] + P(22,17)*SK_MX[4] - P(22,18)*SK_MX[3]);
+            Kfusion(23) = SK_MX[0]*(P(23,19) + P(23,1)*SH_MAG[0] - P(23,2)*SH_MAG[1] + P(23,3)*SH_MAG[2] + P(23,0)*SK_MX[2] - P(23,16)*SK_MX[1] + P(23,17)*SK_MX[4] - P(23,18)*SK_MX[3]);
+        }
+
+        Kfusion(16) = SK_MX[0]*(P(16,19) + P(16,1)*SH_MAG[0] - P(16,2)*SH_MAG[1] + P(16,3)*SH_MAG[2] + P(16,0)*SK_MX[2] - P(16,16)*SK_MX[1] + P(16,17)*SK_MX[4] - P(16,18)*SK_MX[3]);
+        Kfusion(17) = SK_MX[0]*(P(17,19) + P(17,1)*SH_MAG[0] - P(17,2)*SH_MAG[1] + P(17,3)*SH_MAG[2] + P(17,0)*SK_MX[2] - P(17,16)*SK_MX[1] + P(17,17)*SK_MX[4] - P(17,18)*SK_MX[3]);
+        Kfusion(18) = SK_MX[0]*(P(18,19) + P(18,1)*SH_MAG[0] - P(18,2)*SH_MAG[1] + P(18,3)*SH_MAG[2] + P(18,0)*SK_MX[2] - P(18,16)*SK_MX[1] + P(18,17)*SK_MX[4] - P(18,18)*SK_MX[3]);
+        Kfusion(19) = SK_MX[0]*(P(19,19) + P(19,1)*SH_MAG[0] - P(19,2)*SH_MAG[1] + P(19,3)*SH_MAG[2] + P(19,0)*SK_MX[2] - P(19,16)*SK_MX[1] + P(19,17)*SK_MX[4] - P(19,18)*SK_MX[3]);
+        Kfusion(20) = SK_MX[0]*(P(20,19) + P(20,1)*SH_MAG[0] - P(20,2)*SH_MAG[1] + P(20,3)*SH_MAG[2] + P(20,0)*SK_MX[2] - P(20,16)*SK_MX[1] + P(20,17)*SK_MX[4] - P(20,18)*SK_MX[3]);
+        Kfusion(21) = SK_MX[0]*(P(21,19) + P(21,1)*SH_MAG[0] - P(21,2)*SH_MAG[1] + P(21,3)*SH_MAG[2] + P(21,0)*SK_MX[2] - P(21,16)*SK_MX[1] + P(21,17)*SK_MX[4] - P(21,18)*SK_MX[3]);
+
+        // find largest observation variance difference as a fraction of the matlab value
+        float max_diff_fraction = 0.0f;
+        int max_row;
+        float max_old, max_new;
+        for (int row=0; row<24; row++) {
+            float diff_fraction;
+            if (H_MAG(row) != 0.0f) {
+                diff_fraction = fabsf(Hfusion_sympy[row] - H_MAG(row)) / fabsf(H_MAG(row));
+            } else if (Hfusion_sympy[row] != 0.0f) {
+                diff_fraction = fabsf(Hfusion_sympy[row] - H_MAG(row)) / fabsf(Hfusion_sympy[row]);
+            } else {
+                diff_fraction = 0.0f;
+            }
+            if (diff_fraction > max_diff_fraction) {
+                max_diff_fraction = diff_fraction;
+                max_row = row;
+                max_old = H_MAG(row);
+                max_new = Hfusion_sympy[row];
+            }
+        }
+
+        if (max_diff_fraction > 1E-5f) {
+            printf("Fail: Magnetomer X axis Hfusion max diff fraction = %e , old = %e , new = %e , location index = %i\n",max_diff_fraction, max_old, max_new, max_row);
+        } else {
+            printf("Pass: Magnetomer X axis Hfusion max diff fraction = %e\n",max_diff_fraction);
+        }
+
+        // find largest Kalman gain difference as a fraction of the matlab value
+        max_diff_fraction = 0.0f;
+        for (int row=0; row<4; row++) {
+            float diff_fraction;
+            if (Kfusion(row) != 0.0f) {
+                diff_fraction = fabsf(Kfusion_sympy(row) - Kfusion(row)) / fabsf(Kfusion(row));
+            } else if (Kfusion_sympy(row) != 0.0f) {
+                diff_fraction = fabsf(Kfusion_sympy(row) - Kfusion(row)) / fabsf(Kfusion_sympy(row));
+            } else {
+                diff_fraction = 0.0f;
+            }
+            if (diff_fraction > max_diff_fraction) {
+                max_diff_fraction = diff_fraction;
+                max_row = row;
+                max_old = Kfusion(row);
+                max_new = Kfusion_sympy(row);
+            }
+        }
+
+        if (max_diff_fraction > 1E-5f) {
+            printf("Fail: Magnetomer X axis Kfusion max diff fraction = %e , old = %e , new = %e , location index = %i\n",max_diff_fraction, max_old, max_new, max_row);
+        } else {
+            printf("Pass: Magnetomer X axis Kfusion max diff fraction = %e\n",max_diff_fraction);
+        }
+
+    }
+
+    // Compare Y axis equations
+    {
+        // recalculate innovation variance becasue states and covariances have changed due to previous fusion
+        const float HKY0 = magD*q1 + magE*q0 - magN*q3;
+        const float HKY1 = magD*q0 - magE*q1 + magN*q2;
+        const float HKY2 = magD*q3 + magE*q2 + magN*q1;
+        const float HKY3 = magD*q2;
+        const float HKY4 = magE*q3;
+        const float HKY5 = magN*q0;
+        const float HKY6 = q1*q2;
+        const float HKY7 = q0*q3;
+        const float HKY8 = powf(q0, 2) - powf(q1, 2) + powf(q2, 2) - powf(q3, 2);
+        const float HKY9 = q0*q1 + q2*q3;
+        const float HKY10 = 2*HKY9;
+        const float HKY11 = -2*HKY6 + 2*HKY7;
+        const float HKY12 = 2*HKY2;
+        const float HKY13 = 2*HKY0;
+        const float HKY14 = 2*HKY1;
+        const float HKY15 = -2*HKY3 + 2*HKY4 + 2*HKY5;
+        const float HKY16 = HKY10*P(0,18) - HKY11*P(0,16) + HKY12*P(0,2) + HKY13*P(0,0) + HKY14*P(0,1) - HKY15*P(0,3) + HKY8*P(0,17) + P(0,20);
+        const float HKY17 = HKY10*P(17,18) - HKY11*P(16,17) + HKY12*P(2,17) + HKY13*P(0,17) + HKY14*P(1,17) - HKY15*P(3,17) + HKY8*P(17,17) + P(17,20);
+        const float HKY18 = HKY10*P(16,18) - HKY11*P(16,16) + HKY12*P(2,16) + HKY13*P(0,16) + HKY14*P(1,16) - HKY15*P(3,16) + HKY8*P(16,17) + P(16,20);
+        const float HKY19 = HKY10*P(3,18) - HKY11*P(3,16) + HKY12*P(2,3) + HKY13*P(0,3) + HKY14*P(1,3) - HKY15*P(3,3) + HKY8*P(3,17) + P(3,20);
+        const float HKY20 = HKY10*P(18,18) - HKY11*P(16,18) + HKY12*P(2,18) + HKY13*P(0,18) + HKY14*P(1,18) - HKY15*P(3,18) + HKY8*P(17,18) + P(18,20);
+        const float HKY21 = HKY10*P(1,18) - HKY11*P(1,16) + HKY12*P(1,2) + HKY13*P(0,1) + HKY14*P(1,1) - HKY15*P(1,3) + HKY8*P(1,17) + P(1,20);
+        const float HKY22 = HKY10*P(2,18) - HKY11*P(2,16) + HKY12*P(2,2) + HKY13*P(0,2) + HKY14*P(1,2) - HKY15*P(2,3) + HKY8*P(2,17) + P(2,20);
+        const float HKY23 = HKY10*P(18,20) - HKY11*P(16,20) + HKY12*P(2,20) + HKY13*P(0,20) + HKY14*P(1,20) - HKY15*P(3,20) + HKY8*P(17,20) + P(20,20);
+        const float HKY24 = 1.0F/(HKY10*HKY20 - HKY11*HKY18 + HKY12*HKY22 + HKY13*HKY16 + HKY14*HKY21 - HKY15*HKY19 + HKY17*HKY8 + HKY23 + R_MAG);
+
+        // Calculate Y axis observation jacobians
+        memset(Hfusion, 0, sizeof(Hfusion));
+        Hfusion[0] = 2*HKY0;
+        Hfusion[1] = 2*HKY1;
+        Hfusion[2] = 2*HKY2;
+        Hfusion[3] = 2*HKY3 - 2*HKY4 - 2*HKY5;
+        Hfusion[16] = 2*HKY6 - 2*HKY7;
+        Hfusion[17] = HKY8;
+        Hfusion[18] = 2*HKY9;
+        Hfusion[20] = 1;
+
+        // Calculate Y axis Kalman gains
+        if (update_all_states) {
+            Kfusion(0) = HKY16*HKY24;
+            Kfusion(1) = HKY21*HKY24;
+            Kfusion(2) = HKY22*HKY24;
+            Kfusion(3) = HKY19*HKY24;
+
+            for (unsigned row = 4; row <= 15; row++) {
+                Kfusion(row) = HKY24*(HKY10*P(row,18) - HKY11*P(row,16) + HKY12*P(2,row) + HKY13*P(0,row) + HKY14*P(1,row) - HKY15*P(3,row) + HKY8*P(row,17) + P(row,20));
+            }
+
+            for (unsigned row = 22; row <= 23; row++) {
+                Kfusion(row) = HKY24*(HKY10*P(18,row) - HKY11*P(16,row) + HKY12*P(2,row) + HKY13*P(0,row) + HKY14*P(1,row) - HKY15*P(3,row) + HKY8*P(17,row) + P(20,row));
+            }
+        }
+
+        Kfusion(16) = HKY18*HKY24;
+        Kfusion(17) = HKY17*HKY24;
+        Kfusion(18) = HKY20*HKY24;
+        Kfusion(19) = HKY24*(HKY10*P(18,19) - HKY11*P(16,19) + HKY12*P(2,19) + HKY13*P(0,19) + HKY14*P(1,19) - HKY15*P(3,19) + HKY8*P(17,19) + P(19,20));
+        Kfusion(20) = HKY23*HKY24;
+        Kfusion(21) = HKY24*(HKY10*P(18,21) - HKY11*P(16,21) + HKY12*P(2,21) + HKY13*P(0,21) + HKY14*P(1,21) - HKY15*P(3,21) + HKY8*P(17,21) + P(20,21));
+
+        // save output and repeat calculation using legacy matlab generated code
+        float Hfusion_sympy[24];
+        Vector24f Kfusion_sympy;
+        for (int row=0; row<24; row++) {
+            Hfusion_sympy[row] = Hfusion[row];
+            Kfusion_sympy(row) = Kfusion(row);
+        }
+
+        // repeat calculation using matlab generated equations
+
+        // Y axis innovation variance
+        mag_innov_var = (P(20,20) + R_MAG + P(0,20)*SH_MAG[2] + P(1,20)*SH_MAG[1] + P(2,20)*SH_MAG[0] - P(17,20)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - (2.0f*q0*q3 - 2.0f*q1*q2)*(P(20,16) + P(0,16)*SH_MAG[2] + P(1,16)*SH_MAG[1] + P(2,16)*SH_MAG[0] - P(17,16)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P(16,16)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,16)*(2.0f*q0*q1 + 2.0f*q2*q3) - P(3,16)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + (2.0f*q0*q1 + 2.0f*q2*q3)*(P(20,18) + P(0,18)*SH_MAG[2] + P(1,18)*SH_MAG[1] + P(2,18)*SH_MAG[0] - P(17,18)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P(16,18)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,18)*(2.0f*q0*q1 + 2.0f*q2*q3) - P(3,18)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - (SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)*(P(20,3) + P(0,3)*SH_MAG[2] + P(1,3)*SH_MAG[1] + P(2,3)*SH_MAG[0] - P(17,3)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P(16,3)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,3)*(2.0f*q0*q1 + 2.0f*q2*q3) - P(3,3)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - P(16,20)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,20)*(2.0f*q0*q1 + 2.0f*q2*q3) + SH_MAG[2]*(P(20,0) + P(0,0)*SH_MAG[2] + P(1,0)*SH_MAG[1] + P(2,0)*SH_MAG[0] - P(17,0)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P(16,0)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,0)*(2.0f*q0*q1 + 2.0f*q2*q3) - P(3,0)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + SH_MAG[1]*(P(20,1) + P(0,1)*SH_MAG[2] + P(1,1)*SH_MAG[1] + P(2,1)*SH_MAG[0] - P(17,1)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P(16,1)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,1)*(2.0f*q0*q1 + 2.0f*q2*q3) - P(3,1)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + SH_MAG[0]*(P(20,2) + P(0,2)*SH_MAG[2] + P(1,2)*SH_MAG[1] + P(2,2)*SH_MAG[0] - P(17,2)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P(16,2)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,2)*(2.0f*q0*q1 + 2.0f*q2*q3) - P(3,2)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - (SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6])*(P(20,17) + P(0,17)*SH_MAG[2] + P(1,17)*SH_MAG[1] + P(2,17)*SH_MAG[0] - P(17,17)*(SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6]) - P(16,17)*(2.0f*q0*q3 - 2.0f*q1*q2) + P(18,17)*(2.0f*q0*q1 + 2.0f*q2*q3) - P(3,17)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - P(3,20)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2));
+
+        // Calculate Y axis observation jacobians
+        H_MAG.setZero();
+        H_MAG(0) = SH_MAG[2];
+        H_MAG(1) = SH_MAG[1];
+        H_MAG(2) = SH_MAG[0];
+        H_MAG(3) = 2.0f*magD*q2 - SH_MAG[8] - SH_MAG[7];
+        H_MAG(16) = 2.0f*q1*q2 - 2.0f*q0*q3;
+        H_MAG(17) = SH_MAG[4] - SH_MAG[3] - SH_MAG[5] + SH_MAG[6];
+        H_MAG(18) = 2.0f*q0*q1 + 2.0f*q2*q3;
+        H_MAG(20) = 1.0f;
+
+        // Calculate Y axis Kalman gains
+        float SK_MY[5];
+        SK_MY[0] = 1.0f / mag_innov_var;
+        SK_MY[1] = SH_MAG[3] - SH_MAG[4] + SH_MAG[5] - SH_MAG[6];
+        SK_MY[2] = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
+        SK_MY[3] = 2.0f*q0*q3 - 2.0f*q1*q2;
+        SK_MY[4] = 2.0f*q0*q1 + 2.0f*q2*q3;
+
+        if (update_all_states) {
+            Kfusion(0) = SK_MY[0]*(P(0,20) + P(0,0)*SH_MAG[2] + P(0,1)*SH_MAG[1] + P(0,2)*SH_MAG[0] - P(0,3)*SK_MY[2] - P(0,17)*SK_MY[1] - P(0,16)*SK_MY[3] + P(0,18)*SK_MY[4]);
+            Kfusion(1) = SK_MY[0]*(P(1,20) + P(1,0)*SH_MAG[2] + P(1,1)*SH_MAG[1] + P(1,2)*SH_MAG[0] - P(1,3)*SK_MY[2] - P(1,17)*SK_MY[1] - P(1,16)*SK_MY[3] + P(1,18)*SK_MY[4]);
+            Kfusion(2) = SK_MY[0]*(P(2,20) + P(2,0)*SH_MAG[2] + P(2,1)*SH_MAG[1] + P(2,2)*SH_MAG[0] - P(2,3)*SK_MY[2] - P(2,17)*SK_MY[1] - P(2,16)*SK_MY[3] + P(2,18)*SK_MY[4]);
+            Kfusion(3) = SK_MY[0]*(P(3,20) + P(3,0)*SH_MAG[2] + P(3,1)*SH_MAG[1] + P(3,2)*SH_MAG[0] - P(3,3)*SK_MY[2] - P(3,17)*SK_MY[1] - P(3,16)*SK_MY[3] + P(3,18)*SK_MY[4]);
+            Kfusion(4) = SK_MY[0]*(P(4,20) + P(4,0)*SH_MAG[2] + P(4,1)*SH_MAG[1] + P(4,2)*SH_MAG[0] - P(4,3)*SK_MY[2] - P(4,17)*SK_MY[1] - P(4,16)*SK_MY[3] + P(4,18)*SK_MY[4]);
+            Kfusion(5) = SK_MY[0]*(P(5,20) + P(5,0)*SH_MAG[2] + P(5,1)*SH_MAG[1] + P(5,2)*SH_MAG[0] - P(5,3)*SK_MY[2] - P(5,17)*SK_MY[1] - P(5,16)*SK_MY[3] + P(5,18)*SK_MY[4]);
+            Kfusion(6) = SK_MY[0]*(P(6,20) + P(6,0)*SH_MAG[2] + P(6,1)*SH_MAG[1] + P(6,2)*SH_MAG[0] - P(6,3)*SK_MY[2] - P(6,17)*SK_MY[1] - P(6,16)*SK_MY[3] + P(6,18)*SK_MY[4]);
+            Kfusion(7) = SK_MY[0]*(P(7,20) + P(7,0)*SH_MAG[2] + P(7,1)*SH_MAG[1] + P(7,2)*SH_MAG[0] - P(7,3)*SK_MY[2] - P(7,17)*SK_MY[1] - P(7,16)*SK_MY[3] + P(7,18)*SK_MY[4]);
+            Kfusion(8) = SK_MY[0]*(P(8,20) + P(8,0)*SH_MAG[2] + P(8,1)*SH_MAG[1] + P(8,2)*SH_MAG[0] - P(8,3)*SK_MY[2] - P(8,17)*SK_MY[1] - P(8,16)*SK_MY[3] + P(8,18)*SK_MY[4]);
+            Kfusion(9) = SK_MY[0]*(P(9,20) + P(9,0)*SH_MAG[2] + P(9,1)*SH_MAG[1] + P(9,2)*SH_MAG[0] - P(9,3)*SK_MY[2] - P(9,17)*SK_MY[1] - P(9,16)*SK_MY[3] + P(9,18)*SK_MY[4]);
+            Kfusion(10) = SK_MY[0]*(P(10,20) + P(10,0)*SH_MAG[2] + P(10,1)*SH_MAG[1] + P(10,2)*SH_MAG[0] - P(10,3)*SK_MY[2] - P(10,17)*SK_MY[1] - P(10,16)*SK_MY[3] + P(10,18)*SK_MY[4]);
+            Kfusion(11) = SK_MY[0]*(P(11,20) + P(11,0)*SH_MAG[2] + P(11,1)*SH_MAG[1] + P(11,2)*SH_MAG[0] - P(11,3)*SK_MY[2] - P(11,17)*SK_MY[1] - P(11,16)*SK_MY[3] + P(11,18)*SK_MY[4]);
+            Kfusion(12) = SK_MY[0]*(P(12,20) + P(12,0)*SH_MAG[2] + P(12,1)*SH_MAG[1] + P(12,2)*SH_MAG[0] - P(12,3)*SK_MY[2] - P(12,17)*SK_MY[1] - P(12,16)*SK_MY[3] + P(12,18)*SK_MY[4]);
+            Kfusion(13) = SK_MY[0]*(P(13,20) + P(13,0)*SH_MAG[2] + P(13,1)*SH_MAG[1] + P(13,2)*SH_MAG[0] - P(13,3)*SK_MY[2] - P(13,17)*SK_MY[1] - P(13,16)*SK_MY[3] + P(13,18)*SK_MY[4]);
+            Kfusion(14) = SK_MY[0]*(P(14,20) + P(14,0)*SH_MAG[2] + P(14,1)*SH_MAG[1] + P(14,2)*SH_MAG[0] - P(14,3)*SK_MY[2] - P(14,17)*SK_MY[1] - P(14,16)*SK_MY[3] + P(14,18)*SK_MY[4]);
+            Kfusion(15) = SK_MY[0]*(P(15,20) + P(15,0)*SH_MAG[2] + P(15,1)*SH_MAG[1] + P(15,2)*SH_MAG[0] - P(15,3)*SK_MY[2] - P(15,17)*SK_MY[1] - P(15,16)*SK_MY[3] + P(15,18)*SK_MY[4]);
+            Kfusion(22) = SK_MY[0]*(P(22,20) + P(22,0)*SH_MAG[2] + P(22,1)*SH_MAG[1] + P(22,2)*SH_MAG[0] - P(22,3)*SK_MY[2] - P(22,17)*SK_MY[1] - P(22,16)*SK_MY[3] + P(22,18)*SK_MY[4]);
+            Kfusion(23) = SK_MY[0]*(P(23,20) + P(23,0)*SH_MAG[2] + P(23,1)*SH_MAG[1] + P(23,2)*SH_MAG[0] - P(23,3)*SK_MY[2] - P(23,17)*SK_MY[1] - P(23,16)*SK_MY[3] + P(23,18)*SK_MY[4]);
+        }
+
+        Kfusion(16) = SK_MY[0]*(P(16,20) + P(16,0)*SH_MAG[2] + P(16,1)*SH_MAG[1] + P(16,2)*SH_MAG[0] - P(16,3)*SK_MY[2] - P(16,17)*SK_MY[1] - P(16,16)*SK_MY[3] + P(16,18)*SK_MY[4]);
+        Kfusion(17) = SK_MY[0]*(P(17,20) + P(17,0)*SH_MAG[2] + P(17,1)*SH_MAG[1] + P(17,2)*SH_MAG[0] - P(17,3)*SK_MY[2] - P(17,17)*SK_MY[1] - P(17,16)*SK_MY[3] + P(17,18)*SK_MY[4]);
+        Kfusion(18) = SK_MY[0]*(P(18,20) + P(18,0)*SH_MAG[2] + P(18,1)*SH_MAG[1] + P(18,2)*SH_MAG[0] - P(18,3)*SK_MY[2] - P(18,17)*SK_MY[1] - P(18,16)*SK_MY[3] + P(18,18)*SK_MY[4]);
+        Kfusion(19) = SK_MY[0]*(P(19,20) + P(19,0)*SH_MAG[2] + P(19,1)*SH_MAG[1] + P(19,2)*SH_MAG[0] - P(19,3)*SK_MY[2] - P(19,17)*SK_MY[1] - P(19,16)*SK_MY[3] + P(19,18)*SK_MY[4]);
+        Kfusion(20) = SK_MY[0]*(P(20,20) + P(20,0)*SH_MAG[2] + P(20,1)*SH_MAG[1] + P(20,2)*SH_MAG[0] - P(20,3)*SK_MY[2] - P(20,17)*SK_MY[1] - P(20,16)*SK_MY[3] + P(20,18)*SK_MY[4]);
+        Kfusion(21) = SK_MY[0]*(P(21,20) + P(21,0)*SH_MAG[2] + P(21,1)*SH_MAG[1] + P(21,2)*SH_MAG[0] - P(21,3)*SK_MY[2] - P(21,17)*SK_MY[1] - P(21,16)*SK_MY[3] + P(21,18)*SK_MY[4]);
+
+        // find largest observation variance difference as a fraction of the matlab value
+        float max_diff_fraction = 0.0f;
+        int max_row;
+        float max_old, max_new;
+        for (int row=0; row<24; row++) {
+            float diff_fraction;
+            if (H_MAG(row) != 0.0f) {
+                diff_fraction = fabsf(Hfusion_sympy[row] - H_MAG(row)) / fabsf(H_MAG(row));
+            } else if (Hfusion_sympy[row] != 0.0f) {
+                diff_fraction = fabsf(Hfusion_sympy[row] - H_MAG(row)) / fabsf(Hfusion_sympy[row]);
+            } else {
+                diff_fraction = 0.0f;
+            }
+            if (diff_fraction > max_diff_fraction) {
+                max_diff_fraction = diff_fraction;
+                max_row = row;
+                max_old = H_MAG(row);
+                max_new = Hfusion_sympy[row];
+            }
+        }
+
+        if (max_diff_fraction > 1E-5f) {
+            printf("Fail: Magnetomer Y axis Hfusion max diff fraction = %e , old = %e , new = %e , location index = %i\n",max_diff_fraction, max_old, max_new, max_row);
+        } else {
+            printf("Pass: Magnetomer Y axis Hfusion max diff fraction = %e\n",max_diff_fraction);
+        }
+
+        // find largest Kalman gain difference as a fraction of the matlab value
+        max_diff_fraction = 0.0f;
+        for (int row=0; row<4; row++) {
+            float diff_fraction;
+            if (Kfusion(row) != 0.0f) {
+                diff_fraction = fabsf(Kfusion_sympy(row) - Kfusion(row)) / fabsf(Kfusion(row));
+            } else if (Kfusion_sympy(row) != 0.0f) {
+                diff_fraction = fabsf(Kfusion_sympy(row) - Kfusion(row)) / fabsf(Kfusion_sympy(row));
+            } else {
+                diff_fraction = 0.0f;
+            }
+            if (diff_fraction > max_diff_fraction) {
+                max_diff_fraction = diff_fraction;
+                max_row = row;
+                max_old = Kfusion(row);
+                max_new = Kfusion_sympy(row);
+            }
+        }
+
+        if (max_diff_fraction > 1E-5f) {
+            printf("Fail: Magnetomer Y axis Kfusion max diff fraction = %e , old = %e , new = %e , location index = %i\n",max_diff_fraction, max_old, max_new, max_row);
+        } else {
+            printf("Pass: Magnetomer Y axis Kfusion max diff fraction = %e\n",max_diff_fraction);
+        }
+
+    }
+
+    // Compare Z axis equations
+    {
+        // recalculate innovation variance becasue states and covariances have changed due to previous fusion
+        const float HKZ0 = magD*q0 - magE*q1 + magN*q2;
+        const float HKZ1 = magN*q3;
+        const float HKZ2 = magD*q1;
+        const float HKZ3 = magE*q0;
+        const float HKZ4 = -magD*q2 + magE*q3 + magN*q0;
+        const float HKZ5 = magD*q3 + magE*q2 + magN*q1;
+        const float HKZ6 = q0*q2 + q1*q3;
+        const float HKZ7 = q2*q3;
+        const float HKZ8 = q0*q1;
+        const float HKZ9 = powf(q0, 2) - powf(q1, 2) - powf(q2, 2) + powf(q3, 2);
+        const float HKZ10 = 2*HKZ6;
+        const float HKZ11 = -2*HKZ7 + 2*HKZ8;
+        const float HKZ12 = 2*HKZ5;
+        const float HKZ13 = 2*HKZ0;
+        const float HKZ14 = -2*HKZ1 + 2*HKZ2 + 2*HKZ3;
+        const float HKZ15 = 2*HKZ4;
+        const float HKZ16 = HKZ10*P(0,16) - HKZ11*P(0,17) + HKZ12*P(0,3) + HKZ13*P(0,0) - HKZ14*P(0,1) + HKZ15*P(0,2) + HKZ9*P(0,18) + P(0,21);
+        const float HKZ17 = HKZ10*P(16,18) - HKZ11*P(17,18) + HKZ12*P(3,18) + HKZ13*P(0,18) - HKZ14*P(1,18) + HKZ15*P(2,18) + HKZ9*P(18,18) + P(18,21);
+        const float HKZ18 = HKZ10*P(16,17) - HKZ11*P(17,17) + HKZ12*P(3,17) + HKZ13*P(0,17) - HKZ14*P(1,17) + HKZ15*P(2,17) + HKZ9*P(17,18) + P(17,21);
+        const float HKZ19 = HKZ10*P(1,16) - HKZ11*P(1,17) + HKZ12*P(1,3) + HKZ13*P(0,1) - HKZ14*P(1,1) + HKZ15*P(1,2) + HKZ9*P(1,18) + P(1,21);
+        const float HKZ20 = HKZ10*P(16,16) - HKZ11*P(16,17) + HKZ12*P(3,16) + HKZ13*P(0,16) - HKZ14*P(1,16) + HKZ15*P(2,16) + HKZ9*P(16,18) + P(16,21);
+        const float HKZ21 = HKZ10*P(3,16) - HKZ11*P(3,17) + HKZ12*P(3,3) + HKZ13*P(0,3) - HKZ14*P(1,3) + HKZ15*P(2,3) + HKZ9*P(3,18) + P(3,21);
+        const float HKZ22 = HKZ10*P(2,16) - HKZ11*P(2,17) + HKZ12*P(2,3) + HKZ13*P(0,2) - HKZ14*P(1,2) + HKZ15*P(2,2) + HKZ9*P(2,18) + P(2,21);
+        const float HKZ23 = HKZ10*P(16,21) - HKZ11*P(17,21) + HKZ12*P(3,21) + HKZ13*P(0,21) - HKZ14*P(1,21) + HKZ15*P(2,21) + HKZ9*P(18,21) + P(21,21);
+        const float HKZ24 = 1.0F/(HKZ10*HKZ20 - HKZ11*HKZ18 + HKZ12*HKZ21 + HKZ13*HKZ16 - HKZ14*HKZ19 + HKZ15*HKZ22 + HKZ17*HKZ9 + HKZ23 + R_MAG);
+
+        // calculate Z axis observation jacobians
+        memset(Hfusion, 0, sizeof(Hfusion));
+        Hfusion[0] = 2*HKZ0;
+        Hfusion[1] = 2*HKZ1 - 2*HKZ2 - 2*HKZ3;
+        Hfusion[2] = 2*HKZ4;
+        Hfusion[3] = 2*HKZ5;
+        Hfusion[16] = 2*HKZ6;
+        Hfusion[17] = 2*HKZ7 - 2*HKZ8;
+        Hfusion[18] = HKZ9;
+        Hfusion[21] = 1;
+
+        // Calculate Z axis Kalman gains
+        if (update_all_states) {
+            Kfusion(0) = HKZ16*HKZ24;
+            Kfusion(1) = HKZ19*HKZ24;
+            Kfusion(2) = HKZ22*HKZ24;
+            Kfusion(3) = HKZ21*HKZ24;
+
+            for (unsigned row = 4; row <= 15; row++) {
+                Kfusion(row) = HKZ24*(HKZ10*P(row,16) - HKZ11*P(row,17) + HKZ12*P(3,row) + HKZ13*P(0,row) - HKZ14*P(1,row) + HKZ15*P(2,row) + HKZ9*P(row,18) + P(row,21));
+            }
+
+            for (unsigned row = 22; row <= 23; row++) {
+                Kfusion(row) = HKZ24*(HKZ10*P(16,row) - HKZ11*P(17,row) + HKZ12*P(3,row) + HKZ13*P(0,row) - HKZ14*P(1,row) + HKZ15*P(2,row) + HKZ9*P(18,row) + P(21,row));
+            }
+        }
+
+        Kfusion(16) = HKZ20*HKZ24;
+        Kfusion(17) = HKZ18*HKZ24;
+        Kfusion(18) = HKZ17*HKZ24;
+
+        for (unsigned row = 19; row <= 20; row++) {
+            Kfusion(row) = HKZ24*(HKZ10*P(16,row) - HKZ11*P(17,row) + HKZ12*P(3,row) + HKZ13*P(0,row) - HKZ14*P(1,row) + HKZ15*P(2,row) + HKZ9*P(18,row) + P(row,21));
+        }
+
+        Kfusion(21) = HKZ23*HKZ24;
+
+        // save output and repeat calculation using legacy matlab generated code
+        float Hfusion_sympy[24];
+        Vector24f Kfusion_sympy;
+        for (int row=0; row<24; row++) {
+            Hfusion_sympy[row] = Hfusion[row];
+            Kfusion_sympy(row) = Kfusion(row);
+        }
+
+        // repeat calculation using matlab generated equations
+
+        // Z axis innovation variance
+        mag_innov_var = (P(21,21) + R_MAG + P(0,21)*SH_MAG[1] - P(1,21)*SH_MAG[2] + P(3,21)*SH_MAG[0] + P(18,21)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + (2.0f*q0*q2 + 2.0f*q1*q3)*(P(21,16) + P(0,16)*SH_MAG[1] - P(1,16)*SH_MAG[2] + P(3,16)*SH_MAG[0] + P(18,16)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P(16,16)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,16)*(2.0f*q0*q1 - 2.0f*q2*q3) + P(2,16)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - (2.0f*q0*q1 - 2.0f*q2*q3)*(P(21,17) + P(0,17)*SH_MAG[1] - P(1,17)*SH_MAG[2] + P(3,17)*SH_MAG[0] + P(18,17)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P(16,17)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,17)*(2.0f*q0*q1 - 2.0f*q2*q3) + P(2,17)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + (SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)*(P(21,2) + P(0,2)*SH_MAG[1] - P(1,2)*SH_MAG[2] + P(3,2)*SH_MAG[0] + P(18,2)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P(16,2)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,2)*(2.0f*q0*q1 - 2.0f*q2*q3) + P(2,2)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + P(16,21)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,21)*(2.0f*q0*q1 - 2.0f*q2*q3) + SH_MAG[1]*(P(21,0) + P(0,0)*SH_MAG[1] - P(1,0)*SH_MAG[2] + P(3,0)*SH_MAG[0] + P(18,0)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P(16,0)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,0)*(2.0f*q0*q1 - 2.0f*q2*q3) + P(2,0)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) - SH_MAG[2]*(P(21,1) + P(0,1)*SH_MAG[1] - P(1,1)*SH_MAG[2] + P(3,1)*SH_MAG[0] + P(18,1)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P(16,1)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,1)*(2.0f*q0*q1 - 2.0f*q2*q3) + P(2,1)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + SH_MAG[0]*(P(21,3) + P(0,3)*SH_MAG[1] - P(1,3)*SH_MAG[2] + P(3,3)*SH_MAG[0] + P(18,3)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P(16,3)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,3)*(2.0f*q0*q1 - 2.0f*q2*q3) + P(2,3)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + (SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6])*(P(21,18) + P(0,18)*SH_MAG[1] - P(1,18)*SH_MAG[2] + P(3,18)*SH_MAG[0] + P(18,18)*(SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6]) + P(16,18)*(2.0f*q0*q2 + 2.0f*q1*q3) - P(17,18)*(2.0f*q0*q1 - 2.0f*q2*q3) + P(2,18)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2)) + P(2,21)*(SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2));
+
+        // calculate Z axis observation jacobians
+        H_MAG.setZero();
+        H_MAG(0) = SH_MAG[1];
+        H_MAG(1) = -SH_MAG[2];
+        H_MAG(2) = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
+        H_MAG(3) = SH_MAG[0];
+        H_MAG(16) = 2.0f*q0*q2 + 2.0f*q1*q3;
+        H_MAG(17) = 2.0f*q2*q3 - 2.0f*q0*q1;
+        H_MAG(18) = SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6];
+        H_MAG(21) = 1.0f;
+
+        // Calculate Z axis Kalman gains
+        float SK_MZ[5];
+        SK_MZ[0] = 1.0f / mag_innov_var;
+        SK_MZ[1] = SH_MAG[3] - SH_MAG[4] - SH_MAG[5] + SH_MAG[6];
+        SK_MZ[2] = SH_MAG[7] + SH_MAG[8] - 2.0f*magD*q2;
+        SK_MZ[3] = 2.0f*q0*q1 - 2.0f*q2*q3;
+        SK_MZ[4] = 2.0f*q0*q2 + 2.0f*q1*q3;
+
+        if (update_all_states) {
+            Kfusion(0) = SK_MZ[0]*(P(0,21) + P(0,0)*SH_MAG[1] - P(0,1)*SH_MAG[2] + P(0,3)*SH_MAG[0] + P(0,2)*SK_MZ[2] + P(0,18)*SK_MZ[1] + P(0,16)*SK_MZ[4] - P(0,17)*SK_MZ[3]);
+            Kfusion(1) = SK_MZ[0]*(P(1,21) + P(1,0)*SH_MAG[1] - P(1,1)*SH_MAG[2] + P(1,3)*SH_MAG[0] + P(1,2)*SK_MZ[2] + P(1,18)*SK_MZ[1] + P(1,16)*SK_MZ[4] - P(1,17)*SK_MZ[3]);
+            Kfusion(2) = SK_MZ[0]*(P(2,21) + P(2,0)*SH_MAG[1] - P(2,1)*SH_MAG[2] + P(2,3)*SH_MAG[0] + P(2,2)*SK_MZ[2] + P(2,18)*SK_MZ[1] + P(2,16)*SK_MZ[4] - P(2,17)*SK_MZ[3]);
+            Kfusion(3) = SK_MZ[0]*(P(3,21) + P(3,0)*SH_MAG[1] - P(3,1)*SH_MAG[2] + P(3,3)*SH_MAG[0] + P(3,2)*SK_MZ[2] + P(3,18)*SK_MZ[1] + P(3,16)*SK_MZ[4] - P(3,17)*SK_MZ[3]);
+            Kfusion(4) = SK_MZ[0]*(P(4,21) + P(4,0)*SH_MAG[1] - P(4,1)*SH_MAG[2] + P(4,3)*SH_MAG[0] + P(4,2)*SK_MZ[2] + P(4,18)*SK_MZ[1] + P(4,16)*SK_MZ[4] - P(4,17)*SK_MZ[3]);
+            Kfusion(5) = SK_MZ[0]*(P(5,21) + P(5,0)*SH_MAG[1] - P(5,1)*SH_MAG[2] + P(5,3)*SH_MAG[0] + P(5,2)*SK_MZ[2] + P(5,18)*SK_MZ[1] + P(5,16)*SK_MZ[4] - P(5,17)*SK_MZ[3]);
+            Kfusion(6) = SK_MZ[0]*(P(6,21) + P(6,0)*SH_MAG[1] - P(6,1)*SH_MAG[2] + P(6,3)*SH_MAG[0] + P(6,2)*SK_MZ[2] + P(6,18)*SK_MZ[1] + P(6,16)*SK_MZ[4] - P(6,17)*SK_MZ[3]);
+            Kfusion(7) = SK_MZ[0]*(P(7,21) + P(7,0)*SH_MAG[1] - P(7,1)*SH_MAG[2] + P(7,3)*SH_MAG[0] + P(7,2)*SK_MZ[2] + P(7,18)*SK_MZ[1] + P(7,16)*SK_MZ[4] - P(7,17)*SK_MZ[3]);
+            Kfusion(8) = SK_MZ[0]*(P(8,21) + P(8,0)*SH_MAG[1] - P(8,1)*SH_MAG[2] + P(8,3)*SH_MAG[0] + P(8,2)*SK_MZ[2] + P(8,18)*SK_MZ[1] + P(8,16)*SK_MZ[4] - P(8,17)*SK_MZ[3]);
+            Kfusion(9) = SK_MZ[0]*(P(9,21) + P(9,0)*SH_MAG[1] - P(9,1)*SH_MAG[2] + P(9,3)*SH_MAG[0] + P(9,2)*SK_MZ[2] + P(9,18)*SK_MZ[1] + P(9,16)*SK_MZ[4] - P(9,17)*SK_MZ[3]);
+            Kfusion(10) = SK_MZ[0]*(P(10,21) + P(10,0)*SH_MAG[1] - P(10,1)*SH_MAG[2] + P(10,3)*SH_MAG[0] + P(10,2)*SK_MZ[2] + P(10,18)*SK_MZ[1] + P(10,16)*SK_MZ[4] - P(10,17)*SK_MZ[3]);
+            Kfusion(11) = SK_MZ[0]*(P(11,21) + P(11,0)*SH_MAG[1] - P(11,1)*SH_MAG[2] + P(11,3)*SH_MAG[0] + P(11,2)*SK_MZ[2] + P(11,18)*SK_MZ[1] + P(11,16)*SK_MZ[4] - P(11,17)*SK_MZ[3]);
+            Kfusion(12) = SK_MZ[0]*(P(12,21) + P(12,0)*SH_MAG[1] - P(12,1)*SH_MAG[2] + P(12,3)*SH_MAG[0] + P(12,2)*SK_MZ[2] + P(12,18)*SK_MZ[1] + P(12,16)*SK_MZ[4] - P(12,17)*SK_MZ[3]);
+            Kfusion(13) = SK_MZ[0]*(P(13,21) + P(13,0)*SH_MAG[1] - P(13,1)*SH_MAG[2] + P(13,3)*SH_MAG[0] + P(13,2)*SK_MZ[2] + P(13,18)*SK_MZ[1] + P(13,16)*SK_MZ[4] - P(13,17)*SK_MZ[3]);
+            Kfusion(14) = SK_MZ[0]*(P(14,21) + P(14,0)*SH_MAG[1] - P(14,1)*SH_MAG[2] + P(14,3)*SH_MAG[0] + P(14,2)*SK_MZ[2] + P(14,18)*SK_MZ[1] + P(14,16)*SK_MZ[4] - P(14,17)*SK_MZ[3]);
+            Kfusion(15) = SK_MZ[0]*(P(15,21) + P(15,0)*SH_MAG[1] - P(15,1)*SH_MAG[2] + P(15,3)*SH_MAG[0] + P(15,2)*SK_MZ[2] + P(15,18)*SK_MZ[1] + P(15,16)*SK_MZ[4] - P(15,17)*SK_MZ[3]);
+            Kfusion(22) = SK_MZ[0]*(P(22,21) + P(22,0)*SH_MAG[1] - P(22,1)*SH_MAG[2] + P(22,3)*SH_MAG[0] + P(22,2)*SK_MZ[2] + P(22,18)*SK_MZ[1] + P(22,16)*SK_MZ[4] - P(22,17)*SK_MZ[3]);
+            Kfusion(23) = SK_MZ[0]*(P(23,21) + P(23,0)*SH_MAG[1] - P(23,1)*SH_MAG[2] + P(23,3)*SH_MAG[0] + P(23,2)*SK_MZ[2] + P(23,18)*SK_MZ[1] + P(23,16)*SK_MZ[4] - P(23,17)*SK_MZ[3]);
+        }
+
+        Kfusion(16) = SK_MZ[0]*(P(16,21) + P(16,0)*SH_MAG[1] - P(16,1)*SH_MAG[2] + P(16,3)*SH_MAG[0] + P(16,2)*SK_MZ[2] + P(16,18)*SK_MZ[1] + P(16,16)*SK_MZ[4] - P(16,17)*SK_MZ[3]);
+        Kfusion(17) = SK_MZ[0]*(P(17,21) + P(17,0)*SH_MAG[1] - P(17,1)*SH_MAG[2] + P(17,3)*SH_MAG[0] + P(17,2)*SK_MZ[2] + P(17,18)*SK_MZ[1] + P(17,16)*SK_MZ[4] - P(17,17)*SK_MZ[3]);
+        Kfusion(18) = SK_MZ[0]*(P(18,21) + P(18,0)*SH_MAG[1] - P(18,1)*SH_MAG[2] + P(18,3)*SH_MAG[0] + P(18,2)*SK_MZ[2] + P(18,18)*SK_MZ[1] + P(18,16)*SK_MZ[4] - P(18,17)*SK_MZ[3]);
+        Kfusion(19) = SK_MZ[0]*(P(19,21) + P(19,0)*SH_MAG[1] - P(19,1)*SH_MAG[2] + P(19,3)*SH_MAG[0] + P(19,2)*SK_MZ[2] + P(19,18)*SK_MZ[1] + P(19,16)*SK_MZ[4] - P(19,17)*SK_MZ[3]);
+        Kfusion(20) = SK_MZ[0]*(P(20,21) + P(20,0)*SH_MAG[1] - P(20,1)*SH_MAG[2] + P(20,3)*SH_MAG[0] + P(20,2)*SK_MZ[2] + P(20,18)*SK_MZ[1] + P(20,16)*SK_MZ[4] - P(20,17)*SK_MZ[3]);
+        Kfusion(21) = SK_MZ[0]*(P(21,21) + P(21,0)*SH_MAG[1] - P(21,1)*SH_MAG[2] + P(21,3)*SH_MAG[0] + P(21,2)*SK_MZ[2] + P(21,18)*SK_MZ[1] + P(21,16)*SK_MZ[4] - P(21,17)*SK_MZ[3]);
+
+        // find largest observation variance difference as a fraction of the matlab value
+        float max_diff_fraction = 0.0f;
+        int max_row;
+        float max_old, max_new;
+        for (int row=0; row<24; row++) {
+            float diff_fraction;
+            if (H_MAG(row) != 0.0f) {
+                diff_fraction = fabsf(Hfusion_sympy[row] - H_MAG(row)) / fabsf(H_MAG(row));
+            } else if (Hfusion_sympy[row] != 0.0f) {
+                diff_fraction = fabsf(Hfusion_sympy[row] - H_MAG(row)) / fabsf(Hfusion_sympy[row]);
+            } else {
+                diff_fraction = 0.0f;
+            }
+            if (diff_fraction > max_diff_fraction) {
+                max_diff_fraction = diff_fraction;
+                max_row = row;
+                max_old = H_MAG(row);
+                max_new = Hfusion_sympy[row];
+            }
+        }
+
+        if (max_diff_fraction > 1E-5f) {
+            printf("Fail: Magnetomer Z axis Hfusion max diff fraction = %e , old = %e , new = %e , location index = %i\n",max_diff_fraction, max_old, max_new, max_row);
+        } else {
+            printf("Pass: Magnetomer Z axis Hfusion max diff fraction = %e\n",max_diff_fraction);
+        }
+
+        // find largest Kalman gain difference as a fraction of the matlab value
+        max_diff_fraction = 0.0f;
+        for (int row=0; row<4; row++) {
+            float diff_fraction;
+            if (Kfusion(row) != 0.0f) {
+                diff_fraction = fabsf(Kfusion_sympy(row) - Kfusion(row)) / fabsf(Kfusion(row));
+            } else if (Kfusion_sympy(row) != 0.0f) {
+                diff_fraction = fabsf(Kfusion_sympy(row) - Kfusion(row)) / fabsf(Kfusion_sympy(row));
+            } else {
+                diff_fraction = 0.0f;
+            }
+            if (diff_fraction > max_diff_fraction) {
+                max_diff_fraction = diff_fraction;
+                max_row = row;
+                max_old = Kfusion(row);
+                max_new = Kfusion_sympy(row);
+            }
+        }
+
+        if (max_diff_fraction > 1E-5f) {
+            printf("Fail: Magnetomer Z axis Kfusion max diff fraction = %e , old = %e , new = %e , location index = %i\n",max_diff_fraction, max_old, max_new, max_row);
+        } else {
+            printf("Pass: Magnetomer Z axis Kfusion max diff fraction = %e\n",max_diff_fraction);
+        }
+
+    }
+
+    return 0;
+}

EKF/python/ekf_derivation/generated/3Dmag_generated.cpp

@@ -0,0 +1,249 @@
+// Axis 0 equations
+// Sub Expressions
+const float HKX0 = -magD*q2 + magE*q3 + magN*q0;
+const float HKX1 = magD*q3 + magE*q2 + magN*q1;
+const float HKX2 = magE*q1;
+const float HKX3 = magD*q0;
+const float HKX4 = magN*q2;
+const float HKX5 = magD*q1 + magE*q0 - magN*q3;
+const float HKX6 = powf(q0, 2) + powf(q1, 2) - powf(q2, 2) - powf(q3, 2);
+const float HKX7 = q0*q3 + q1*q2;
+const float HKX8 = q1*q3;
+const float HKX9 = q0*q2;
+const float HKX10 = 2*HKX7;
+const float HKX11 = -2*HKX8 + 2*HKX9;
+const float HKX12 = 2*HKX1;
+const float HKX13 = 2*HKX0;
+const float HKX14 = -2*HKX2 + 2*HKX3 + 2*HKX4;
+const float HKX15 = 2*HKX5;
+const float HKX16 = HKX10*P(0,17) - HKX11*P(0,18) + HKX12*P(0,1) + HKX13*P(0,0) - HKX14*P(0,2) + HKX15*P(0,3) + HKX6*P(0,16) + P(0,19);
+const float HKX17 = HKX10*P(16,17) - HKX11*P(16,18) + HKX12*P(1,16) + HKX13*P(0,16) - HKX14*P(2,16) + HKX15*P(3,16) + HKX6*P(16,16) + P(16,19);
+const float HKX18 = HKX10*P(17,18) - HKX11*P(18,18) + HKX12*P(1,18) + HKX13*P(0,18) - HKX14*P(2,18) + HKX15*P(3,18) + HKX6*P(16,18) + P(18,19);
+const float HKX19 = HKX10*P(2,17) - HKX11*P(2,18) + HKX12*P(1,2) + HKX13*P(0,2) - HKX14*P(2,2) + HKX15*P(2,3) + HKX6*P(2,16) + P(2,19);
+const float HKX20 = HKX10*P(17,17) - HKX11*P(17,18) + HKX12*P(1,17) + HKX13*P(0,17) - HKX14*P(2,17) + HKX15*P(3,17) + HKX6*P(16,17) + P(17,19);
+const float HKX21 = HKX10*P(3,17) - HKX11*P(3,18) + HKX12*P(1,3) + HKX13*P(0,3) - HKX14*P(2,3) + HKX15*P(3,3) + HKX6*P(3,16) + P(3,19);
+const float HKX22 = HKX10*P(1,17) - HKX11*P(1,18) + HKX12*P(1,1) + HKX13*P(0,1) - HKX14*P(1,2) + HKX15*P(1,3) + HKX6*P(1,16) + P(1,19);
+const float HKX23 = HKX10*P(17,19) - HKX11*P(18,19) + HKX12*P(1,19) + HKX13*P(0,19) - HKX14*P(2,19) + HKX15*P(3,19) + HKX6*P(16,19) + P(19,19);
+const float HKX24 = 1.0F/(HKX10*HKX20 - HKX11*HKX18 + HKX12*HKX22 + HKX13*HKX16 - HKX14*HKX19 + HKX15*HKX21 + HKX17*HKX6 + HKX23 + R_MAG);
+
+
+// Observation Jacobians
+Hfusion.at<0>() = 2*HKX0;
+Hfusion.at<1>() = 2*HKX1;
+Hfusion.at<2>() = 2*HKX2 - 2*HKX3 - 2*HKX4;
+Hfusion.at<3>() = 2*HKX5;
+Hfusion.at<4>() = 0;
+Hfusion.at<5>() = 0;
+Hfusion.at<6>() = 0;
+Hfusion.at<7>() = 0;
+Hfusion.at<8>() = 0;
+Hfusion.at<9>() = 0;
+Hfusion.at<10>() = 0;
+Hfusion.at<11>() = 0;
+Hfusion.at<12>() = 0;
+Hfusion.at<13>() = 0;
+Hfusion.at<14>() = 0;
+Hfusion.at<15>() = 0;
+Hfusion.at<16>() = HKX6;
+Hfusion.at<17>() = 2*HKX7;
+Hfusion.at<18>() = 2*HKX8 - 2*HKX9;
+Hfusion.at<19>() = 1;
+Hfusion.at<20>() = 0;
+Hfusion.at<21>() = 0;
+Hfusion.at<22>() = 0;
+Hfusion.at<23>() = 0;
+
+
+// Kalman gains
+Kfusion(0) = HKX16*HKX24;
+Kfusion(1) = HKX22*HKX24;
+Kfusion(2) = HKX19*HKX24;
+Kfusion(3) = HKX21*HKX24;
+Kfusion(4) = HKX24*(HKX10*P(4,17) - HKX11*P(4,18) + HKX12*P(1,4) + HKX13*P(0,4) - HKX14*P(2,4) + HKX15*P(3,4) + HKX6*P(4,16) + P(4,19));
+Kfusion(5) = HKX24*(HKX10*P(5,17) - HKX11*P(5,18) + HKX12*P(1,5) + HKX13*P(0,5) - HKX14*P(2,5) + HKX15*P(3,5) + HKX6*P(5,16) + P(5,19));
+Kfusion(6) = HKX24*(HKX10*P(6,17) - HKX11*P(6,18) + HKX12*P(1,6) + HKX13*P(0,6) - HKX14*P(2,6) + HKX15*P(3,6) + HKX6*P(6,16) + P(6,19));
+Kfusion(7) = HKX24*(HKX10*P(7,17) - HKX11*P(7,18) + HKX12*P(1,7) + HKX13*P(0,7) - HKX14*P(2,7) + HKX15*P(3,7) + HKX6*P(7,16) + P(7,19));
+Kfusion(8) = HKX24*(HKX10*P(8,17) - HKX11*P(8,18) + HKX12*P(1,8) + HKX13*P(0,8) - HKX14*P(2,8) + HKX15*P(3,8) + HKX6*P(8,16) + P(8,19));
+Kfusion(9) = HKX24*(HKX10*P(9,17) - HKX11*P(9,18) + HKX12*P(1,9) + HKX13*P(0,9) - HKX14*P(2,9) + HKX15*P(3,9) + HKX6*P(9,16) + P(9,19));
+Kfusion(10) = HKX24*(HKX10*P(10,17) - HKX11*P(10,18) + HKX12*P(1,10) + HKX13*P(0,10) - HKX14*P(2,10) + HKX15*P(3,10) + HKX6*P(10,16) + P(10,19));
+Kfusion(11) = HKX24*(HKX10*P(11,17) - HKX11*P(11,18) + HKX12*P(1,11) + HKX13*P(0,11) - HKX14*P(2,11) + HKX15*P(3,11) + HKX6*P(11,16) + P(11,19));
+Kfusion(12) = HKX24*(HKX10*P(12,17) - HKX11*P(12,18) + HKX12*P(1,12) + HKX13*P(0,12) - HKX14*P(2,12) + HKX15*P(3,12) + HKX6*P(12,16) + P(12,19));
+Kfusion(13) = HKX24*(HKX10*P(13,17) - HKX11*P(13,18) + HKX12*P(1,13) + HKX13*P(0,13) - HKX14*P(2,13) + HKX15*P(3,13) + HKX6*P(13,16) + P(13,19));
+Kfusion(14) = HKX24*(HKX10*P(14,17) - HKX11*P(14,18) + HKX12*P(1,14) + HKX13*P(0,14) - HKX14*P(2,14) + HKX15*P(3,14) + HKX6*P(14,16) + P(14,19));
+Kfusion(15) = HKX24*(HKX10*P(15,17) - HKX11*P(15,18) + HKX12*P(1,15) + HKX13*P(0,15) - HKX14*P(2,15) + HKX15*P(3,15) + HKX6*P(15,16) + P(15,19));
+Kfusion(16) = HKX17*HKX24;
+Kfusion(17) = HKX20*HKX24;
+Kfusion(18) = HKX18*HKX24;
+Kfusion(19) = HKX23*HKX24;
+Kfusion(20) = HKX24*(HKX10*P(17,20) - HKX11*P(18,20) + HKX12*P(1,20) + HKX13*P(0,20) - HKX14*P(2,20) + HKX15*P(3,20) + HKX6*P(16,20) + P(19,20));
+Kfusion(21) = HKX24*(HKX10*P(17,21) - HKX11*P(18,21) + HKX12*P(1,21) + HKX13*P(0,21) - HKX14*P(2,21) + HKX15*P(3,21) + HKX6*P(16,21) + P(19,21));
+Kfusion(22) = HKX24*(HKX10*P(17,22) - HKX11*P(18,22) + HKX12*P(1,22) + HKX13*P(0,22) - HKX14*P(2,22) + HKX15*P(3,22) + HKX6*P(16,22) + P(19,22));
+Kfusion(23) = HKX24*(HKX10*P(17,23) - HKX11*P(18,23) + HKX12*P(1,23) + HKX13*P(0,23) - HKX14*P(2,23) + HKX15*P(3,23) + HKX6*P(16,23) + P(19,23));
+
+
+// Axis 1 equations
+// Sub Expressions
+const float HKY0 = magD*q1 + magE*q0 - magN*q3;
+const float HKY1 = magD*q0 - magE*q1 + magN*q2;
+const float HKY2 = magD*q3 + magE*q2 + magN*q1;
+const float HKY3 = magD*q2;
+const float HKY4 = magE*q3;
+const float HKY5 = magN*q0;
+const float HKY6 = q1*q2;
+const float HKY7 = q0*q3;
+const float HKY8 = powf(q0, 2) - powf(q1, 2) + powf(q2, 2) - powf(q3, 2);
+const float HKY9 = q0*q1 + q2*q3;
+const float HKY10 = 2*HKY9;
+const float HKY11 = -2*HKY6 + 2*HKY7;
+const float HKY12 = 2*HKY2;
+const float HKY13 = 2*HKY0;
+const float HKY14 = 2*HKY1;
+const float HKY15 = -2*HKY3 + 2*HKY4 + 2*HKY5;
+const float HKY16 = HKY10*P(0,18) - HKY11*P(0,16) + HKY12*P(0,2) + HKY13*P(0,0) + HKY14*P(0,1) - HKY15*P(0,3) + HKY8*P(0,17) + P(0,20);
+const float HKY17 = HKY10*P(17,18) - HKY11*P(16,17) + HKY12*P(2,17) + HKY13*P(0,17) + HKY14*P(1,17) - HKY15*P(3,17) + HKY8*P(17,17) + P(17,20);
+const float HKY18 = HKY10*P(16,18) - HKY11*P(16,16) + HKY12*P(2,16) + HKY13*P(0,16) + HKY14*P(1,16) - HKY15*P(3,16) + HKY8*P(16,17) + P(16,20);
+const float HKY19 = HKY10*P(3,18) - HKY11*P(3,16) + HKY12*P(2,3) + HKY13*P(0,3) + HKY14*P(1,3) - HKY15*P(3,3) + HKY8*P(3,17) + P(3,20);
+const float HKY20 = HKY10*P(18,18) - HKY11*P(16,18) + HKY12*P(2,18) + HKY13*P(0,18) + HKY14*P(1,18) - HKY15*P(3,18) + HKY8*P(17,18) + P(18,20);
+const float HKY21 = HKY10*P(1,18) - HKY11*P(1,16) + HKY12*P(1,2) + HKY13*P(0,1) + HKY14*P(1,1) - HKY15*P(1,3) + HKY8*P(1,17) + P(1,20);
+const float HKY22 = HKY10*P(2,18) - HKY11*P(2,16) + HKY12*P(2,2) + HKY13*P(0,2) + HKY14*P(1,2) - HKY15*P(2,3) + HKY8*P(2,17) + P(2,20);
+const float HKY23 = HKY10*P(18,20) - HKY11*P(16,20) + HKY12*P(2,20) + HKY13*P(0,20) + HKY14*P(1,20) - HKY15*P(3,20) + HKY8*P(17,20) + P(20,20);
+const float HKY24 = 1.0F/(HKY10*HKY20 - HKY11*HKY18 + HKY12*HKY22 + HKY13*HKY16 + HKY14*HKY21 - HKY15*HKY19 + HKY17*HKY8 + HKY23 + R_MAG);
+
+
+// Observation Jacobians
+Hfusion.at<0>() = 2*HKY0;
+Hfusion.at<1>() = 2*HKY1;
+Hfusion.at<2>() = 2*HKY2;
+Hfusion.at<3>() = 2*HKY3 - 2*HKY4 - 2*HKY5;
+Hfusion.at<4>() = 0;
+Hfusion.at<5>() = 0;
+Hfusion.at<6>() = 0;
+Hfusion.at<7>() = 0;
+Hfusion.at<8>() = 0;
+Hfusion.at<9>() = 0;
+Hfusion.at<10>() = 0;
+Hfusion.at<11>() = 0;
+Hfusion.at<12>() = 0;
+Hfusion.at<13>() = 0;
+Hfusion.at<14>() = 0;
+Hfusion.at<15>() = 0;
+Hfusion.at<16>() = 2*HKY6 - 2*HKY7;
+Hfusion.at<17>() = HKY8;
+Hfusion.at<18>() = 2*HKY9;
+Hfusion.at<19>() = 0;
+Hfusion.at<20>() = 1;
+Hfusion.at<21>() = 0;
+Hfusion.at<22>() = 0;
+Hfusion.at<23>() = 0;
+
+
+// Kalman gains
+Kfusion(0) = HKY16*HKY24;
+Kfusion(1) = HKY21*HKY24;
+Kfusion(2) = HKY22*HKY24;
+Kfusion(3) = HKY19*HKY24;
+Kfusion(4) = HKY24*(HKY10*P(4,18) - HKY11*P(4,16) + HKY12*P(2,4) + HKY13*P(0,4) + HKY14*P(1,4) - HKY15*P(3,4) + HKY8*P(4,17) + P(4,20));
+Kfusion(5) = HKY24*(HKY10*P(5,18) - HKY11*P(5,16) + HKY12*P(2,5) + HKY13*P(0,5) + HKY14*P(1,5) - HKY15*P(3,5) + HKY8*P(5,17) + P(5,20));
+Kfusion(6) = HKY24*(HKY10*P(6,18) - HKY11*P(6,16) + HKY12*P(2,6) + HKY13*P(0,6) + HKY14*P(1,6) - HKY15*P(3,6) + HKY8*P(6,17) + P(6,20));
+Kfusion(7) = HKY24*(HKY10*P(7,18) - HKY11*P(7,16) + HKY12*P(2,7) + HKY13*P(0,7) + HKY14*P(1,7) - HKY15*P(3,7) + HKY8*P(7,17) + P(7,20));
+Kfusion(8) = HKY24*(HKY10*P(8,18) - HKY11*P(8,16) + HKY12*P(2,8) + HKY13*P(0,8) + HKY14*P(1,8) - HKY15*P(3,8) + HKY8*P(8,17) + P(8,20));
+Kfusion(9) = HKY24*(HKY10*P(9,18) - HKY11*P(9,16) + HKY12*P(2,9) + HKY13*P(0,9) + HKY14*P(1,9) - HKY15*P(3,9) + HKY8*P(9,17) + P(9,20));
+Kfusion(10) = HKY24*(HKY10*P(10,18) - HKY11*P(10,16) + HKY12*P(2,10) + HKY13*P(0,10) + HKY14*P(1,10) - HKY15*P(3,10) + HKY8*P(10,17) + P(10,20));
+Kfusion(11) = HKY24*(HKY10*P(11,18) - HKY11*P(11,16) + HKY12*P(2,11) + HKY13*P(0,11) + HKY14*P(1,11) - HKY15*P(3,11) + HKY8*P(11,17) + P(11,20));
+Kfusion(12) = HKY24*(HKY10*P(12,18) - HKY11*P(12,16) + HKY12*P(2,12) + HKY13*P(0,12) + HKY14*P(1,12) - HKY15*P(3,12) + HKY8*P(12,17) + P(12,20));
+Kfusion(13) = HKY24*(HKY10*P(13,18) - HKY11*P(13,16) + HKY12*P(2,13) + HKY13*P(0,13) + HKY14*P(1,13) - HKY15*P(3,13) + HKY8*P(13,17) + P(13,20));
+Kfusion(14) = HKY24*(HKY10*P(14,18) - HKY11*P(14,16) + HKY12*P(2,14) + HKY13*P(0,14) + HKY14*P(1,14) - HKY15*P(3,14) + HKY8*P(14,17) + P(14,20));
+Kfusion(15) = HKY24*(HKY10*P(15,18) - HKY11*P(15,16) + HKY12*P(2,15) + HKY13*P(0,15) + HKY14*P(1,15) - HKY15*P(3,15) + HKY8*P(15,17) + P(15,20));
+Kfusion(16) = HKY18*HKY24;
+Kfusion(17) = HKY17*HKY24;
+Kfusion(18) = HKY20*HKY24;
+Kfusion(19) = HKY24*(HKY10*P(18,19) - HKY11*P(16,19) + HKY12*P(2,19) + HKY13*P(0,19) + HKY14*P(1,19) - HKY15*P(3,19) + HKY8*P(17,19) + P(19,20));
+Kfusion(20) = HKY23*HKY24;
+Kfusion(21) = HKY24*(HKY10*P(18,21) - HKY11*P(16,21) + HKY12*P(2,21) + HKY13*P(0,21) + HKY14*P(1,21) - HKY15*P(3,21) + HKY8*P(17,21) + P(20,21));
+Kfusion(22) = HKY24*(HKY10*P(18,22) - HKY11*P(16,22) + HKY12*P(2,22) + HKY13*P(0,22) + HKY14*P(1,22) - HKY15*P(3,22) + HKY8*P(17,22) + P(20,22));
+Kfusion(23) = HKY24*(HKY10*P(18,23) - HKY11*P(16,23) + HKY12*P(2,23) + HKY13*P(0,23) + HKY14*P(1,23) - HKY15*P(3,23) + HKY8*P(17,23) + P(20,23));
+
+
+// Axis 2 equations
+// Sub Expressions
+const float HKZ0 = magD*q0 - magE*q1 + magN*q2;
+const float HKZ1 = magN*q3;
+const float HKZ2 = magD*q1;
+const float HKZ3 = magE*q0;
+const float HKZ4 = -magD*q2 + magE*q3 + magN*q0;
+const float HKZ5 = magD*q3 + magE*q2 + magN*q1;
+const float HKZ6 = q0*q2 + q1*q3;
+const float HKZ7 = q2*q3;
+const float HKZ8 = q0*q1;
+const float HKZ9 = powf(q0, 2) - powf(q1, 2) - powf(q2, 2) + powf(q3, 2);
+const float HKZ10 = 2*HKZ6;
+const float HKZ11 = -2*HKZ7 + 2*HKZ8;
+const float HKZ12 = 2*HKZ5;
+const float HKZ13 = 2*HKZ0;
+const float HKZ14 = -2*HKZ1 + 2*HKZ2 + 2*HKZ3;
+const float HKZ15 = 2*HKZ4;
+const float HKZ16 = HKZ10*P(0,16) - HKZ11*P(0,17) + HKZ12*P(0,3) + HKZ13*P(0,0) - HKZ14*P(0,1) + HKZ15*P(0,2) + HKZ9*P(0,18) + P(0,21);
+const float HKZ17 = HKZ10*P(16,18) - HKZ11*P(17,18) + HKZ12*P(3,18) + HKZ13*P(0,18) - HKZ14*P(1,18) + HKZ15*P(2,18) + HKZ9*P(18,18) + P(18,21);
+const float HKZ18 = HKZ10*P(16,17) - HKZ11*P(17,17) + HKZ12*P(3,17) + HKZ13*P(0,17) - HKZ14*P(1,17) + HKZ15*P(2,17) + HKZ9*P(17,18) + P(17,21);
+const float HKZ19 = HKZ10*P(1,16) - HKZ11*P(1,17) + HKZ12*P(1,3) + HKZ13*P(0,1) - HKZ14*P(1,1) + HKZ15*P(1,2) + HKZ9*P(1,18) + P(1,21);
+const float HKZ20 = HKZ10*P(16,16) - HKZ11*P(16,17) + HKZ12*P(3,16) + HKZ13*P(0,16) - HKZ14*P(1,16) + HKZ15*P(2,16) + HKZ9*P(16,18) + P(16,21);
+const float HKZ21 = HKZ10*P(3,16) - HKZ11*P(3,17) + HKZ12*P(3,3) + HKZ13*P(0,3) - HKZ14*P(1,3) + HKZ15*P(2,3) + HKZ9*P(3,18) + P(3,21);
+const float HKZ22 = HKZ10*P(2,16) - HKZ11*P(2,17) + HKZ12*P(2,3) + HKZ13*P(0,2) - HKZ14*P(1,2) + HKZ15*P(2,2) + HKZ9*P(2,18) + P(2,21);
+const float HKZ23 = HKZ10*P(16,21) - HKZ11*P(17,21) + HKZ12*P(3,21) + HKZ13*P(0,21) - HKZ14*P(1,21) + HKZ15*P(2,21) + HKZ9*P(18,21) + P(21,21);
+const float HKZ24 = 1.0F/(HKZ10*HKZ20 - HKZ11*HKZ18 + HKZ12*HKZ21 + HKZ13*HKZ16 - HKZ14*HKZ19 + HKZ15*HKZ22 + HKZ17*HKZ9 + HKZ23 + R_MAG);
+
+
+// Observation Jacobians
+Hfusion.at<0>() = 2*HKZ0;
+Hfusion.at<1>() = 2*HKZ1 - 2*HKZ2 - 2*HKZ3;
+Hfusion.at<2>() = 2*HKZ4;
+Hfusion.at<3>() = 2*HKZ5;
+Hfusion.at<4>() = 0;
+Hfusion.at<5>() = 0;
+Hfusion.at<6>() = 0;
+Hfusion.at<7>() = 0;
+Hfusion.at<8>() = 0;
+Hfusion.at<9>() = 0;
+Hfusion.at<10>() = 0;
+Hfusion.at<11>() = 0;
+Hfusion.at<12>() = 0;
+Hfusion.at<13>() = 0;
+Hfusion.at<14>() = 0;
+Hfusion.at<15>() = 0;
+Hfusion.at<16>() = 2*HKZ6;
+Hfusion.at<17>() = 2*HKZ7 - 2*HKZ8;
+Hfusion.at<18>() = HKZ9;
+Hfusion.at<19>() = 0;
+Hfusion.at<20>() = 0;
+Hfusion.at<21>() = 1;
+Hfusion.at<22>() = 0;
+Hfusion.at<23>() = 0;
+
+
+// Kalman gains
+Kfusion(0) = HKZ16*HKZ24;
+Kfusion(1) = HKZ19*HKZ24;
+Kfusion(2) = HKZ22*HKZ24;
+Kfusion(3) = HKZ21*HKZ24;
+Kfusion(4) = HKZ24*(HKZ10*P(4,16) - HKZ11*P(4,17) + HKZ12*P(3,4) + HKZ13*P(0,4) - HKZ14*P(1,4) + HKZ15*P(2,4) + HKZ9*P(4,18) + P(4,21));
+Kfusion(5) = HKZ24*(HKZ10*P(5,16) - HKZ11*P(5,17) + HKZ12*P(3,5) + HKZ13*P(0,5) - HKZ14*P(1,5) + HKZ15*P(2,5) + HKZ9*P(5,18) + P(5,21));
+Kfusion(6) = HKZ24*(HKZ10*P(6,16) - HKZ11*P(6,17) + HKZ12*P(3,6) + HKZ13*P(0,6) - HKZ14*P(1,6) + HKZ15*P(2,6) + HKZ9*P(6,18) + P(6,21));
+Kfusion(7) = HKZ24*(HKZ10*P(7,16) - HKZ11*P(7,17) + HKZ12*P(3,7) + HKZ13*P(0,7) - HKZ14*P(1,7) + HKZ15*P(2,7) + HKZ9*P(7,18) + P(7,21));
+Kfusion(8) = HKZ24*(HKZ10*P(8,16) - HKZ11*P(8,17) + HKZ12*P(3,8) + HKZ13*P(0,8) - HKZ14*P(1,8) + HKZ15*P(2,8) + HKZ9*P(8,18) + P(8,21));
+Kfusion(9) = HKZ24*(HKZ10*P(9,16) - HKZ11*P(9,17) + HKZ12*P(3,9) + HKZ13*P(0,9) - HKZ14*P(1,9) + HKZ15*P(2,9) + HKZ9*P(9,18) + P(9,21));
+Kfusion(10) = HKZ24*(HKZ10*P(10,16) - HKZ11*P(10,17) + HKZ12*P(3,10) + HKZ13*P(0,10) - HKZ14*P(1,10) + HKZ15*P(2,10) + HKZ9*P(10,18) + P(10,21));
+Kfusion(11) = HKZ24*(HKZ10*P(11,16) - HKZ11*P(11,17) + HKZ12*P(3,11) + HKZ13*P(0,11) - HKZ14*P(1,11) + HKZ15*P(2,11) + HKZ9*P(11,18) + P(11,21));
+Kfusion(12) = HKZ24*(HKZ10*P(12,16) - HKZ11*P(12,17) + HKZ12*P(3,12) + HKZ13*P(0,12) - HKZ14*P(1,12) + HKZ15*P(2,12) + HKZ9*P(12,18) + P(12,21));
+Kfusion(13) = HKZ24*(HKZ10*P(13,16) - HKZ11*P(13,17) + HKZ12*P(3,13) + HKZ13*P(0,13) - HKZ14*P(1,13) + HKZ15*P(2,13) + HKZ9*P(13,18) + P(13,21));
+Kfusion(14) = HKZ24*(HKZ10*P(14,16) - HKZ11*P(14,17) + HKZ12*P(3,14) + HKZ13*P(0,14) - HKZ14*P(1,14) + HKZ15*P(2,14) + HKZ9*P(14,18) + P(14,21));
+Kfusion(15) = HKZ24*(HKZ10*P(15,16) - HKZ11*P(15,17) + HKZ12*P(3,15) + HKZ13*P(0,15) - HKZ14*P(1,15) + HKZ15*P(2,15) + HKZ9*P(15,18) + P(15,21));
+Kfusion(16) = HKZ20*HKZ24;
+Kfusion(17) = HKZ18*HKZ24;
+Kfusion(18) = HKZ17*HKZ24;
+Kfusion(19) = HKZ24*(HKZ10*P(16,19) - HKZ11*P(17,19) + HKZ12*P(3,19) + HKZ13*P(0,19) - HKZ14*P(1,19) + HKZ15*P(2,19) + HKZ9*P(18,19) + P(19,21));
+Kfusion(20) = HKZ24*(HKZ10*P(16,20) - HKZ11*P(17,20) + HKZ12*P(3,20) + HKZ13*P(0,20) - HKZ14*P(1,20) + HKZ15*P(2,20) + HKZ9*P(18,20) + P(20,21));
+Kfusion(21) = HKZ23*HKZ24;
+Kfusion(22) = HKZ24*(HKZ10*P(16,22) - HKZ11*P(17,22) + HKZ12*P(3,22) + HKZ13*P(0,22) - HKZ14*P(1,22) + HKZ15*P(2,22) + HKZ9*P(18,22) + P(21,22));
+Kfusion(23) = HKZ24*(HKZ10*P(16,23) - HKZ11*P(17,23) + HKZ12*P(3,23) + HKZ13*P(0,23) - HKZ14*P(1,23) + HKZ15*P(2,23) + HKZ9*P(18,23) + P(21,23));
+
+

EKF/python/ekf_derivation/generated/3Dmag_generated_alt.cpp

@@ -0,0 +1,250 @@
+// Sub Expressions
+const float HK0 = magE*q3;
+const float HK1 = magN*q0;
+const float HK2 = magD*q2;
+const float HK3 = HK0 + HK1 - HK2;
+const float HK4 = 2*HK3;
+const float HK5 = magD*q3 + magE*q2 + magN*q1;
+const float HK6 = 2*HK5;
+const float HK7 = magE*q1;
+const float HK8 = magD*q0;
+const float HK9 = magN*q2;
+const float HK10 = magD*q1;
+const float HK11 = magE*q0;
+const float HK12 = magN*q3;
+const float HK13 = HK10 + HK11 - HK12;
+const float HK14 = 2*HK13;
+const float HK15 = powf(q1, 2);
+const float HK16 = powf(q2, 2);
+const float HK17 = -HK16;
+const float HK18 = powf(q0, 2);
+const float HK19 = powf(q3, 2);
+const float HK20 = HK18 - HK19;
+const float HK21 = HK15 + HK17 + HK20;
+const float HK22 = q0*q3;
+const float HK23 = q1*q2;
+const float HK24 = HK22 + HK23;
+const float HK25 = q1*q3;
+const float HK26 = q0*q2;
+const float HK27 = 2*HK24;
+const float HK28 = -2*HK25 + 2*HK26;
+const float HK29 = 2*HK5;
+const float HK30 = 2*HK3;
+const float HK31 = -HK7 + HK8 + HK9;
+const float HK32 = 2*HK31;
+const float HK33 = HK32*P(0,2);
+const float HK34 = 2*HK13;
+const float HK35 = HK34*P(0,3);
+const float HK36 = HK21*P(0,16) + HK27*P(0,17) - HK28*P(0,18) + HK29*P(0,1) + HK30*P(0,0) - HK33 + HK35 + P(0,19);
+const float HK37 = HK21*P(16,16) + HK27*P(16,17) - HK28*P(16,18) + HK29*P(1,16) + HK30*P(0,16) - HK32*P(2,16) + HK34*P(3,16) + P(16,19);
+const float HK38 = HK21*P(16,18) + HK27*P(17,18) - HK28*P(18,18) + HK29*P(1,18) + HK30*P(0,18) - HK32*P(2,18) + HK34*P(3,18) + P(18,19);
+const float HK39 = HK29*P(1,2);
+const float HK40 = HK30*P(0,2);
+const float HK41 = HK21*P(2,16) + HK27*P(2,17) - HK28*P(2,18) - HK32*P(2,2) + HK34*P(2,3) + HK39 + HK40 + P(2,19);
+const float HK42 = HK21*P(16,17) + HK27*P(17,17) - HK28*P(17,18) + HK29*P(1,17) + HK30*P(0,17) - HK32*P(2,17) + HK34*P(3,17) + P(17,19);
+const float HK43 = HK29*P(1,3);
+const float HK44 = HK30*P(0,3);
+const float HK45 = HK21*P(3,16) + HK27*P(3,17) - HK28*P(3,18) - HK32*P(2,3) + HK34*P(3,3) + HK43 + HK44 + P(3,19);
+const float HK46 = HK32*P(1,2);
+const float HK47 = HK34*P(1,3);
+const float HK48 = HK21*P(1,16) + HK27*P(1,17) - HK28*P(1,18) + HK29*P(1,1) + HK30*P(0,1) - HK46 + HK47 + P(1,19);
+const float HK49 = HK21*P(16,19) + HK27*P(17,19) - HK28*P(18,19) + HK29*P(1,19) + HK30*P(0,19) - HK32*P(2,19) + HK34*P(3,19) + P(19,19);
+const float HK50 = 1.0F/(HK21*HK37 + HK27*HK42 - HK28*HK38 + HK29*HK48 + HK30*HK36 - HK32*HK41 + HK34*HK45 + HK49 + R_MAG);
+const float HK51 = 2*HK31;
+const float HK52 = -HK15;
+const float HK53 = HK16 + HK20 + HK52;
+const float HK54 = q0*q1;
+const float HK55 = q2*q3;
+const float HK56 = HK54 + HK55;
+const float HK57 = 2*HK56;
+const float HK58 = 2*HK22 - 2*HK23;
+const float HK59 = HK32*P(0,1);
+const float HK60 = HK29*P(0,2) + HK34*P(0,0) - HK44 + HK53*P(0,17) + HK57*P(0,18) - HK58*P(0,16) + HK59 + P(0,20);
+const float HK61 = HK29*P(2,17) - HK30*P(3,17) + HK32*P(1,17) + HK34*P(0,17) + HK53*P(17,17) + HK57*P(17,18) - HK58*P(16,17) + P(17,20);
+const float HK62 = HK29*P(2,16) - HK30*P(3,16) + HK32*P(1,16) + HK34*P(0,16) + HK53*P(16,17) + HK57*P(16,18) - HK58*P(16,16) + P(16,20);
+const float HK63 = HK29*P(2,3);
+const float HK64 = -HK30*P(3,3) + HK32*P(1,3) + HK35 + HK53*P(3,17) + HK57*P(3,18) - HK58*P(3,16) + HK63 + P(3,20);
+const float HK65 = HK29*P(2,18) - HK30*P(3,18) + HK32*P(1,18) + HK34*P(0,18) + HK53*P(17,18) + HK57*P(18,18) - HK58*P(16,18) + P(18,20);
+const float HK66 = HK34*P(0,1);
+const float HK67 = -HK30*P(1,3) + HK32*P(1,1) + HK39 + HK53*P(1,17) + HK57*P(1,18) - HK58*P(1,16) + HK66 + P(1,20);
+const float HK68 = HK30*P(2,3);
+const float HK69 = HK29*P(2,2) + HK34*P(0,2) + HK46 + HK53*P(2,17) + HK57*P(2,18) - HK58*P(2,16) - HK68 + P(2,20);
+const float HK70 = HK29*P(2,20) - HK30*P(3,20) + HK32*P(1,20) + HK34*P(0,20) + HK53*P(17,20) + HK57*P(18,20) - HK58*P(16,20) + P(20,20);
+const float HK71 = 1.0F/(HK29*HK69 - HK30*HK64 + HK32*HK67 + HK34*HK60 + HK53*HK61 + HK57*HK65 - HK58*HK62 + HK70 + R_MAG);
+const float HK72 = HK25 + HK26;
+const float HK73 = HK17 + HK18 + HK19 + HK52;
+const float HK74 = 2*HK72;
+const float HK75 = 2*HK54 - 2*HK55;
+const float HK76 = HK29*P(0,3) + HK32*P(0,0) + HK40 - HK66 + HK73*P(0,18) + HK74*P(0,16) - HK75*P(0,17) + P(0,21);
+const float HK77 = HK29*P(3,18) + HK30*P(2,18) + HK32*P(0,18) - HK34*P(1,18) + HK73*P(18,18) + HK74*P(16,18) - HK75*P(17,18) + P(18,21);
+const float HK78 = HK29*P(3,17) + HK30*P(2,17) + HK32*P(0,17) - HK34*P(1,17) + HK73*P(17,18) + HK74*P(16,17) - HK75*P(17,17) + P(17,21);
+const float HK79 = HK30*P(1,2) - HK34*P(1,1) + HK43 + HK59 + HK73*P(1,18) + HK74*P(1,16) - HK75*P(1,17) + P(1,21);
+const float HK80 = HK29*P(3,16) + HK30*P(2,16) + HK32*P(0,16) - HK34*P(1,16) + HK73*P(16,18) + HK74*P(16,16) - HK75*P(16,17) + P(16,21);
+const float HK81 = HK29*P(3,3) + HK32*P(0,3) - HK47 + HK68 + HK73*P(3,18) + HK74*P(3,16) - HK75*P(3,17) + P(3,21);
+const float HK82 = HK30*P(2,2) + HK33 - HK34*P(1,2) + HK63 + HK73*P(2,18) + HK74*P(2,16) - HK75*P(2,17) + P(2,21);
+const float HK83 = HK29*P(3,21) + HK30*P(2,21) + HK32*P(0,21) - HK34*P(1,21) + HK73*P(18,21) + HK74*P(16,21) - HK75*P(17,21) + P(21,21);
+const float HK84 = 1.0F/(HK29*HK81 + HK30*HK82 + HK32*HK76 - HK34*HK79 + HK73*HK77 + HK74*HK80 - HK75*HK78 + HK83 + R_MAG);
+
+
+// Observation Jacobians - axis 0
+Hfusion.at<0>() = HK4;
+Hfusion.at<1>() = HK6;
+Hfusion.at<2>() = 2*HK7 - 2*HK8 - 2*HK9;
+Hfusion.at<3>() = HK14;
+Hfusion.at<4>() = 0;
+Hfusion.at<5>() = 0;
+Hfusion.at<6>() = 0;
+Hfusion.at<7>() = 0;
+Hfusion.at<8>() = 0;
+Hfusion.at<9>() = 0;
+Hfusion.at<10>() = 0;
+Hfusion.at<11>() = 0;
+Hfusion.at<12>() = 0;
+Hfusion.at<13>() = 0;
+Hfusion.at<14>() = 0;
+Hfusion.at<15>() = 0;
+Hfusion.at<16>() = HK21;
+Hfusion.at<17>() = 2*HK24;
+Hfusion.at<18>() = 2*HK25 - 2*HK26;
+Hfusion.at<19>() = 1;
+Hfusion.at<20>() = 0;
+Hfusion.at<21>() = 0;
+Hfusion.at<22>() = 0;
+Hfusion.at<23>() = 0;
+
+
+// Kalman gains - axis 0
+Kfusion(0) = HK36*HK50;
+Kfusion(1) = HK48*HK50;
+Kfusion(2) = HK41*HK50;
+Kfusion(3) = HK45*HK50;
+Kfusion(4) = HK50*(HK21*P(4,16) + HK27*P(4,17) - HK28*P(4,18) + HK29*P(1,4) + HK30*P(0,4) - HK32*P(2,4) + HK34*P(3,4) + P(4,19));
+Kfusion(5) = HK50*(HK21*P(5,16) + HK27*P(5,17) - HK28*P(5,18) + HK29*P(1,5) + HK30*P(0,5) - HK32*P(2,5) + HK34*P(3,5) + P(5,19));
+Kfusion(6) = HK50*(HK21*P(6,16) + HK27*P(6,17) - HK28*P(6,18) + HK29*P(1,6) + HK30*P(0,6) - HK32*P(2,6) + HK34*P(3,6) + P(6,19));
+Kfusion(7) = HK50*(HK21*P(7,16) + HK27*P(7,17) - HK28*P(7,18) + HK29*P(1,7) + HK30*P(0,7) - HK32*P(2,7) + HK34*P(3,7) + P(7,19));
+Kfusion(8) = HK50*(HK21*P(8,16) + HK27*P(8,17) - HK28*P(8,18) + HK29*P(1,8) + HK30*P(0,8) - HK32*P(2,8) + HK34*P(3,8) + P(8,19));
+Kfusion(9) = HK50*(HK21*P(9,16) + HK27*P(9,17) - HK28*P(9,18) + HK29*P(1,9) + HK30*P(0,9) - HK32*P(2,9) + HK34*P(3,9) + P(9,19));
+Kfusion(10) = HK50*(HK21*P(10,16) + HK27*P(10,17) - HK28*P(10,18) + HK29*P(1,10) + HK30*P(0,10) - HK32*P(2,10) + HK34*P(3,10) + P(10,19));
+Kfusion(11) = HK50*(HK21*P(11,16) + HK27*P(11,17) - HK28*P(11,18) + HK29*P(1,11) + HK30*P(0,11) - HK32*P(2,11) + HK34*P(3,11) + P(11,19));
+Kfusion(12) = HK50*(HK21*P(12,16) + HK27*P(12,17) - HK28*P(12,18) + HK29*P(1,12) + HK30*P(0,12) - HK32*P(2,12) + HK34*P(3,12) + P(12,19));
+Kfusion(13) = HK50*(HK21*P(13,16) + HK27*P(13,17) - HK28*P(13,18) + HK29*P(1,13) + HK30*P(0,13) - HK32*P(2,13) + HK34*P(3,13) + P(13,19));
+Kfusion(14) = HK50*(HK21*P(14,16) + HK27*P(14,17) - HK28*P(14,18) + HK29*P(1,14) + HK30*P(0,14) - HK32*P(2,14) + HK34*P(3,14) + P(14,19));
+Kfusion(15) = HK50*(HK21*P(15,16) + HK27*P(15,17) - HK28*P(15,18) + HK29*P(1,15) + HK30*P(0,15) - HK32*P(2,15) + HK34*P(3,15) + P(15,19));
+Kfusion(16) = HK37*HK50;
+Kfusion(17) = HK42*HK50;
+Kfusion(18) = HK38*HK50;
+Kfusion(19) = HK49*HK50;
+Kfusion(20) = HK50*(HK21*P(16,20) + HK27*P(17,20) - HK28*P(18,20) + HK29*P(1,20) + HK30*P(0,20) - HK32*P(2,20) + HK34*P(3,20) + P(19,20));
+Kfusion(21) = HK50*(HK21*P(16,21) + HK27*P(17,21) - HK28*P(18,21) + HK29*P(1,21) + HK30*P(0,21) - HK32*P(2,21) + HK34*P(3,21) + P(19,21));
+Kfusion(22) = HK50*(HK21*P(16,22) + HK27*P(17,22) - HK28*P(18,22) + HK29*P(1,22) + HK30*P(0,22) - HK32*P(2,22) + HK34*P(3,22) + P(19,22));
+Kfusion(23) = HK50*(HK21*P(16,23) + HK27*P(17,23) - HK28*P(18,23) + HK29*P(1,23) + HK30*P(0,23) - HK32*P(2,23) + HK34*P(3,23) + P(19,23));
+
+
+// Observation Jacobians - axis 1
+Hfusion.at<0>() = HK14;
+Hfusion.at<1>() = HK51;
+Hfusion.at<2>() = HK6;
+Hfusion.at<3>() = -2*HK0 - 2*HK1 + 2*HK2;
+Hfusion.at<4>() = 0;
+Hfusion.at<5>() = 0;
+Hfusion.at<6>() = 0;
+Hfusion.at<7>() = 0;
+Hfusion.at<8>() = 0;
+Hfusion.at<9>() = 0;
+Hfusion.at<10>() = 0;
+Hfusion.at<11>() = 0;
+Hfusion.at<12>() = 0;
+Hfusion.at<13>() = 0;
+Hfusion.at<14>() = 0;
+Hfusion.at<15>() = 0;
+Hfusion.at<16>() = -2*HK22 + 2*HK23;
+Hfusion.at<17>() = HK53;
+Hfusion.at<18>() = 2*HK56;
+Hfusion.at<19>() = 0;
+Hfusion.at<20>() = 1;
+Hfusion.at<21>() = 0;
+Hfusion.at<22>() = 0;
+Hfusion.at<23>() = 0;
+
+
+// Kalman gains - axis 1
+Kfusion(0) = HK60*HK71;
+Kfusion(1) = HK67*HK71;
+Kfusion(2) = HK69*HK71;
+Kfusion(3) = HK64*HK71;
+Kfusion(4) = HK71*(HK29*P(2,4) - HK30*P(3,4) + HK32*P(1,4) + HK34*P(0,4) + HK53*P(4,17) + HK57*P(4,18) - HK58*P(4,16) + P(4,20));
+Kfusion(5) = HK71*(HK29*P(2,5) - HK30*P(3,5) + HK32*P(1,5) + HK34*P(0,5) + HK53*P(5,17) + HK57*P(5,18) - HK58*P(5,16) + P(5,20));
+Kfusion(6) = HK71*(HK29*P(2,6) - HK30*P(3,6) + HK32*P(1,6) + HK34*P(0,6) + HK53*P(6,17) + HK57*P(6,18) - HK58*P(6,16) + P(6,20));
+Kfusion(7) = HK71*(HK29*P(2,7) - HK30*P(3,7) + HK32*P(1,7) + HK34*P(0,7) + HK53*P(7,17) + HK57*P(7,18) - HK58*P(7,16) + P(7,20));
+Kfusion(8) = HK71*(HK29*P(2,8) - HK30*P(3,8) + HK32*P(1,8) + HK34*P(0,8) + HK53*P(8,17) + HK57*P(8,18) - HK58*P(8,16) + P(8,20));
+Kfusion(9) = HK71*(HK29*P(2,9) - HK30*P(3,9) + HK32*P(1,9) + HK34*P(0,9) + HK53*P(9,17) + HK57*P(9,18) - HK58*P(9,16) + P(9,20));
+Kfusion(10) = HK71*(HK29*P(2,10) - HK30*P(3,10) + HK32*P(1,10) + HK34*P(0,10) + HK53*P(10,17) + HK57*P(10,18) - HK58*P(10,16) + P(10,20));
+Kfusion(11) = HK71*(HK29*P(2,11) - HK30*P(3,11) + HK32*P(1,11) + HK34*P(0,11) + HK53*P(11,17) + HK57*P(11,18) - HK58*P(11,16) + P(11,20));
+Kfusion(12) = HK71*(HK29*P(2,12) - HK30*P(3,12) + HK32*P(1,12) + HK34*P(0,12) + HK53*P(12,17) + HK57*P(12,18) - HK58*P(12,16) + P(12,20));
+Kfusion(13) = HK71*(HK29*P(2,13) - HK30*P(3,13) + HK32*P(1,13) + HK34*P(0,13) + HK53*P(13,17) + HK57*P(13,18) - HK58*P(13,16) + P(13,20));
+Kfusion(14) = HK71*(HK29*P(2,14) - HK30*P(3,14) + HK32*P(1,14) + HK34*P(0,14) + HK53*P(14,17) + HK57*P(14,18) - HK58*P(14,16) + P(14,20));
+Kfusion(15) = HK71*(HK29*P(2,15) - HK30*P(3,15) + HK32*P(1,15) + HK34*P(0,15) + HK53*P(15,17) + HK57*P(15,18) - HK58*P(15,16) + P(15,20));
+Kfusion(16) = HK62*HK71;
+Kfusion(17) = HK61*HK71;
+Kfusion(18) = HK65*HK71;
+Kfusion(19) = HK71*(HK29*P(2,19) - HK30*P(3,19) + HK32*P(1,19) + HK34*P(0,19) + HK53*P(17,19) + HK57*P(18,19) - HK58*P(16,19) + P(19,20));
+Kfusion(20) = HK70*HK71;
+Kfusion(21) = HK71*(HK29*P(2,21) - HK30*P(3,21) + HK32*P(1,21) + HK34*P(0,21) + HK53*P(17,21) + HK57*P(18,21) - HK58*P(16,21) + P(20,21));
+Kfusion(22) = HK71*(HK29*P(2,22) - HK30*P(3,22) + HK32*P(1,22) + HK34*P(0,22) + HK53*P(17,22) + HK57*P(18,22) - HK58*P(16,22) + P(20,22));
+Kfusion(23) = HK71*(HK29*P(2,23) - HK30*P(3,23) + HK32*P(1,23) + HK34*P(0,23) + HK53*P(17,23) + HK57*P(18,23) - HK58*P(16,23) + P(20,23));
+
+
+// Observation Jacobians - axis 2
+Hfusion.at<0>() = HK51;
+Hfusion.at<1>() = -2*HK10 - 2*HK11 + 2*HK12;
+Hfusion.at<2>() = HK4;
+Hfusion.at<3>() = HK6;
+Hfusion.at<4>() = 0;
+Hfusion.at<5>() = 0;
+Hfusion.at<6>() = 0;
+Hfusion.at<7>() = 0;
+Hfusion.at<8>() = 0;
+Hfusion.at<9>() = 0;
+Hfusion.at<10>() = 0;
+Hfusion.at<11>() = 0;
+Hfusion.at<12>() = 0;
+Hfusion.at<13>() = 0;
+Hfusion.at<14>() = 0;
+Hfusion.at<15>() = 0;
+Hfusion.at<16>() = 2*HK72;
+Hfusion.at<17>() = -2*HK54 + 2*HK55;
+Hfusion.at<18>() = HK73;
+Hfusion.at<19>() = 0;
+Hfusion.at<20>() = 0;
+Hfusion.at<21>() = 1;
+Hfusion.at<22>() = 0;
+Hfusion.at<23>() = 0;
+
+
+// Kalman gains - axis 2
+Kfusion(0) = HK76*HK84;
+Kfusion(1) = HK79*HK84;
+Kfusion(2) = HK82*HK84;
+Kfusion(3) = HK81*HK84;
+Kfusion(4) = HK84*(HK29*P(3,4) + HK30*P(2,4) + HK32*P(0,4) - HK34*P(1,4) + HK73*P(4,18) + HK74*P(4,16) - HK75*P(4,17) + P(4,21));
+Kfusion(5) = HK84*(HK29*P(3,5) + HK30*P(2,5) + HK32*P(0,5) - HK34*P(1,5) + HK73*P(5,18) + HK74*P(5,16) - HK75*P(5,17) + P(5,21));
+Kfusion(6) = HK84*(HK29*P(3,6) + HK30*P(2,6) + HK32*P(0,6) - HK34*P(1,6) + HK73*P(6,18) + HK74*P(6,16) - HK75*P(6,17) + P(6,21));
+Kfusion(7) = HK84*(HK29*P(3,7) + HK30*P(2,7) + HK32*P(0,7) - HK34*P(1,7) + HK73*P(7,18) + HK74*P(7,16) - HK75*P(7,17) + P(7,21));
+Kfusion(8) = HK84*(HK29*P(3,8) + HK30*P(2,8) + HK32*P(0,8) - HK34*P(1,8) + HK73*P(8,18) + HK74*P(8,16) - HK75*P(8,17) + P(8,21));
+Kfusion(9) = HK84*(HK29*P(3,9) + HK30*P(2,9) + HK32*P(0,9) - HK34*P(1,9) + HK73*P(9,18) + HK74*P(9,16) - HK75*P(9,17) + P(9,21));
+Kfusion(10) = HK84*(HK29*P(3,10) + HK30*P(2,10) + HK32*P(0,10) - HK34*P(1,10) + HK73*P(10,18) + HK74*P(10,16) - HK75*P(10,17) + P(10,21));
+Kfusion(11) = HK84*(HK29*P(3,11) + HK30*P(2,11) + HK32*P(0,11) - HK34*P(1,11) + HK73*P(11,18) + HK74*P(11,16) - HK75*P(11,17) + P(11,21));
+Kfusion(12) = HK84*(HK29*P(3,12) + HK30*P(2,12) + HK32*P(0,12) - HK34*P(1,12) + HK73*P(12,18) + HK74*P(12,16) - HK75*P(12,17) + P(12,21));
+Kfusion(13) = HK84*(HK29*P(3,13) + HK30*P(2,13) + HK32*P(0,13) - HK34*P(1,13) + HK73*P(13,18) + HK74*P(13,16) - HK75*P(13,17) + P(13,21));
+Kfusion(14) = HK84*(HK29*P(3,14) + HK30*P(2,14) + HK32*P(0,14) - HK34*P(1,14) + HK73*P(14,18) + HK74*P(14,16) - HK75*P(14,17) + P(14,21));
+Kfusion(15) = HK84*(HK29*P(3,15) + HK30*P(2,15) + HK32*P(0,15) - HK34*P(1,15) + HK73*P(15,18) + HK74*P(15,16) - HK75*P(15,17) + P(15,21));
+Kfusion(16) = HK80*HK84;
+Kfusion(17) = HK78*HK84;
+Kfusion(18) = HK77*HK84;
+Kfusion(19) = HK84*(HK29*P(3,19) + HK30*P(2,19) + HK32*P(0,19) - HK34*P(1,19) + HK73*P(18,19) + HK74*P(16,19) - HK75*P(17,19) + P(19,21));
+Kfusion(20) = HK84*(HK29*P(3,20) + HK30*P(2,20) + HK32*P(0,20) - HK34*P(1,20) + HK73*P(18,20) + HK74*P(16,20) - HK75*P(17,20) + P(20,21));
+Kfusion(21) = HK83*HK84;
+Kfusion(22) = HK84*(HK29*P(3,22) + HK30*P(2,22) + HK32*P(0,22) - HK34*P(1,22) + HK73*P(18,22) + HK74*P(16,22) - HK75*P(17,22) + P(21,22));
+Kfusion(23) = HK84*(HK29*P(3,23) + HK30*P(2,23) + HK32*P(0,23) - HK34*P(1,23) + HK73*P(18,23) + HK74*P(16,23) - HK75*P(17,23) + P(21,23));
+
+

EKF/python/ekf_derivation/generated/3Dmag_innov_var_generated.cpp

@@ -0,0 +1,43 @@
+// Sub Expressions
+const float IV0 = q0*q1;
+const float IV1 = q2*q3;
+const float IV2 = 2*IV0 + 2*IV1;
+const float IV3 = 2*q0*q3 - 2*q1*q2;
+const float IV4 = 2*magD*q3 + 2*magE*q2 + 2*magN*q1;
+const float IV5 = 2*magD*q1 + 2*magE*q0 - 2*magN*q3;
+const float IV6 = 2*magD*q0 - 2*magE*q1 + 2*magN*q2;
+const float IV7 = -2*magD*q2 + 2*magE*q3 + 2*magN*q0;
+const float IV8 = powf(q2, 2);
+const float IV9 = powf(q3, 2);
+const float IV10 = powf(q0, 2) - powf(q1, 2);
+const float IV11 = IV10 + IV8 - IV9;
+const float IV12 = IV7*P(2,3);
+const float IV13 = IV5*P(0,1);
+const float IV14 = IV6*P(0,1);
+const float IV15 = IV4*P(2,3);
+const float IV16 = 2*q0*q2 + 2*q1*q3;
+const float IV17 = 2*IV0 - 2*IV1;
+const float IV18 = IV10 - IV8 + IV9;
+
+
+// Observation Jacobians - axis 0
+Hfusion.at<0>() = R_MAG;
+Hfusion.at<1>() = IV11*P(17,20) + IV11*(IV11*P(17,17) + IV2*P(17,18) - IV3*P(16,17) + IV4*P(2,17) + IV5*P(0,17) + IV6*P(1,17) - IV7*P(3,17) + P(17,20)) + IV2*P(18,20) + IV2*(IV11*P(17,18) + IV2*P(18,18) - IV3*P(16,18) + IV4*P(2,18) + IV5*P(0,18) + IV6*P(1,18) - IV7*P(3,18) + P(18,20)) - IV3*P(16,20) - IV3*(IV11*P(16,17) + IV2*P(16,18) - IV3*P(16,16) + IV4*P(2,16) + IV5*P(0,16) + IV6*P(1,16) - IV7*P(3,16) + P(16,20)) + IV4*P(2,20) + IV4*(IV11*P(2,17) - IV12 + IV2*P(2,18) - IV3*P(2,16) + IV4*P(2,2) + IV5*P(0,2) + IV6*P(1,2) + P(2,20)) + IV5*P(0,20) + IV5*(IV11*P(0,17) + IV14 + IV2*P(0,18) - IV3*P(0,16) + IV4*P(0,2) + IV5*P(0,0) - IV7*P(0,3) + P(0,20)) + IV6*P(1,20) + IV6*(IV11*P(1,17) + IV13 + IV2*P(1,18) - IV3*P(1,16) + IV4*P(1,2) + IV6*P(1,1) - IV7*P(1,3) + P(1,20)) - IV7*P(3,20) - IV7*(IV11*P(3,17) + IV15 + IV2*P(3,18) - IV3*P(3,16) + IV5*P(0,3) + IV6*P(1,3) - IV7*P(3,3) + P(3,20)) + P(20,20) + R_MAG;
+Hfusion.at<2>() = IV16*P(16,21) + IV16*(IV16*P(16,16) - IV17*P(16,17) + IV18*P(16,18) + IV4*P(3,16) - IV5*P(1,16) + IV6*P(0,16) + IV7*P(2,16) + P(16,21)) - IV17*P(17,21) - IV17*(IV16*P(16,17) - IV17*P(17,17) + IV18*P(17,18) + IV4*P(3,17) - IV5*P(1,17) + IV6*P(0,17) + IV7*P(2,17) + P(17,21)) + IV18*P(18,21) + IV18*(IV16*P(16,18) - IV17*P(17,18) + IV18*P(18,18) + IV4*P(3,18) - IV5*P(1,18) + IV6*P(0,18) + IV7*P(2,18) + P(18,21)) + IV4*P(3,21) + IV4*(IV12 + IV16*P(3,16) - IV17*P(3,17) + IV18*P(3,18) + IV4*P(3,3) - IV5*P(1,3) + IV6*P(0,3) + P(3,21)) - IV5*P(1,21) - IV5*(IV14 + IV16*P(1,16) - IV17*P(1,17) + IV18*P(1,18) + IV4*P(1,3) - IV5*P(1,1) + IV7*P(1,2) + P(1,21)) + IV6*P(0,21) + IV6*(-IV13 + IV16*P(0,16) - IV17*P(0,17) + IV18*P(0,18) + IV4*P(0,3) + IV6*P(0,0) + IV7*P(0,2) + P(0,21)) + IV7*P(2,21) + IV7*(IV15 + IV16*P(2,16) - IV17*P(2,17) + IV18*P(2,18) - IV5*P(1,2) + IV6*P(0,2) + IV7*P(2,2) + P(2,21)) + P(21,21) + R_MAG;
+
+
+// Kalman gains - axis 0
+
+
+// Observation Jacobians - axis 1
+
+
+// Kalman gains - axis 1
+
+
+// Observation Jacobians - axis 2
+
+
+// Kalman gains - axis 2
+
+

EKF/python/ekf_derivation/generated/mag_decl_fusion_generated_compare.cpp

@@ -0,0 +1,227 @@
+#include <math.h>
+#include <stdio.h>
+#include <cstdlib>
+#include "../../../../../matrix/matrix/math.hpp"
+
+typedef matrix::Vector<float, 24> Vector24f;
+typedef matrix::SquareMatrix<float, 24> SquareMatrix24f;
+
+float sq(float in) {
+    return in * in;
+}
+
+int main()
+{
+    // Compare calculation of observation Jacobians and Kalman gains for sympy and matlab generated equations
+
+	float Hfusion[24] = {};
+    Vector24f H_DECL;
+    Vector24f Kfusion;
+    float decl_innov_var;
+
+	const float R_DECL = sq(0.3f);
+
+    const float _gps_yaw_offset = 1.5f;
+
+    // quaternion inputs must be normalised
+    float q0 = 2.0f * ((float)rand() - 0.5f);
+    float q1 = 2.0f * ((float)rand() - 0.5f);
+    float q2 = 2.0f * ((float)rand() - 0.5f);
+    float q3 = 2.0f * ((float)rand() - 0.5f);
+    const float length = sqrtf(sq(q0) + sq(q1) + sq(q2) + sq(q3));
+    q0 /= length;
+    q1 /= length;
+    q2 /= length;
+    q3 /= length;
+
+	const float magN = 0.04f;
+	const float magE = -0.03f;
+
+    const float h_field_min = 1e-3f;
+
+    // create a symmetrical positive dfinite matrix with off diagonals between -1 and 1 and diagonals between 0 and 1
+    SquareMatrix24f P;
+    for (int col=0; col<=23; col++) {
+        for (int row=0; row<=col; row++) {
+            if (row == col) {
+                P(row,col) = (float)rand();
+            } else {
+                P(col,row) = P(row,col) = 2.0f * ((float)rand() - 0.5f);
+            }
+        }
+    }
+
+    // First calculate observationjacobians and Kalman gains using sympy generated equations
+
+	// Calculate intermediate variables
+	const float magN_sq = sq(magN);
+	if (magN_sq < sq(h_field_min)) {
+		printf("bad numerical conditioning\n");
+        return 0;
+	}
+	const float HK0 = 1.0F / magN_sq;
+	const float HK1 = HK0*sq(magE) + 1.0F;
+	const float HK2 = 1.0F/HK1;
+	const float HK3 = 1.0F/magN;
+	const float HK4 = HK2*HK3;
+	const float HK5 = HK3*magE;
+	const float HK6 = HK5*P(16,17) - P(17,17);
+	const float HK7 = 1.0F/sq(HK1);
+	const float HK8 = HK5*P(16,16) - P(16,17);
+	const float innovation_variance = -HK0*HK6*HK7 + HK7*HK8*magE/(magN * magN_sq) + R_DECL;
+	float HK9;
+	if (innovation_variance > R_DECL) {
+		HK9 = HK4/innovation_variance;
+	} else {
+		printf("bad numerical conditioning\n");
+	}
+
+	// Calculate the observation Jacobian
+	// Note only 2 terms are non-zero which can be used in matrix operations for calculation of Kalman gains and covariance update to significantly reduce cost
+	Hfusion[16] = -HK0*HK2*magE;
+	Hfusion[17] = HK4;
+
+	// Calculate the Kalman gains
+	for (unsigned row = 0; row <= 15; row++) {
+		Kfusion(row) = -HK9*(HK5*P(row,16) - P(row,17));
+	}
+
+	Kfusion(16) = -HK8*HK9;
+	Kfusion(17) = -HK6*HK9;
+
+	for (unsigned row = 18; row <= 23; row++) {
+		Kfusion(row) = -HK9*(HK5*P(16,row) - P(17,row));
+	}
+
+    // save output and repeat calculation using legacy matlab generated code
+    float Hfusion_sympy[24];
+    Vector24f Kfusion_sympy;
+    for (int row=0; row<24; row++) {
+        Hfusion_sympy[row] = Hfusion[row];
+        Kfusion_sympy(row) = Kfusion(row);
+    }
+
+    // repeat calculation using matlab generated equations
+	// Calculate intermediate variables
+	float t2 = magE*magE;
+	float t3 = magN*magN;
+	float t4 = t2+t3;
+	// if the horizontal magnetic field is too small, this calculation will be badly conditioned
+	if (t4 < h_field_min*h_field_min) {
+		printf("bad numerical conditioning\n");
+        return 0;
+	}
+	float t5 = P(16,16)*t2;
+	float t6 = P(17,17)*t3;
+	float t7 = t2*t2;
+	float t8 = R_DECL*t7;
+	float t9 = t3*t3;
+	float t10 = R_DECL*t9;
+	float t11 = R_DECL*t2*t3*2.0f;
+	float t14 = P(16,17)*magE*magN;
+	float t15 = P(17,16)*magE*magN;
+	float t12 = t5+t6+t8+t10+t11-t14-t15;
+	float t13;
+	if (fabsf(t12) > 1e-6f) {
+		t13 = 1.0f / t12;
+	} else {
+		printf("bad numerical conditioning\n");
+        return 0;
+	}
+	float t18 = magE*magE;
+	float t19 = magN*magN;
+	float t20 = t18+t19;
+	float t21;
+	if (fabsf(t20) > 1e-6f) {
+		t21 = 1.0f/t20;
+	} else {
+		printf("bad numerical conditioning\n");
+        return 0;
+	}
+
+	// Calculate the observation Jacobian
+	// Note only 2 terms are non-zero which can be used in matrix operations for calculation of Kalman gains and covariance update to significantly reduce cost
+    memset(&H_DECL, 0, sizeof(H_DECL));
+	H_DECL(16) = -magE*t21;
+	H_DECL(17) = magN*t21;
+
+	// Calculate the Kalman gains
+	Kfusion(0) = -t4*t13*(P(0,16)*magE-P(0,17)*magN);
+	Kfusion(1) = -t4*t13*(P(1,16)*magE-P(1,17)*magN);
+	Kfusion(2) = -t4*t13*(P(2,16)*magE-P(2,17)*magN);
+	Kfusion(3) = -t4*t13*(P(3,16)*magE-P(3,17)*magN);
+	Kfusion(4) = -t4*t13*(P(4,16)*magE-P(4,17)*magN);
+	Kfusion(5) = -t4*t13*(P(5,16)*magE-P(5,17)*magN);
+	Kfusion(6) = -t4*t13*(P(6,16)*magE-P(6,17)*magN);
+	Kfusion(7) = -t4*t13*(P(7,16)*magE-P(7,17)*magN);
+	Kfusion(8) = -t4*t13*(P(8,16)*magE-P(8,17)*magN);
+	Kfusion(9) = -t4*t13*(P(9,16)*magE-P(9,17)*magN);
+	Kfusion(10) = -t4*t13*(P(10,16)*magE-P(10,17)*magN);
+	Kfusion(11) = -t4*t13*(P(11,16)*magE-P(11,17)*magN);
+	Kfusion(12) = -t4*t13*(P(12,16)*magE-P(12,17)*magN);
+	Kfusion(13) = -t4*t13*(P(13,16)*magE-P(13,17)*magN);
+	Kfusion(14) = -t4*t13*(P(14,16)*magE-P(14,17)*magN);
+	Kfusion(15) = -t4*t13*(P(15,16)*magE-P(15,17)*magN);
+	Kfusion(16) = -t4*t13*(P(16,16)*magE-P(16,17)*magN);
+	Kfusion(17) = -t4*t13*(P(17,16)*magE-P(17,17)*magN);
+	Kfusion(18) = -t4*t13*(P(18,16)*magE-P(18,17)*magN);
+	Kfusion(19) = -t4*t13*(P(19,16)*magE-P(19,17)*magN);
+	Kfusion(20) = -t4*t13*(P(20,16)*magE-P(20,17)*magN);
+	Kfusion(21) = -t4*t13*(P(21,16)*magE-P(21,17)*magN);
+	Kfusion(22) = -t4*t13*(P(22,16)*magE-P(22,17)*magN);
+	Kfusion(23) = -t4*t13*(P(23,16)*magE-P(23,17)*magN);
+
+    // find largest observation variance difference as a fraction of the matlab value
+    float max_diff_fraction = 0.0f;
+    int max_row;
+    float max_old, max_new;
+    for (int row=0; row<24; row++) {
+        float diff_fraction;
+        if (H_DECL(row) != 0.0f) {
+            diff_fraction = fabsf(Hfusion_sympy[row] - H_DECL(row)) / fabsf(H_DECL(row));
+        } else if (Hfusion_sympy[row] != 0.0f) {
+            diff_fraction = fabsf(Hfusion_sympy[row] - H_DECL(row)) / fabsf(Hfusion_sympy[row]);
+        } else {
+            diff_fraction = 0.0f;
+        }
+        if (diff_fraction > max_diff_fraction) {
+            max_diff_fraction = diff_fraction;
+            max_row = row;
+            max_old = H_DECL(row);
+            max_new = Hfusion_sympy[row];
+        }
+    }
+
+	if (max_diff_fraction > 1E-5f) {
+		printf("Fail: Mag Declination Hfusion max diff fraction = %e , old = %e , new = %e , location index = %i\n",max_diff_fraction, max_old, max_new, max_row);
+	} else {
+		printf("Pass: Mag Declination Hfusion max diff fraction = %e\n",max_diff_fraction);
+	}
+
+    // find largest Kalman gain difference as a fraction of the matlab value
+    max_diff_fraction = 0.0f;
+    for (int row=0; row<4; row++) {
+        float diff_fraction;
+        if (Kfusion(row) != 0.0f) {
+            diff_fraction = fabsf(Kfusion_sympy(row) - Kfusion(row)) / fabsf(Kfusion(row));
+        } else if (Kfusion_sympy(row) != 0.0f) {
+            diff_fraction = fabsf(Kfusion_sympy(row) - Kfusion(row)) / fabsf(Kfusion_sympy(row));
+        } else {
+            diff_fraction = 0.0f;
+        }
+        if (diff_fraction > max_diff_fraction) {
+            max_diff_fraction = diff_fraction;
+            max_row = row;
+            max_old = Kfusion(row);
+            max_new = Kfusion_sympy(row);
+        }
+    }
+
+	if (max_diff_fraction > 1E-5f) {
+		printf("Fail: Mag Declination Kfusion max diff fraction = %e , old = %e , new = %e , location index = %i\n",max_diff_fraction, max_old, max_new, max_row);
+	} else {
+		printf("Pass: Mag Declination Kfusion max diff fraction = %e\n",max_diff_fraction);
+	}
+
+    return 0;
+}

EKF/python/ekf_derivation/generated/mag_decl_generated.cpp

@@ -0,0 +1,67 @@
+// Sub Expressions
+const float HK0 = powf(magN, -2);
+const float HK1 = HK0*powf(magE, 2) + 1;
+const float HK2 = 1.0F/HK1;
+const float HK3 = 1.0F/magN;
+const float HK4 = HK2*HK3;
+const float HK5 = HK3*magE;
+const float HK6 = HK5*P(16,17) - P(17,17);
+const float HK7 = powf(HK1, -2);
+const float HK8 = HK5*P(16,16) - P(16,17);
+const float HK9 = HK4/(-HK0*HK6*HK7 + HK7*HK8*magE/powf(magN, 3) + R_DECL);
+
+
+// Observation Jacobians
+Hfusion.at<0>() = 0;
+Hfusion.at<1>() = 0;
+Hfusion.at<2>() = 0;
+Hfusion.at<3>() = 0;
+Hfusion.at<4>() = 0;
+Hfusion.at<5>() = 0;
+Hfusion.at<6>() = 0;
+Hfusion.at<7>() = 0;
+Hfusion.at<8>() = 0;
+Hfusion.at<9>() = 0;
+Hfusion.at<10>() = 0;
+Hfusion.at<11>() = 0;
+Hfusion.at<12>() = 0;
+Hfusion.at<13>() = 0;
+Hfusion.at<14>() = 0;
+Hfusion.at<15>() = 0;
+Hfusion.at<16>() = -HK0*HK2*magE;
+Hfusion.at<17>() = HK4;
+Hfusion.at<18>() = 0;
+Hfusion.at<19>() = 0;
+Hfusion.at<20>() = 0;
+Hfusion.at<21>() = 0;
+Hfusion.at<22>() = 0;
+Hfusion.at<23>() = 0;
+
+
+// Kalman gains
+Kfusion(0) = -HK9*(HK5*P(0,16) - P(0,17));
+Kfusion(1) = -HK9*(HK5*P(1,16) - P(1,17));
+Kfusion(2) = -HK9*(HK5*P(2,16) - P(2,17));
+Kfusion(3) = -HK9*(HK5*P(3,16) - P(3,17));
+Kfusion(4) = -HK9*(HK5*P(4,16) - P(4,17));
+Kfusion(5) = -HK9*(HK5*P(5,16) - P(5,17));
+Kfusion(6) = -HK9*(HK5*P(6,16) - P(6,17));
+Kfusion(7) = -HK9*(HK5*P(7,16) - P(7,17));
+Kfusion(8) = -HK9*(HK5*P(8,16) - P(8,17));
+Kfusion(9) = -HK9*(HK5*P(9,16) - P(9,17));
+Kfusion(10) = -HK9*(HK5*P(10,16) - P(10,17));
+Kfusion(11) = -HK9*(HK5*P(11,16) - P(11,17));
+Kfusion(12) = -HK9*(HK5*P(12,16) - P(12,17));
+Kfusion(13) = -HK9*(HK5*P(13,16) - P(13,17));
+Kfusion(14) = -HK9*(HK5*P(14,16) - P(14,17));
+Kfusion(15) = -HK9*(HK5*P(15,16) - P(15,17));
+Kfusion(16) = -HK8*HK9;
+Kfusion(17) = -HK6*HK9;
+Kfusion(18) = -HK9*(HK5*P(16,18) - P(17,18));
+Kfusion(19) = -HK9*(HK5*P(16,19) - P(17,19));
+Kfusion(20) = -HK9*(HK5*P(16,20) - P(17,20));
+Kfusion(21) = -HK9*(HK5*P(16,21) - P(17,21));
+Kfusion(22) = -HK9*(HK5*P(16,22) - P(17,22));
+Kfusion(23) = -HK9*(HK5*P(16,23) - P(17,23));
+
+

EKF/python/ekf_derivation/generated/yaw_fusion_generated_compare.cpp

@@ -0,0 +1,315 @@
+#include <math.h>
+#include <stdio.h>
+#include <cstdlib>
+#include "../../../../../matrix/matrix/math.hpp"
+
+typedef matrix::Vector<float, 24> Vector24f;
+typedef matrix::SquareMatrix<float, 24> SquareMatrix24f;
+
+float sq(float in) {
+    return in * in;
+}
+
+int main()
+{
+    // Compare calculation of observation Jacobian for sympy and matlab generated equations
+
+    // observation Jacobians
+	float H_YAW[4];
+
+    // quaternion inputs must be normalised
+    float q0 = 2.0f * ((float)rand() - 0.5f);
+    float q1 = 2.0f * ((float)rand() - 0.5f);
+    float q2 = 2.0f * ((float)rand() - 0.5f);
+    float q3 = 2.0f * ((float)rand() - 0.5f);
+    const float length = sqrtf(sq(q0) + sq(q1) + sq(q2) + sq(q3));
+    q0 /= length;
+    q1 /= length;
+    q2 /= length;
+    q3 /= length;
+
+
+    // calculate 321 yaw observation matrix using two computational paths to work around singularities
+    // in calculation of the Jacobians.
+
+    {
+        // This first comparison is for the 321 sequence option A equations that have a singularity when
+        // yaw is at +- 90 deg
+
+        // perform calculation using sympy generated equations
+        const float SA0 = 2*q3;
+        const float SA1 = 2*q2;
+        const float SA2 = SA0*q0 + SA1*q1;
+        const float SA3 = powf(q0, 2) + powf(q1, 2) - powf(q2, 2) - powf(q3, 2);
+        const float SA4 = powf(SA3, -2);
+        const float SA5 = 1.0F/(powf(SA2, 2)*SA4 + 1);
+        const float SA6 = 1.0F/SA3;
+        const float SA7 = SA2*SA4;
+        const float SA8 = 2*SA7;
+        const float SA9 = 2*SA6;
+
+        H_YAW[0] = SA5*(SA0*SA6 - SA8*q0);
+        H_YAW[1] = SA5*(SA1*SA6 - SA8*q1);
+        H_YAW[2] = SA5*(SA1*SA7 + SA9*q1);
+        H_YAW[3] = SA5*(SA0*SA7 + SA9*q0);
+
+        // save output and repeat calculation using legacy matlab generated code
+        float H_YAW_sympy[4];
+        for (int row=0; row<4; row++) {
+            H_YAW_sympy[row] = H_YAW[row];
+        }
+
+        // repeat calculation using matlab generated equations
+        float t9 = q0*q3;
+        float t10 = q1*q2;
+        float t2 = t9+t10;
+        float t3 = q0*q0;
+        float t4 = q1*q1;
+        float t5 = q2*q2;
+        float t6 = q3*q3;
+        float t7 = t3+t4-t5-t6;
+        float t16 = q3*t3;
+        float t17 = q3*t5;
+        float t18 = q0*q1*q2*2.0f;
+        float t19 = t16+t17+t18-q3*t4+q3*t6;
+        float t24 = q2*t4;
+        float t25 = q2*t6;
+        float t26 = q0*q1*q3*2.0f;
+        float t27 = t24+t25+t26-q2*t3+q2*t5;
+        float t28 = q1*t3;
+        float t29 = q1*t5;
+        float t30 = q0*q2*q3*2.0f;
+        float t31 = t28+t29+t30+q1*t4-q1*t6;
+        float t32 = q0*t4;
+        float t33 = q0*t6;
+        float t34 = q1*q2*q3*2.0f;
+        float t35 = t32+t33+t34+q0*t3-q0*t5;
+        float t8 = t7*t7;
+        t8 = 1.0f/t8;
+        float t11 = t2*t2;
+        float t12 = t8*t11*4.0f;
+        float t13 = t12+1.0f;
+        float t14 = 1.0f/t13;
+
+        H_YAW[0] = t8*t14*t19*(-2.0f);
+        H_YAW[1] = t8*t14*t27*(-2.0f);
+        H_YAW[2] = t8*t14*t31*2.0f;
+        H_YAW[3] = t8*t14*t35*2.0f;
+
+        // find largest difference as a fraction of the matlab value
+        float max_diff_fraction = 0.0f;
+        int max_row;
+        float max_old, max_new;
+        for (int row=0; row<4; row++) {
+            float diff_fraction = fabsf(H_YAW_sympy[row] - H_YAW[row]) / fabsf(H_YAW[row]);
+            if (diff_fraction > max_diff_fraction) {
+                max_diff_fraction = diff_fraction;
+                max_row = row;
+                max_old = H_YAW[row];
+                max_new = H_YAW_sympy[row];
+            }
+        }
+
+        if (max_diff_fraction > 1E-5f) {
+            printf("Fail: 321 yaw option A Hfusion max diff fraction = %e , old = %e , new = %e , location index = %i\n",max_diff_fraction, max_old, max_new, max_row);
+        } else {
+            printf("Pass: 321 yaw option A Hfusion max diff fraction = %e\n",max_diff_fraction);
+        }
+
+        // This second comparison for the 321 sequence option B equations that have a singularity when
+        // yaw is at 0 and +-190 deg
+
+        // perform calculation using sympy generated equations
+        const float SB0 = 2*q0;
+        const float SB1 = 2*q1;
+        const float SB2 = SB0*q3 + SB1*q2;
+        const float SB3 = powf(SB2, -2);
+        const float SB4 = powf(q0, 2) + powf(q1, 2) - powf(q2, 2) - powf(q3, 2);
+        const float SB5 = 1.0F/(SB3*powf(SB4, 2) + 1);
+        const float SB6 = 1.0F/SB2;
+        const float SB7 = SB3*SB4;
+        const float SB8 = 2*SB7;
+        const float SB9 = 2*SB6;
+
+        H_YAW[0] = -SB5*(SB0*SB6 - SB8*q3);
+        H_YAW[1] = -SB5*(SB1*SB6 - SB8*q2);
+        H_YAW[2] = -SB5*(-SB1*SB7 - SB9*q2);
+        H_YAW[3] = -SB5*(-SB0*SB7 - SB9*q3);
+
+        // save output and repeat calculation using legacy matlab generated code
+        for (int row=0; row<4; row++) {
+            H_YAW_sympy[row] = H_YAW[row];
+        }
+
+        float t15 = t2*t2;
+        t15 = 1.0f/t15;
+        float t20 = t7*t7;
+        float t21 = t15*t20*0.25f;
+        float t22 = t21+1.0f;
+        float t23 = 1.0f/t22;
+
+        H_YAW[0] = t15*t19*t23*(-0.5f);
+        H_YAW[1] = t15*t23*t27*(-0.5f);
+        H_YAW[2] = t15*t23*t31*0.5f;
+        H_YAW[3] = t15*t23*t35*0.5f;
+
+        // find largest difference as a fraction of the matlab value
+        max_diff_fraction = 0.0f;
+        for (int row=0; row<4; row++) {
+            float diff_fraction = fabsf(H_YAW_sympy[row] - H_YAW[row]) / fabsf(H_YAW[row]);
+            if (diff_fraction > max_diff_fraction) {
+                max_diff_fraction = diff_fraction;
+                max_row = row;
+                max_old = H_YAW[row];
+                max_new = H_YAW_sympy[row];
+            }
+        }
+
+        if (max_diff_fraction > 1E-5f) {
+            printf("Fail: 321 yaw option B Hfusion max diff fraction = %e , old = %e , new = %e , location index = %i\n",max_diff_fraction, max_old, max_new, max_row);
+        } else {
+            printf("Pass: 321 yaw option B Hfusion max diff fraction = %e\n",max_diff_fraction);
+        }
+    }
+
+    // calculate 312 yaw observation matrix using two computational paths to work around singularities
+    // in calculation of the Jacobians.
+
+    {
+        // This first comparison is for the 312 sequence option A equations that have a singularity when
+        // yaw is at +- 90 deg
+
+        // perform calculation using sympy generated equations
+        const float SA0 = 2*q3;
+        const float SA1 = 2*q2;
+        const float SA2 = SA0*q0 - SA1*q1;
+        const float SA3 = powf(q0, 2) - powf(q1, 2) + powf(q2, 2) - powf(q3, 2);
+        const float SA4 = powf(SA3, -2);
+        const float SA5 = 1.0F/(powf(SA2, 2)*SA4 + 1);
+        const float SA6 = 1.0F/SA3;
+        const float SA7 = SA2*SA4;
+        const float SA8 = 2*SA7;
+        const float SA9 = 2*SA6;
+
+        H_YAW[0] = SA5*(SA0*SA6 - SA8*q0);
+        H_YAW[1] = SA5*(-SA1*SA6 + SA8*q1);
+        H_YAW[2] = SA5*(-SA1*SA7 - SA9*q1);
+        H_YAW[3] = SA5*(SA0*SA7 + SA9*q0);
+
+        // save output and repeat calculation using legacy matlab generated code
+        float H_YAW_sympy[4];
+        for (int row=0; row<4; row++) {
+            H_YAW_sympy[row] = H_YAW[row];
+        }
+
+        // repeat calculation using matlab generated equations
+        float t9 = q0*q3;
+        float t10 = q1*q2;
+        float t2 = t9-t10;
+        float t3 = q0*q0;
+        float t4 = q1*q1;
+        float t5 = q2*q2;
+        float t6 = q3*q3;
+        float t7 = t3-t4+t5-t6;
+        float t16 = q3*t3;
+        float t17 = q3*t4;
+        float t18 = t16+t17-q3*t5+q3*t6-q0*q1*q2*2.0f;
+        float t23 = q2*t3;
+        float t24 = q2*t4;
+        float t25 = t23+t24+q2*t5-q2*t6-q0*q1*q3*2.0f;
+        float t26 = q1*t5;
+        float t27 = q1*t6;
+        float t28 = t26+t27-q1*t3+q1*t4-q0*q2*q3*2.0f;
+        float t29 = q0*t5;
+        float t30 = q0*t6;
+        float t31 = t29+t30+q0*t3-q0*t4-q1*q2*q3*2.0f;
+        float t8 = t7*t7;
+        float t15 = t2*t2;
+		t8 = 1.0f/t8;
+		float t11 = t2*t2;
+		float t12 = t8*t11*4.0f;
+		float t13 = t12+1.0f;
+		float t14 = 1.0f/t13;
+
+		H_YAW[0] = t8*t14*t18*(-2.0f);
+		H_YAW[1] = t8*t14*t25*(-2.0f);
+		H_YAW[2] = t8*t14*t28*2.0f;
+		H_YAW[3] = t8*t14*t31*2.0f;
+
+        // find largest difference as a fraction of the matlab value
+        float max_diff_fraction = 0.0f;
+        int max_row;
+        float max_old, max_new;
+        for (int row=0; row<4; row++) {
+            float diff_fraction = fabsf(H_YAW_sympy[row] - H_YAW[row]) / fabsf(H_YAW[row]);
+            if (diff_fraction > max_diff_fraction) {
+                max_diff_fraction = diff_fraction;
+                max_row = row;
+                max_old = H_YAW[row];
+                max_new = H_YAW_sympy[row];
+            }
+        }
+
+        if (max_diff_fraction > 1E-5f) {
+            printf("Fail: 312 yaw option A Hfusion max diff fraction = %e , old = %e , new = %e , location index = %i\n",max_diff_fraction, max_old, max_new, max_row);
+        } else {
+            printf("Pass: 312 yaw option A Hfusion max diff fraction = %e\n",max_diff_fraction);
+        }
+
+        // This second comparison for the 321 sequence option B equations that have a singularity when
+        // yaw is at 0 and +-190 deg
+
+        // perform calculation using sympy generated equations
+        const float SB0 = 2*q0;
+        const float SB1 = 2*q1;
+        const float SB2 = -SB0*q3 + SB1*q2;
+        const float SB3 = powf(SB2, -2);
+        const float SB4 = -powf(q0, 2) + powf(q1, 2) - powf(q2, 2) + powf(q3, 2);
+        const float SB5 = 1.0F/(SB3*powf(SB4, 2) + 1);
+        const float SB6 = 1.0F/SB2;
+        const float SB7 = SB3*SB4;
+        const float SB8 = 2*SB7;
+        const float SB9 = 2*SB6;
+
+        H_YAW[0] = -SB5*(-SB0*SB6 + SB8*q3);
+        H_YAW[1] = -SB5*(SB1*SB6 - SB8*q2);
+        H_YAW[2] = -SB5*(-SB1*SB7 - SB9*q2);
+        H_YAW[3] = -SB5*(SB0*SB7 + SB9*q3);
+
+        // save output and repeat calculation using legacy matlab generated code
+        for (int row=0; row<4; row++) {
+            H_YAW_sympy[row] = H_YAW[row];
+        }
+
+		t15 = 1.0f/t15;
+		float t19 = t7*t7;
+		float t20 = t15*t19*0.25f;
+		float t21 = t20+1.0f;
+		float t22 = 1.0f/t21;
+
+        H_YAW[0] = t15*t18*t22*(-0.5f);
+        H_YAW[1] = t15*t22*t25*(-0.5f);
+        H_YAW[2] = t15*t22*t28*0.5f;
+        H_YAW[3] = t15*t22*t31*0.5f;
+
+        // find largest difference as a fraction of the matlab value
+        max_diff_fraction = 0.0f;
+        for (int row=0; row<4; row++) {
+            float diff_fraction = fabsf(H_YAW_sympy[row] - H_YAW[row]) / fabsf(H_YAW[row]);
+            if (diff_fraction > max_diff_fraction) {
+                max_diff_fraction = diff_fraction;
+                max_row = row;
+                max_old = H_YAW[row];
+                max_new = H_YAW_sympy[row];
+            }
+        }
+
+        if (max_diff_fraction > 1E-5f) {
+            printf("Fail: 312 yaw option B Hfusion max diff fraction = %e , old = %e , new = %e , location index = %i\n",max_diff_fraction, max_old, max_new, max_row);
+        } else {
+            printf("Pass: 312 yaw option B Hfusion max diff fraction = %e\n",max_diff_fraction);
+        }
+    }
+
+    return 0;
+}

EKF/python/ekf_derivation/main.py

@@ -48,14 +48,28 @@ def create_symmetric_cov_matrix():
 
     return P
 
+# generate equations for observation vector innovation variances
+def generate_observation_vector_innovation_variances(P,state,observation,variance,n_obs):
+    H = observation.jacobian(state)
+    innovation_variance = zeros(n_obs,1)
+    for index in range(n_obs):
+        H[index,:] = Matrix([observation[index]]).jacobian(state)
+        innovation_variance[index] = H[index,:] * P * H[index,:].T + Matrix([variance])
+
+    IV_simple = cse(innovation_variance, symbols("IV0:1000"), optimizations='basic')
+
+    return IV_simple
+
 # generate equations for observation Jacobian and Kalman gain
-def generate_observation_equations(P,state,observation,variance):
+def generate_observation_equations(P,state,observation,variance,varname="HK"):
     H = Matrix([observation]).jacobian(state)
     innov_var = H * P * H.T + Matrix([variance])
     assert(innov_var.shape[0] == 1)
     assert(innov_var.shape[1] == 1)
     K = P * H.T / innov_var[0,0]
-    HK_simple = cse(Matrix([H.transpose(), K]), symbols("HK0:1000"), optimizations='basic')
+    extension="0:1000"
+    var_string = varname+extension
+    HK_simple = cse(Matrix([H.transpose(), K]), symbols(var_string), optimizations='basic')
 
     return HK_simple
 
@@ -86,18 +100,18 @@ def write_equations_to_file(equations,code_generator_id,n_obs):
         code_generator_id.print_string("Sub Expressions")
         code_generator_id.write_subexpressions(equations[0])
         code_generator_id.print_string("Observation Jacobians")
-        code_generator_id.write_matrix(Matrix(equations[1][0][0:24]), "Hfusion")
+        code_generator_id.write_matrix(Matrix(equations[1][0][0:24]), "Hfusion", False, ".at<", ">()")
         code_generator_id.print_string("Kalman gains")
-        code_generator_id.write_matrix(Matrix(equations[1][0][24:]), "Kfusion")
+        code_generator_id.write_matrix(Matrix(equations[1][0][24:]), "Kfusion", False, "(", ")")
     else:
         code_generator_id.print_string("Sub Expressions")
         code_generator_id.write_subexpressions(equations[0])
         for axis_index in range(n_obs):
             start_index = axis_index*48
             code_generator_id.print_string("Observation Jacobians - axis %i" % axis_index)
-            code_generator_id.write_matrix(Matrix(equations[1][0][start_index:start_index+24]), "Hfusion")
+            code_generator_id.write_matrix(Matrix(equations[1][0][start_index:start_index+24]), "Hfusion", False, ".at<", ">()")
             code_generator_id.print_string("Kalman gains - axis %i" % axis_index)
-            code_generator_id.write_matrix(Matrix(equations[1][0][start_index+24:start_index+48]), "Kfusion")
+            code_generator_id.write_matrix(Matrix(equations[1][0][start_index+24:start_index+48]), "Kfusion", False, "(", ")")
 
     return
 
@@ -157,8 +171,8 @@ def body_frame_velocity_observation(P,state,R_to_body,vx,vy,vz):
 
         vel_bf_code_generator.print_string("axis %i" % index)
         vel_bf_code_generator.write_subexpressions(equations[0])
-        vel_bf_code_generator.write_matrix(Matrix(equations[1][0][0:24]), "H_VEL")
-        vel_bf_code_generator.write_matrix(Matrix(equations[1][0][24:]), "Kfusion")
+        vel_bf_code_generator.write_matrix(Matrix(equations[1][0][0:24]), "H_VEL", False, "(", ")")
+        vel_bf_code_generator.write_matrix(Matrix(equations[1][0][24:]), "Kfusion", False, "(", ")")
 
     vel_bf_code_generator.close()
 
@@ -267,11 +281,11 @@ def yaw_observation(P,state,R_to_earth):
 
     yaw_code_generator.print_string("calculate 321 yaw observation matrix - option A")
     yaw_code_generator.write_subexpressions(H_YAW321_A_simple[0])
-    yaw_code_generator.write_matrix(Matrix(H_YAW321_A_simple[1]).T, "H_YAW")
+    yaw_code_generator.write_matrix(Matrix(H_YAW321_A_simple[1]).T, "H_YAW", False, ".at<", ">()")
 
     yaw_code_generator.print_string("calculate 321 yaw observation matrix - option B")
     yaw_code_generator.write_subexpressions(H_YAW321_B_simple[0])
-    yaw_code_generator.write_matrix(Matrix(H_YAW321_B_simple[1]).T, "H_YAW")
+    yaw_code_generator.write_matrix(Matrix(H_YAW321_B_simple[1]).T, "H_YAW", False, ".at<", ">()")
 
     # Derive observation Jacobian for fusion of 312 sequence yaw measurement
     # Calculate the yaw (first rotation) angle from an Euler 312 sequence
@@ -286,16 +300,31 @@ def yaw_observation(P,state,R_to_earth):
 
     yaw_code_generator.print_string("calculate 312 yaw observation matrix - option A")
     yaw_code_generator.write_subexpressions(H_YAW312_A_simple[0])
-    yaw_code_generator.write_matrix(Matrix(H_YAW312_A_simple[1]).T, "H_YAW")
+    yaw_code_generator.write_matrix(Matrix(H_YAW312_A_simple[1]).T, "H_YAW", False, ".at<", ">()")
 
     yaw_code_generator.print_string("calculate 312 yaw observation matrix - option B")
     yaw_code_generator.write_subexpressions(H_YAW312_B_simple[0])
-    yaw_code_generator.write_matrix(Matrix(H_YAW312_B_simple[1]).T, "H_YAW")
+    yaw_code_generator.write_matrix(Matrix(H_YAW312_B_simple[1]).T, "H_YAW", False, ".at<", ">()")
 
     yaw_code_generator.close()
 
     return
 
+# 3D magnetometer fusion
+def mag_observation_variance(P,state,R_to_body,i,ib):
+    obs_var = symbols("R_MAG", real=True)  # magnetometer measurement noise variance
+
+    m_mag = R_to_body * i + ib
+
+    # separate calculation of innovation variance equations for the y and z axes
+    m_mag[0]=0
+    innov_var_equations = generate_observation_vector_innovation_variances(P,state,m_mag,obs_var,3)
+    mag_innov_var_code_generator = CodeGenerator("./generated/3Dmag_innov_var_generated.cpp")
+    write_equations_to_file(innov_var_equations,mag_innov_var_code_generator,3)
+    mag_innov_var_code_generator.close()
+
+    return
+
 # 3D magnetometer fusion
 def mag_observation(P,state,R_to_body,i,ib):
     obs_var = symbols("R_MAG", real=True)  # magnetometer measurement noise variance
@@ -306,8 +335,17 @@ def mag_observation(P,state,R_to_body,i,ib):
     mag_code_generator = CodeGenerator("./generated/3Dmag_generated.cpp")
 
     axes = [0,1,2]
+    label="HK"
     for index in axes:
-        equations = generate_observation_equations(P,state,m_mag[index],obs_var)
+        if (index==0):
+            label="HKX"
+        elif (index==1):
+            label="HKY"
+        elif (index==2):
+            label="HKZ"
+        else:
+            return
+        equations = generate_observation_equations(P,state,m_mag[index],obs_var,varname=label)
         mag_code_generator.print_string("Axis %i equations" % index)
         write_equations_to_file(equations,mag_code_generator,1)
 
@@ -459,7 +497,7 @@ def generate_code():
     cov_code_generator = CodeGenerator("./generated/covariance_generated.cpp")
     cov_code_generator.print_string("Equations for covariance matrix prediction, without process noise!")
     cov_code_generator.write_subexpressions(P_new_simple[0])
-    cov_code_generator.write_matrix(Matrix(P_new_simple[1]), "nextP", True)
+    cov_code_generator.write_matrix(Matrix(P_new_simple[1]), "nextP", True, "(", ")")
 
     cov_code_generator.close()
 
@@ -469,6 +507,7 @@ def generate_code():
     print('Generating gps heading observation code ...')
     gps_yaw_observation(P,state,R_to_body)
     print('Generating mag observation code ...')
+    mag_observation_variance(P,state,R_to_body,i,ib)
     mag_observation(P,state,R_to_body,i,ib)
     print('Generating declination observation code ...')
     declination_observation(P,state,ix,iy)

test/change_indication/iris_gps.csv

@@ -4,348 +4,348 @@ Timestamp,state[0],state[1],state[2],state[3],state[4],state[5],state[6],state[7
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 285000,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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-485000,0.983207,-0.00779267,-0.0137988,0.181806,0.00149516,0.000487556,-0.0226199,0.000128857,3.88731e-05,0.012004,3.89716e-08,1.3818e-10,1.63937e-06,0,0,5.50648e-08,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,9.05599e-05,0.00251394,0.0025137,0.00257812,25.0144,25.0144,0.56266,0.609418,0.609418,0.802449,9.99999e-07,1e-06,9.98121e-07,0,0,4.00001e-06,0,0,0,0,0,0,0,0
-585000,0.983235,-0.00781283,-0.0140176,0.181633,0.000142817,0.000425494,-0.0407873,4.57242e-05,1.65576e-05,0.00559437,4.92314e-08,-1.10894e-10,2.06611e-06,0,0,1.69579e-07,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,6.31735e-05,0.00260317,0.00260303,0.00179033,7.81663,7.81663,0.561469,0.228172,0.228172,0.451638,9.99994e-07,9.99999e-07,9.91443e-07,0,0,4e-06,0,0,0,0,0,0,0,0
-685000,0.983166,-0.00784229,-0.0143846,0.181978,0.00273131,0.00149319,-0.0490414,0.00022836,0.000116917,0.0168581,1.00722e-08,-3.07713e-10,4.61971e-07,0,0,-3.88273e-07,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,4.99495e-05,0.00274313,0.00274301,0.00140913,7.85794,7.85794,0.557235,0.486139,0.486139,0.322026,9.99986e-07,9.99999e-07,9.77538e-07,0,0,3.99989e-06,0,0,0,0,0,0,0,0
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-885000,0.983035,-0.0078867,-0.0149611,0.182637,0.00537375,0.00623852,-0.0766231,0.000540952,0.000537906,-0.000216641,-1.6477e-07,-9.61095e-09,-6.50679e-06,0,0,9.87685e-08,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.87062e-05,0.00316568,0.00316556,0.00108283,2.66545,2.66547,0.534816,0.329581,0.329582,0.225286,9.99866e-07,9.99914e-07,9.23082e-07,0,0,3.99856e-06,0,0,0,0,0,0,0,0
-985000,0.982858,-0.00782901,-0.0152572,0.183566,0.00823652,0.00902617,-0.0901081,0.00123165,0.00123919,-0.00832501,-4.8827e-07,-1.48091e-08,-1.91202e-05,0,0,-1.56205e-07,0.203406,-9.31323e-10,0.43452,0,0,0,0,0,3.82301e-05,0.0034554,0.00345523,0.00106637,2.75673,2.75676,0.52163,0.517615,0.517616,0.218362,9.99846e-07,9.99914e-07,8.92597e-07,0,0,3.99721e-06,0,0,0,0,0,0,0,0
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