protected MatrixLibrary.Matrix magneticCompensation(MyQuaternion q, double m_x, double m_y, double m_z)
{
MatrixLibrary.Matrix h = new MatrixLibrary.Matrix(4, 1);
MatrixLibrary.Matrix temp;
//compute the direction of the magnetic field
MatrixLibrary.Matrix quaternion = q.getQuaternionAsVector();
MatrixLibrary.Matrix quaternion_conjugate = q.getConjugate();
//magnetic field compensation
temp = MyQuaternion.quaternionProduct(quaternion, new MyQuaternion(0.0, m_x, m_y, m_z).getQuaternionAsVector());
h = MyQuaternion.quaternionProduct(temp, quaternion_conjugate);
double bx = Math.Sqrt((h[1, 0] * h[1, 0] + h[2, 0] * h[2, 0]));
double bz = h[3, 0];
double norm = Math.Sqrt(bx * bx + bz * bz);
bx /= norm;
bz /= norm;
MatrixLibrary.Matrix result = new MatrixLibrary.Matrix(3, 1);
result[0, 0] = bx;
result[1, 0] = 0;
result[2, 0] = bz;
return(result);
}
public override void filterStep(double w_x, double w_y, double w_z, double a_x, double a_y, double a_z, double m_x, double m_y, double m_z)
{
// normalise the accelerometer measurement
double norm = Math.Sqrt(a_x * a_x + a_y * a_y + a_z * a_z);
a_x /= norm;
a_y /= norm;
a_z /= norm;
// normalise the magnetometer measurement
norm = Math.Sqrt(m_x * m_x + m_y * m_y + m_z * m_z);
m_x /= norm;
m_y /= norm;
m_z /= norm;
if (AccObservX.Count < 10)
{
AccObservX.Add(a_x);
AccObservY.Add(a_y);
AccObservZ.Add(a_z);
}
else
{
AccObservX.RemoveAt(0);
AccObservY.RemoveAt(0);
AccObservZ.RemoveAt(0);
AccObservX.Add(a_x);
AccObservY.Add(a_y);
AccObservZ.Add(a_z);
}
if (MagnObservX.Count < 10)
{
MagnObservX.Add(m_x);
MagnObservY.Add(m_y);
MagnObservZ.Add(m_z);
}
else
{
MagnObservX.RemoveAt(0);
MagnObservY.RemoveAt(0);
MagnObservZ.RemoveAt(0);
MagnObservX.Add(m_x);
MagnObservY.Add(m_y);
MagnObservZ.Add(m_z);
//Filter stabilization
accFilter.Applyfilter(AccObservX, out AccFiltX);
accFilter.Applyfilter(AccObservY, out AccFiltY);
accFilter.Applyfilter(AccObservZ, out AccFiltZ);
magnFilter.Applyfilter(MagnObservX, out MagnFiltX);
magnFilter.Applyfilter(MagnObservY, out MagnFiltY);
magnFilter.Applyfilter(MagnObservZ, out MagnFiltZ);
}
if (step < 10)
{
}
else
{
accFilter.Applyfilter(AccObservX, out AccFiltX);
accFilter.Applyfilter(AccObservY, out AccFiltY);
accFilter.Applyfilter(AccObservZ, out AccFiltZ);
magnFilter.Applyfilter(MagnObservX, out MagnFiltX);
magnFilter.Applyfilter(MagnObservY, out MagnFiltY);
magnFilter.Applyfilter(MagnObservZ, out MagnFiltZ);
a_x = AccFiltX.Last();
a_y = AccFiltY.Last();
a_z = AccFiltZ.Last();
m_x = MagnFiltX.Last();
m_y = MagnFiltY.Last();
m_z = MagnFiltZ.Last();
//Magnetometer Calibration values
//m_x =m_x*1.2+ 0.3;
//m_y = m_y*1.1+0.04;
//m_z += -0.08;
double normA = Math.Sqrt(a_x * a_x + a_y * a_y + a_z * a_z);
double normM = Math.Sqrt(m_x * m_x + m_y * m_y + m_z * m_z);
a_x /= normA;
a_y /= normA;
a_z /= normA;
m_x /= normM;
m_y /= normM;
m_z /= normM;
w_x = (w_x - gyroOffRoll) * Math.PI / 180;
w_y = (w_y - gyroOffPitch) * Math.PI / 180;
w_z = (w_z - gyroOffYaw) * Math.PI / 180;
MatrixLibrary.Matrix dq = 0.5 * (MyQuaternion.quaternionProduct(qFilt, new MyQuaternion(0, w_x, w_y, w_z).getQuaternionAsVector()));
qGyroFilt = qFilt + dq * dt;
norm = Math.Sqrt(qGyroFilt[0, 0] * qGyroFilt[0, 0] + qGyroFilt[1, 0] * qGyroFilt[1, 0] + qGyroFilt[2, 0] * qGyroFilt[2, 0] + qGyroFilt[3, 0] * qGyroFilt[3, 0]);
qGyroFilt /= norm;
double dqNorm = Math.Sqrt(dq[0, 0] * dq[0, 0] + dq[1, 0] * dq[1, 0] + dq[2, 0] * dq[2, 0] + dq[3, 0] * dq[3, 0]);
double mu = 10 * dqNorm * dt;
if (this.obsMethod == 0)
{
qObserv = GradientDescent(a_x, a_y, a_z, m_x, m_y, m_z, mu, qFilt);
}
else
{
qObserv = gaussNewtonMethod(a_x, a_y, a_z, m_x, m_y, m_z, qFilt);
}
qFilt = qGyroFilt * k + qObserv * (1 - k);
norm = Math.Sqrt(qFilt[0, 0] * qFilt[0, 0] + qFilt[1, 0] * qFilt[1, 0] + qFilt[2, 0] * qFilt[2, 0] + qFilt[3, 0] * qFilt[3, 0]);
qFilt /= norm;
}
step++;
}
public override void filterStep(double w_x, double w_y, double w_z, double a_x, double a_y, double a_z, double m_x, double m_y, double m_z)
{
double norm;
Matrix temp;//=new Matrix(4,4);
Matrix dq = new Matrix(4, 1);
double mu;
double k;
// normalise the accelerometer measurement
norm = Math.Sqrt(a_x * a_x + a_y * a_y + a_z * a_z);
a_x /= norm;
a_y /= norm;
a_z /= norm;
// normalise the magnetometer measurement
norm = Math.Sqrt(m_x * m_x + m_y * m_y + m_z * m_z);
m_x /= norm;
m_y /= norm;
m_z /= norm;
/* if (AccObservX.Count < 10)
* {
* AccObservX.Add(a_x);
* AccObservY.Add(a_y);
* AccObservZ.Add(a_z);
* }
* else
* {
* AccObservX.RemoveAt(0);
* AccObservY.RemoveAt(0);
* AccObservZ.RemoveAt(0);
*
* AccObservX.Add(a_x);
* AccObservY.Add(a_y);
* AccObservZ.Add(a_z);
* }
* if (MagnObservX.Count < 10)
* {
* MagnObservX.Add(m_x);
* MagnObservY.Add(m_y);
* MagnObservZ.Add(m_z);
* }
* else
* {
* MagnObservX.RemoveAt(0);
* MagnObservY.RemoveAt(0);
* MagnObservZ.RemoveAt(0);
* MagnObservX.Add(m_x);
* MagnObservY.Add(m_y);
* MagnObservZ.Add(m_z);
*
* //Filter stabilization
* accFilter.Applyfilter(AccObservX, out AccFiltX);
* accFilter.Applyfilter(AccObservY, out AccFiltY);
* accFilter.Applyfilter(AccObservZ, out AccFiltZ);
*
* magnFilter.Applyfilter(MagnObservX, out MagnFiltX);
* magnFilter.Applyfilter(MagnObservY, out MagnFiltY);
* magnFilter.Applyfilter(MagnObservZ, out MagnFiltZ);
* }
*
* if (countdata > 10)
* {
* a_x = AccFiltX.Last();
* a_y = AccFiltY.Last();
* a_z = AccFiltZ.Last();
*
* m_x = MagnFiltX.Last();
* m_y = MagnFiltY.Last();
* m_z = MagnFiltZ.Last();
*
* // normalise the accelerometer measurement
*
* norm = Math.Sqrt(a_x * a_x + a_y * a_y + a_z * a_z);
* a_x /= norm;
* a_y /= norm;
* a_z /= norm;
*
*
* // normalise the magnetometer measurement
* norm = Math.Sqrt(m_x * m_x + m_y * m_y + m_z * m_z);
* m_x /= norm;
* m_y /= norm;
* m_z /= norm;
* }
*
*
*
* countdata++;
*/
// w_x = w_x - gyroOffRoll;
// w_y = w_y - gyroOffPitch;
// w_z = w_z - gyroOffYaw;
w_x = w_x * Math.PI / 180;
w_y = w_y * Math.PI / 180;
w_z = w_z * Math.PI / 180;
if (this.obsMethod == 0)
{
dq = 0.5 * (MyQuaternion.quaternionProduct(state_observed, new MyQuaternion(0.0, w_x, w_y, w_z).getQuaternionAsVector()));
norm = Math.Sqrt(dq[0, 0] * dq[0, 0] + dq[1, 0] * dq[1, 0] + dq[2, 0] * dq[2, 0] + dq[3, 0] * dq[3, 0]);
mu = 10 * norm * dt;
state_observed = GradientDescent(a_x, a_y, a_z, m_x, m_y, m_z, mu, state_filtered);
}
else
{
state_observed = gaussNewtonMethod(a_x, a_y, a_z, m_x, m_y, m_z, state_filtered);
}
//KALMAN FILTERING
//F matrix computing
F[0, 0] = 1;
F[0, 1] = -dt / 2 * w_x;
F[0, 2] = -dt / 2 * w_y;
F[0, 3] = -dt / 2 * w_z;
F[1, 0] = dt / 2 * w_x;
F[1, 1] = 1;
F[1, 2] = dt / 2 * w_z;
F[1, 3] = -dt / 2 * w_y;
F[2, 0] = dt / 2 * w_y;
F[2, 1] = -dt / 2 * w_z;
F[2, 2] = 1;
F[2, 3] = dt / 2 * w_x;
F[3, 0] = dt / 2 * w_z;
F[3, 1] = dt / 2 * w_y;
F[3, 2] = -dt / 2 * w_x;
F[3, 3] = 1;
//state prediction
state_predicted = Matrix.Multiply(F, state_filtered);
//calculate the variance of the prediction
P_predicted = Matrix.Multiply(F, P_Update);
P_predicted = Matrix.Multiply(P_predicted, Matrix.Transpose(F)) + Q;
//compute the gain of the filter K
temp = Matrix.Add(Matrix.Multiply(Matrix.Multiply(H, P_predicted), Matrix.Transpose(H)), R);
temp = Matrix.Inverse(temp);
K = Matrix.Multiply(Matrix.Multiply(P_predicted, Matrix.Transpose(H)), temp);
//update the state of the system (this is the output of the filter)
temp = Matrix.Subtract(state_observed, Matrix.Multiply(H, state_predicted));
state_filtered = Matrix.Add(state_predicted, Matrix.Multiply(K, temp));
//compute the variance of the state filtered
temp = Matrix.Subtract((new Matrix(Matrix.Identity(4))), Matrix.Multiply(K, H));
P_Update = Matrix.Multiply(temp, P_predicted);
norm = Math.Sqrt(state_filtered[0, 0] * state_filtered[0, 0] + state_filtered[1, 0] * state_filtered[1, 0] + state_filtered[2, 0] * state_filtered[2, 0] + state_filtered[3, 0] * state_filtered[3, 0]);
state_filtered = Matrix.ScalarDivide(norm, state_filtered);
q_filt1 = (float)state_filtered[0, 0];
q_filt2 = (float)state_filtered[1, 0];
q_filt3 = (float)state_filtered[2, 0];
q_filt4 = (float)state_filtered[3, 0];
}
protected MatrixLibrary.Matrix gaussNewtonMethod(double a_x, double a_y, double a_z, double m_x, double m_y, double m_z,MatrixLibrary.Matrix qObserv)
{
double norm;
MatrixLibrary.Matrix n = new MatrixLibrary.Matrix(4, 1);
MatrixLibrary.Matrix bRif = new MatrixLibrary.Matrix(3, 1);
MatrixLibrary.Matrix jacobian = new MatrixLibrary.Matrix(6, 4);
MatrixLibrary.Matrix R = new MatrixLibrary.Matrix(6, 6);
MatrixLibrary.Matrix y_e = new MatrixLibrary.Matrix(6, 1);
MatrixLibrary.Matrix y_b = new MatrixLibrary.Matrix(6, 1);
double a = qObserv[1, 0];
double b = qObserv[2, 0];
double c = qObserv[3, 0];
double d = qObserv[0, 0];
int i = 0;
MatrixLibrary.Matrix n_k = new MatrixLibrary.Matrix(4, 1);
n_k[0, 0] = a;
n_k[1, 0] = b;
n_k[2, 0] = c;
n_k[3, 0] = d;
//Magnetometer Calibration values
m_x = m_x * magnSFX + magnOffX;
m_y = m_y * magnSFY + magnOffY;
m_z = m_z * magnSFZ + magnOffZ;
norm = Math.Sqrt(m_x * m_x + m_y * m_y + m_z * m_z);
m_x /= norm;
m_y /= norm;
m_z /= norm;
while (i < 3)
{
MyQuaternion q = new MyQuaternion(d, a, b, c);
bRif = magneticCompensation(q, m_x, m_y, m_z);
double bx = bRif[0, 0];
double by = bRif[1, 0];
double bz = bRif[2, 0];
//Jacobian Computation
double j11 = (2 * a * a_x + 2 * b * a_y + 2 * c * a_z);
double j12 = (-2 * b * a_x + 2 * a * a_y + 2 * d * a_z);
double j13 = (-2 * c * a_x - 2 * d * a_y + 2 * a * a_z);
double j14 = (2 * d * a_x - 2 * c * a_y + 2 * b * a_z);
double j21 = (2 * b * a_x - 2 * a * a_y - 2 * d * a_z);
double j22 = (2 * a * a_x + 2 * b * a_y + 2 * c * a_z);
double j23 = (2 * d * a_x - 2 * c * a_y + 2 * b * a_z);
double j24 = (2 * c * a_x + 2 * d * a_y - 2 * a * a_z);
double j31 = (2 * c * a_x + 2 * d * a_y - 2 * a * a_z);
double j32 = (-2 * d * a_x + 2 * c * a_y - 2 * b * a_z);
double j33 = (2 * a * a_x + 2 * b * a_y + 2 * c * a_z);
double j34 = (-2 * b * a_x + 2 * a * a_y + 2 * d * a_z);
double j41 = (2 * a * m_x + 2 * b * m_y + 2 * c * m_z);
double j42 = (-2 * b * m_x + 2 * a * m_y + 2 * m_z * d);
double j43 = (-2 * c * m_x - 2 * d * m_y + 2 * a * m_z);
double j44 = (2 * d * m_x - 2 * c * m_y + 2 * b * m_z);
double j51 = (2 * b * m_x - 2 * a * m_y - 2 * d * m_z);
double j52 = (2 * a * m_x + 2 * b * m_y + 2 * c * m_z);
double j53 = (2 * d * m_x - 2 * c * m_y + 2 * b * m_z);
double j54 = (2 * c * m_x + 2 * d * m_y - 2 * a * m_z);
double j61 = (2 * c * m_x + 2 * d * m_y - 2 * a * m_z);
double j62 = (-2 * d * m_x + 2 * c * m_y - 2 * b * m_z);
double j63 = (2 * a * m_x + 2 * b * m_y + 2 * c * m_z);
double j64 = (-2 * b * m_x + 2 * a * m_y + 2 * d * m_z);
jacobian[0, 0] = j11;
jacobian[0, 1] = j12;
jacobian[0, 2] = j13;
jacobian[0, 3] = j14;
jacobian[1, 0] = j21;
jacobian[1, 1] = j22;
jacobian[1, 2] = j23;
jacobian[1, 3] = j24;
jacobian[2, 0] = j31;
jacobian[2, 1] = j32;
jacobian[2, 2] = j33;
jacobian[2, 3] = j34;
jacobian[3, 0] = j41;
jacobian[3, 1] = j42;
jacobian[3, 2] = j43;
jacobian[3, 3] = j44;
jacobian[4, 0] = j51;
jacobian[4, 1] = j52;
jacobian[4, 2] = j53;
jacobian[4, 3] = j54;
jacobian[5, 0] = j61;
jacobian[5, 1] = j62;
jacobian[5, 2] = j63;
jacobian[5, 3] = j64;
jacobian = -1 * jacobian;
//End Jacobian Computation
//DCM Rotation Matrix
R[0, 0] = d * d + a * a - b * b - c * c;
R[0, 1] = 2 * (a * b - c * d);
R[0, 2] = 2 * (a * c + b * d);
R[1, 0] = 2 * (a * b + c * d);
R[1, 1] = d * d + b * b - a * a - c * c;
R[1, 2] = 2 * (b * c - a * d);
R[2, 0] = 2 * (a * c - b * d);
R[2, 1] = 2 * (b * c + a * d);
R[2, 2] = d * d + c * c - b * b - a * a;
R[3, 3] = d * d + a * a - b * b - c * c;
R[3, 4] = 2 * (a * b - c * d);
R[3, 5] = 2 * (a * c + b * d);
R[4, 3] = 2 * (a * b + c * d);
R[4, 4] = d * d + b * b - a * a - c * c;
R[4, 5] = 2 * (b * c - a * d);
R[5, 3] = 2 * (a * c - b * d);
R[5, 4] = 2 * (b * c + a * d);
R[5, 5] = d * d + c * c - b * b - a * a;
R[3, 0] = 0;
R[3, 1] = 0;
R[3, 2] = 0;
R[4, 0] = 0;
R[4, 1] = 0;
R[4, 2] = 0;
R[5, 0] = 0;
R[5, 1] = 0;
R[5, 2] = 0;
R[0, 3] = 0;
R[0, 4] = 0;
R[0, 5] = 0;
R[1, 3] = 0;
R[1, 4] = 0;
R[1, 5] = 0;
R[2, 3] = 0;
R[2, 4] = 0;
R[2, 5] = 0;
//End DCM
//Reference Vector
y_e[0, 0] = 0;
y_e[1, 0] = 0;
y_e[2, 0] = 1;
y_e[3, 0] = bx;
y_e[4, 0] = by;
y_e[5, 0] = bz;
//Body frame Vector
y_b[0, 0] = a_x;
y_b[1, 0] = a_y;
y_b[2, 0] = a_z;
y_b[3, 0] = m_x;
y_b[4, 0] = m_y;
y_b[5, 0] = m_z;
//Gauss Newton Step
n = n_k - MatrixLibrary.Matrix.Inverse((MatrixLibrary.Matrix.Transpose(jacobian) * jacobian)) * MatrixLibrary.Matrix.Transpose(jacobian) * (y_e - R * y_b);
double normGauss = Math.Sqrt(n[0, 0] * n[0, 0] + n[1, 0] * n[1, 0] + n[2, 0] * n[2, 0] + n[3, 0] * n[3, 0]);
n /= normGauss;
//Console.Out.WriteLine(n + " "+ norm);
a = n[0, 0];
b = n[1, 0];
c = n[2, 0];
d = n[3, 0];
n_k[0, 0] = a;
n_k[1, 0] = b;
n_k[2, 0] = c;
n_k[3, 0] = d;
i++;
}
return new MyQuaternion(d, a, b, c).getQuaternionAsVector();
}
protected MatrixLibrary.Matrix magneticCompensation(MyQuaternion q, double m_x, double m_y, double m_z)
{
MatrixLibrary.Matrix h = new MatrixLibrary.Matrix(4, 1);
MatrixLibrary.Matrix temp;
//compute the direction of the magnetic field
MatrixLibrary.Matrix quaternion = q.getQuaternionAsVector();
MatrixLibrary.Matrix quaternion_conjugate = q.getConjugate();
//magnetic field compensation
temp = MyQuaternion.quaternionProduct(quaternion, new MyQuaternion(0.0, m_x, m_y, m_z).getQuaternionAsVector());
h = MyQuaternion.quaternionProduct(temp, quaternion_conjugate);
double bx = Math.Sqrt((h[1, 0] * h[1, 0] + h[2, 0] * h[2, 0]));
double bz = h[3, 0];
double norm = Math.Sqrt(bx * bx + bz * bz);
bx /= norm;
bz /= norm;
MatrixLibrary.Matrix result = new MatrixLibrary.Matrix(3, 1);
result[0, 0] = bx;
result[1, 0] = 0;
result[2, 0] = bz;
return result;
}
protected MatrixLibrary.Matrix GradientDescent(double a_x, double a_y, double a_z, double m_x, double m_y, double m_z, double mu,MatrixLibrary.Matrix qObserv)
{
int i = 0;
double q1, q2, q3, q4;
MatrixLibrary.Matrix f_obb = new MatrixLibrary.Matrix(6, 1);
MatrixLibrary.Matrix Jacobian = new MatrixLibrary.Matrix(6, 4);
MatrixLibrary.Matrix Df = new MatrixLibrary.Matrix(4, 1);
double norm;
double bx, bz, by;
MatrixLibrary.Matrix result = new MatrixLibrary.Matrix(4, 1);
q1 = qObserv[0, 0];
q2 = qObserv[1, 0];
q3 = qObserv[2, 0];
q4 = qObserv[3, 0];
//Magnetometer Calibration values
m_x = m_x *magnSFX+ magnOffX;
m_y = m_y *magnSFY+ magnOffY;
m_z= m_z *magnSFZ+ magnOffZ;
norm = Math.Sqrt(m_x * m_x + m_y * m_y + m_z * m_z);
m_x /= norm;
m_y /= norm;
m_z /= norm;
while (i < 10)
{
//compute the direction of the magnetic field
MatrixLibrary.Matrix quaternion = new MyQuaternion(q1, q2, q3, q4).getQuaternionAsVector();
MatrixLibrary.Matrix bRif = magneticCompensation(new MyQuaternion(q1, q2, q3, q4), m_x, m_y, m_z);
bx = bRif[0, 0];
by = bRif[1, 0];
bz = bRif[2, 0];
//compute the objective functions
f_obb[0, 0] = 2 * (q2 * q4 - q1 * q3) - a_x;
f_obb[1, 0] = 2 * (q1 * q2 + q3 * q4) - a_y;
f_obb[2, 0] = 2 * (0.5 - q2 * q2 - q3 * q3) - a_z;
f_obb[3, 0] = 2 * bx * (0.5 - q3 * q3 - q4 * q4) + 2 * by * (q1 * q4 + q2 * q3) + 2 * bz * (q2 * q4 - q1 * q3) - m_x;
f_obb[4, 0] = 2 * bx * (q2 * q3 - q1 * q4) + 2 * by * (0.5 - q2 * q2 - q4 * q4) + 2 * bz * (q1 * q2 + q3 * q4) - m_y;
f_obb[5, 0] = 2 * bx * (q1 * q3 + q2 * q4) + 2 * by * (q3 * q4 - q1 * q2) + 2 * bz * (0.5 - q2 * q2 - q3 * q3) - m_z;
//compute the jacobian
Jacobian[0, 0] = -2 * q3;
Jacobian[0, 1] = 2 * q4;
Jacobian[0, 2] = -2 * q1;
Jacobian[0, 3] = 2 * q2;
Jacobian[1, 0] = 2 * q2;
Jacobian[1, 1] = 2 * q1;
Jacobian[1, 2] = 2 * q4;
Jacobian[1, 3] = 2 * q3;
Jacobian[2, 0] = 0;
Jacobian[2, 1] = -4 * q2;
Jacobian[2, 2] = -4 * q3;
Jacobian[2, 3] = 0;
Jacobian[3, 0] = 2 * by * q4 - 2 * bz * q3;
Jacobian[3, 1] = 2 * by * q3 + 2 * bz * q4;
Jacobian[3, 2] = -4 * bx * q3 + 2 * by * q2 - 2 * bz * q1;
Jacobian[3, 3] = -4 * bx * q4 + 2 * by * q1 + 2 * bz * q2;
Jacobian[4, 0] = -2 * bx * q4 + 2 * bz * q2;
Jacobian[4, 1] = 2 * bx * q3 - 4 * by * q2 + 2 * bz * q1;
Jacobian[4, 2] = 2 * bx * q2 + 2 * bz * q4;
Jacobian[4, 3] = -2 * bx * q1 - 4 * by * q4 + 2 * bz * q3;
Jacobian[5, 0] = 2 * bx * q3 - 2 * by * q2;
Jacobian[5, 1] = 2 * bx * q4 - 2 * by * q1 - 4 * bz * q2;
Jacobian[5, 2] = 2 * bx * q1 + 2 * by * q4 - 4 * bz * q3;
Jacobian[5, 3] = 2 * bx * q2 + 2 * by * q3;
Df = MatrixLibrary.Matrix.Multiply(MatrixLibrary.Matrix.Transpose(Jacobian), f_obb);
norm = Math.Sqrt(Df[0, 0] * Df[0, 0] + Df[1, 0] * Df[1, 0] + Df[2, 0] * Df[2, 0] + Df[3, 0] * Df[3, 0]);
Df = MatrixLibrary.Matrix.ScalarDivide(norm, Df);
result = quaternion - mu * Df;
q1 = result[0, 0];
q2 = result[1, 0];
q3 = result[2, 0];
q4 = result[3, 0];
norm = Math.Sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);
result = MatrixLibrary.Matrix.ScalarDivide(norm, result);
q1 = result[0, 0];
q2 = result[1, 0];
q3 = result[2, 0];
q4 = result[3, 0];
i = i + 1;
}
return result;
}
public static MatrixLibrary.Matrix quaternionProduct(MyQuaternion q_a, MyQuaternion q_b)
{
MatrixLibrary.Matrix v1 = q_a.getQuaternionAsVector();
MatrixLibrary.Matrix v2 = q_b.getQuaternionAsVector();
return(quaternionProduct(v1, v2));
}
//***********************************************
//
// data proccessing
//**********************************************
public void Data_proccessing(int n)
{
/* if (s.Length == 48)
* {
*
* Int32.TryParse(s.Substring(1, 3), out MAG[0]);
* Int32.TryParse(s.Substring(5, 3), out MAG[1]);
* Int32.TryParse(s.Substring(9, 3), out MAG[2]);
*
* UInt32.TryParse(s.Substring(12, 4), out ACC[0]);
* UInt32.TryParse(s.Substring(16, 4), out ACC[1]);
* UInt32.TryParse(s.Substring(20, 4), out ACC[2]);
*
* UInt32.TryParse(s.Substring(24, 4), out GYRO[0]);
* UInt32.TryParse(s.Substring(28, 4), out GYRO[1]);
* UInt32.TryParse(s.Substring(32, 4), out GYRO[2]);
*
* UInt32.TryParse(s.Substring(36, 4), out ENCODER[0]);
* UInt32.TryParse(s.Substring(40, 4), out ENCODER[1]);
* UInt32.TryParse(s.Substring(44, 4), out ENCODER[2]);
*
* if (s.Substring(0, 1) == "-")
* {
* MAG[0] = -MAG[0];
* }
* if (s.Substring(4, 1) == "-")
* {
* MAG[1] = -MAG[1];
* }
* if (s.Substring(8, 1) == "-")
* {
* MAG[2] = -MAG[2];
* }
* }*/
MAG[0] = (Int32)((Input[1] - 0x30) * 100 + (Input[2] - 0x30) * 10 + (Input[3] - 0x30));
MAG[1] = (Int32)((Input[5] - 0x30) * 100 + (Input[6] - 0x30) * 10 + (Input[7] - 0x30));
MAG[2] = (Int32)((Input[9] - 0x30) * 100 + (Input[10] - 0x30) * 10 + (Input[11] - 0x30));
ACC[0] = (UInt32)((Input[12] - 0x30) * 1000 + (Input[13] - 0x30) * 100 + (Input[14] - 0x30) * 10 + (Input[15] - 0x30));
ACC[1] = (UInt32)((Input[16] - 0x30) * 1000 + (Input[17] - 0x30) * 100 + (Input[18] - 0x30) * 10 + (Input[19] - 0x30));
ACC[2] = (UInt32)((Input[20] - 0x30) * 1000 + (Input[21] - 0x30) * 100 + (Input[22] - 0x30) * 10 + (Input[23] - 0x30));
GYRO[0] = (UInt32)((Input[24] - 0x30) * 1000 + (Input[25] - 0x30) * 100 + (Input[26] - 0x30) * 10 + (Input[27] - 0x30));
GYRO[1] = (UInt32)((Input[28] - 0x30) * 1000 + (Input[29] - 0x30) * 100 + (Input[30] - 0x30) * 10 + (Input[31] - 0x30));
GYRO[2] = (UInt32)((Input[32] - 0x30) * 1000 + (Input[33] - 0x30) * 100 + (Input[34] - 0x30) * 10 + (Input[35] - 0x30));
ENCODER[0] = (UInt32)((Input[36] - 0x30) * 1000 + (Input[37] - 0x30) * 100 + (Input[38] - 0x30) * 10 + (Input[39] - 0x30));
ENCODER[1] = (UInt32)((Input[40] - 0x30) * 1000 + (Input[41] - 0x30) * 100 + (Input[42] - 0x30) * 10 + (Input[43] - 0x30));
ENCODER[2] = (UInt32)((Input[44] - 0x30) * 1000 + (Input[45] - 0x30) * 100 + (Input[46] - 0x30) * 10 + (Input[47] - 0x30));
if (Input[0] == '-')
{
MAG[0] = -MAG[0];
}
if (Input[4] == '-')
{
MAG[1] = -MAG[1];
}
if (Input[8] == '-')
{
MAG[2] = -MAG[2];
}
// }
//calculate to real value for filter
int a = MAG[0];
MAG[0] = -MAG[1];
MAG[1] = a;
MAG[2] = MAG[2];
this.form_3DcuboidB.X = (float)MAG[0];
this.form_3DcuboidB.Y = (float)MAG[1];
this.form_3DcuboidB.Z = (float)MAG[2];
ax = ((float)ACC[0] - (float)ACC_OFFSET[0]) * Acc_sensity; // ax real
ay = ((float)ACC[1] - (float)ACC_OFFSET[1]) * Acc_sensity; // ay real
az = ((float)ACC[2] - (float)ACC_OFFSET[2]) * Acc_sensity;
gx = -((float)GYRO[0] - (float)GYRO_OFFSET[0]) * Gyro_sensity;
gy = ((float)GYRO[1] - (float)GYRO_OFFSET[1]) * Gyro_sensity;
gz = ((float)GYRO[2] - (float)GYRO_OFFSET[2]) * Gyro_sensity;
// float norm = (float)Math.Sqrt ( ax * ax + ay * ay + az * az );
// ax /= norm;
// ay /= norm;
// az /= norm;
//
//
//
En_Angle[1] = (float)((ENCODER[0] / 4095.0f) * 2.0f * Math.PI);
En_Angle[0] = (float)((ENCODER[1] / 4095.0f) * 2.0f * Math.PI);
En_Angle[2] = (float)((ENCODER[2] / (6395.0f)) * 2.0f * Math.PI);
if (En_Angle[0] > Math.PI)
{
En_Angle[0] -= (float)Math.PI * 2;
}
if (En_Angle[1] > Math.PI)
{
En_Angle[1] -= (float)Math.PI * 2;
}
if (En_Angle[2] > Math.PI)
{
En_Angle[2] -= (float)Math.PI * 2;
}
/* if(( En_Angle[0]==0)&& (Pre_En_Angle[0]==0))
* {
* En_Angle[0]=0;
* }
* if( ( En_Angle[0]==0) & (Pre_En_Angle[0] != 0))
* {
* En_Angle[0]=Pre_En_Angle[0];
* }
* if (( En_Angle[0] != 0 ))
* {
* Pre_En_Angle[0] = En_Angle[0];
* }
* if (( En_Angle[1] == 0 ) & ( Pre_En_Angle[1] == 0 ))
* {
* En_Angle[1] = 0;
* }
* if (( En_Angle[1] == 0 ) & ( Pre_En_Angle[1] != 0 ))
* {
* En_Angle[1] = Pre_En_Angle[1];
* }
* if (( En_Angle[1] != 0 ) )
* {
* Pre_En_Angle[1] = En_Angle[1];
* }*/
//
//
//this for Encoder
//
// En_Angle[0] = 1;
// En_Angle[1] = 1;
// En_Angle[2] = 1;
// float[] Quatemp = MyQuaternion.getQuaternionFromAngles3(En_Angle);
//En_Angle = MyQuaternion.getAnglesFromQuaternion2(Quatemp);
this.form_3DcuboidA.RotationMatrix = MyQuaternion.getRotaionMatrixFromAngle(En_Angle);
// this.form_3DcuboidA.RotationMatrix = MyQuaternion.getRotaionMatrixFromAngle ( En_Angle );
//MatrixLibrary.Matrix mat = new MatrixLibrary.Matrix(3,3);
//mat[0,0] = rotation[0];
// mat[0, 1] = rotation[1];
//mat[0, 2] = rotation[2];
//mat[1, 0] = rotation[3];
//mat[1, 1] = rotation[4];
//mat[1, 2] = rotation[5];
//mat[2, 0] = rotation[6];
//mat[2, 1] = rotation[7];
//mat[2, 2] = rotation[8];
//double[] dtemp = MyQuaternion.getAngleFromRotation(mat);
//float[] ftemp = new float[3];
//ftemp[0] = (float)dtemp[0];
//ftemp[1] = (float)dtemp[1];
//ftemp[2] = (float)dtemp[2];
//this.form_3DcuboidC.RotationMatrix = MyQuaternion.getRotaionMatrixFromAngle ( ftemp );
//gx =(float) HPfilterp.step ((double) gx ); // 16-bit uint ADC gyrocope values to rad/s (HP filtered)
//gy = (float)HPfilterp.step ( (double)gy);
//gz = (float)HPfilterp.step ( (double)gz);
//
//update
//
// AHRS.Update(gx,gy,gz,ax,ay,az);
// Quaternion = AHRS.Quaternion;
// this.form_3DcuboidA.RotationMatrix = MyQuaternion.getRotationMatrixFromQuaternion3 ( Quatemp );
//
//send data to 3D form
//
this.form_3DcuboidB.Accx = (float)ax;
this.form_3DcuboidB.Accy = (float)ay;
this.form_3DcuboidB.Accz = (float)az;
this.form_3DcuboidB.Gyrox = (float)gx;
this.form_3DcuboidB.Gyroy = (float)gy;
this.form_3DcuboidB.Gyroz = (float)gz;
//
//for accellero only
// AHRS.Update((float)gx, (float)gy, (float)gz, (float)ax, (float)ay, (float)az);
if (n == 1)
{
Kalman.filterStep((double)gx * 180.00f / Math.PI, (double)gy * 180.00f / Math.PI, (double)gz * 180.00f / Math.PI, (double)ax, (double)ay, (double)az, (double)MAG[0], (double)MAG[1], (double)MAG[2]);
// Kalman.filterStep((double)gx , (double)gy, (double)gz, (double)ax, (double)ay, (double)az, (double)MAG[0], (double)MAG[1], (double)MAG[2]);
Quaternion[0] = Kalman.q_filt1;
Quaternion[1] = Kalman.q_filt2;
Quaternion[2] = Kalman.q_filt3;
Quaternion[3] = Kalman.q_filt4;
}
else
{
AHRS.Update((float)gx, (float)gy, (float)gz, (float)ax, (float)ay, (float)az, (float)MAG[0], (float)MAG[1], (float)MAG[2]);//
Quaternion = AHRS.Quaternion;
}
// Quaternion[0] = 1.0f;
// Quaternion[1] = 0.5f;
// Quaternion[2] = 0.0f;
//Quaternion[3] = 0.0f;
//float[] Angle3 = MyQuaternion.getAnglesFromQuaternion2(Quaternion);
//this.form_3DcuboidB.X = (float)Angle3[0];
//this.form_3DcuboidB.Y = (float)Angle3[1];
//this.form_3DcuboidB.Z = (float)Angle3[2];
// float[] temp1 = MyQuaternion.getRotationMatrixFromQuaternion3(Quaternion);
// MatrixLibrary.Matrix mat = new MatrixLibrary.Matrix ( 3, 3 );
float[] temp1 = MyQuaternion.getRotationMatrixFromQuaternion3(Quaternion);
float[] dtemp = MyQuaternion.getAnglesFromQuaternion2(Quaternion);
/* mat[0, 0] = temp1[0];
* mat[0, 1] = temp1[1];
* mat[0, 2] = temp1[2];
* mat[1, 0] = temp1[3];
* mat[1, 1] = temp1[4];
* mat[1, 2] = temp1[5];
* mat[2, 0] = temp1[6];
* mat[2, 1] = temp1[7];
* mat[2, 2] = temp1[8];*/
// double[] dtemp = MyQuaternion.getAngleFromRotation ( mat );
//m double[] Angle5 = new double[3];
//m Angle5[0] = En_Angle2[0];
//m Angle5[1] = En_Angle2[1];
//m Angle5[2] = dtemp[2];
// dtemp[2] = En_Angle[2];
// this.form_3DcuboidB.Gyrox = (float)(dtemp[0] * 180 / Math.PI) ;//Angle5[0];
// this.form_3DcuboidB.Gyroy = (float)(dtemp[1] * 180 / Math.PI);//Angle5[1];
// this.form_3DcuboidB.Gyroz = (float)(dtemp[2] * 180 / Math.PI);//]Angle5[2];
// float[] temp3 = MyQuaternion.getRotaionMatrixFromAngle2(dtemp);//Angle5
this.form_3DcuboidB.RotationMatrix = temp1;
//
//Error angle
//
/*m ERROR[0] = (En_Angle[0] -(float)Angle5[0])*180 / (float)Math.PI;
* ERROR[1] = En_Angle[1] - (float)Angle5[1] * 180 / (float)Math.PI;*/
// ERROR[0] = (float)(dtemp[0] * 180 / Math.PI); ;
//ERROR[1] = (float)(En_Angle[0] * 180 / Math.PI);
// ERROR[2] = (float)(dtemp[0] * 180 / Math.PI);
//ERROR[3] = 0;
//
LIST[0] = (float)(dtemp[0] * 180 / Math.PI);
LIST[1] = (float)(En_Angle[0] * 180 / Math.PI);
LIST[2] = (float)(dtemp[1] * 180 / Math.PI);
LIST[3] = (float)(En_Angle[1] * 180 / Math.PI);
LIST[4] = (float)(dtemp[2] * 180 / Math.PI);
LIST[5] = (float)(En_Angle[2] * 180 / Math.PI);
plotForm.add_graph = LIST;
//
//
//
//
/*MatrixLibrary.Matrix Quaternion12 = new MatrixLibrary.Matrix ( 4, 1 );
* MatrixLibrary.Matrix Angle4 = new MatrixLibrary.Matrix ( 3, 1 );
* Quaternion12[0,0] = 1/Math.Sqrt(4);
* Quaternion12[1, 0] =- 1 / Math.Sqrt ( 4);
* Quaternion12[2, 0] = -1 / Math.Sqrt ( 4 ); ;
* Quaternion12[3, 0] = -1 / Math.Sqrt ( 4 );
*
* Angle4 = MyQuaternion.getAnglesFromQuaternion ( Quaternion12 );
* MatrixLibrary.Matrix Temp_AN = new MatrixLibrary.Matrix ( 3, 1 );
* MatrixLibrary.Matrix QuaRe = new MatrixLibrary.Matrix ( 4, 1 );
* QuaRe = MyQuaternion.getQuaternionFromAngles2 ( Angle4 );
* QuaRe = MyQuaternion.getQuaternionFromAngles ( Angle4 );
* */
//this.form_3DcuboidB.RotationMatrix = temp1;
//QuaRe = MyQuaternion.getQuaternionFromAngles ( Angle4 );
}
public static MatrixLibrary.Matrix quaternionProduct(MyQuaternion q_a, MyQuaternion q_b)
{
MatrixLibrary.Matrix v1 = q_a.getQuaternionAsVector();
MatrixLibrary.Matrix v2 = q_b.getQuaternionAsVector();
return quaternionProduct(v1, v2);
}
protected MatrixLibrary.Matrix GradientDescent(double a_x, double a_y, double a_z, double m_x, double m_y, double m_z, double mu, MatrixLibrary.Matrix qObserv)
{
int i = 0;
double q1, q2, q3, q4;
MatrixLibrary.Matrix f_obb = new MatrixLibrary.Matrix(6, 1);
MatrixLibrary.Matrix Jacobian = new MatrixLibrary.Matrix(6, 4);
MatrixLibrary.Matrix Df = new MatrixLibrary.Matrix(4, 1);
double norm;
double bx, bz, by;
MatrixLibrary.Matrix result = new MatrixLibrary.Matrix(4, 1);
q1 = qObserv[0, 0];
q2 = qObserv[1, 0];
q3 = qObserv[2, 0];
q4 = qObserv[3, 0];
//Magnetometer Calibration values
m_x = m_x * magnSFX + magnOffX;
m_y = m_y * magnSFY + magnOffY;
m_z = m_z * magnSFZ + magnOffZ;
norm = Math.Sqrt(m_x * m_x + m_y * m_y + m_z * m_z);
m_x /= norm;
m_y /= norm;
m_z /= norm;
while (i < 10)
{
//compute the direction of the magnetic field
MatrixLibrary.Matrix quaternion = new MyQuaternion(q1, q2, q3, q4).getQuaternionAsVector();
MatrixLibrary.Matrix bRif = magneticCompensation(new MyQuaternion(q1, q2, q3, q4), m_x, m_y, m_z);
bx = bRif[0, 0];
by = bRif[1, 0];
bz = bRif[2, 0];
//compute the objective functions
f_obb[0, 0] = 2 * (q2 * q4 - q1 * q3) - a_x;
f_obb[1, 0] = 2 * (q1 * q2 + q3 * q4) - a_y;
f_obb[2, 0] = 2 * (0.5 - q2 * q2 - q3 * q3) - a_z;
f_obb[3, 0] = 2 * bx * (0.5 - q3 * q3 - q4 * q4) + 2 * by * (q1 * q4 + q2 * q3) + 2 * bz * (q2 * q4 - q1 * q3) - m_x;
f_obb[4, 0] = 2 * bx * (q2 * q3 - q1 * q4) + 2 * by * (0.5 - q2 * q2 - q4 * q4) + 2 * bz * (q1 * q2 + q3 * q4) - m_y;
f_obb[5, 0] = 2 * bx * (q1 * q3 + q2 * q4) + 2 * by * (q3 * q4 - q1 * q2) + 2 * bz * (0.5 - q2 * q2 - q3 * q3) - m_z;
//compute the jacobian
Jacobian[0, 0] = -2 * q3;
Jacobian[0, 1] = 2 * q4;
Jacobian[0, 2] = -2 * q1;
Jacobian[0, 3] = 2 * q2;
Jacobian[1, 0] = 2 * q2;
Jacobian[1, 1] = 2 * q1;
Jacobian[1, 2] = 2 * q4;
Jacobian[1, 3] = 2 * q3;
Jacobian[2, 0] = 0;
Jacobian[2, 1] = -4 * q2;
Jacobian[2, 2] = -4 * q3;
Jacobian[2, 3] = 0;
Jacobian[3, 0] = 2 * by * q4 - 2 * bz * q3;
Jacobian[3, 1] = 2 * by * q3 + 2 * bz * q4;
Jacobian[3, 2] = -4 * bx * q3 + 2 * by * q2 - 2 * bz * q1;
Jacobian[3, 3] = -4 * bx * q4 + 2 * by * q1 + 2 * bz * q2;
Jacobian[4, 0] = -2 * bx * q4 + 2 * bz * q2;
Jacobian[4, 1] = 2 * bx * q3 - 4 * by * q2 + 2 * bz * q1;
Jacobian[4, 2] = 2 * bx * q2 + 2 * bz * q4;
Jacobian[4, 3] = -2 * bx * q1 - 4 * by * q4 + 2 * bz * q3;
Jacobian[5, 0] = 2 * bx * q3 - 2 * by * q2;
Jacobian[5, 1] = 2 * bx * q4 - 2 * by * q1 - 4 * bz * q2;
Jacobian[5, 2] = 2 * bx * q1 + 2 * by * q4 - 4 * bz * q3;
Jacobian[5, 3] = 2 * bx * q2 + 2 * by * q3;
Df = MatrixLibrary.Matrix.Multiply(MatrixLibrary.Matrix.Transpose(Jacobian), f_obb);
norm = Math.Sqrt(Df[0, 0] * Df[0, 0] + Df[1, 0] * Df[1, 0] + Df[2, 0] * Df[2, 0] + Df[3, 0] * Df[3, 0]);
Df = MatrixLibrary.Matrix.ScalarDivide(norm, Df);
result = quaternion - mu * Df;
q1 = result[0, 0];
q2 = result[1, 0];
q3 = result[2, 0];
q4 = result[3, 0];
norm = Math.Sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);
result = MatrixLibrary.Matrix.ScalarDivide(norm, result);
q1 = result[0, 0];
q2 = result[1, 0];
q3 = result[2, 0];
q4 = result[3, 0];
i = i + 1;
}
return(result);
}
protected MatrixLibrary.Matrix gaussNewtonMethod(double a_x, double a_y, double a_z, double m_x, double m_y, double m_z, MatrixLibrary.Matrix qObserv)
{
double norm;
MatrixLibrary.Matrix n = new MatrixLibrary.Matrix(4, 1);
MatrixLibrary.Matrix bRif = new MatrixLibrary.Matrix(3, 1);
MatrixLibrary.Matrix jacobian = new MatrixLibrary.Matrix(6, 4);
MatrixLibrary.Matrix R = new MatrixLibrary.Matrix(6, 6);
MatrixLibrary.Matrix y_e = new MatrixLibrary.Matrix(6, 1);
MatrixLibrary.Matrix y_b = new MatrixLibrary.Matrix(6, 1);
double a = qObserv[1, 0];
double b = qObserv[2, 0];
double c = qObserv[3, 0];
double d = qObserv[0, 0];
int i = 0;
MatrixLibrary.Matrix n_k = new MatrixLibrary.Matrix(4, 1);
n_k[0, 0] = a;
n_k[1, 0] = b;
n_k[2, 0] = c;
n_k[3, 0] = d;
//Magnetometer Calibration values
m_x = m_x * magnSFX + magnOffX;
m_y = m_y * magnSFY + magnOffY;
m_z = m_z * magnSFZ + magnOffZ;
norm = Math.Sqrt(m_x * m_x + m_y * m_y + m_z * m_z);
m_x /= norm;
m_y /= norm;
m_z /= norm;
while (i < 3)
{
MyQuaternion q = new MyQuaternion(d, a, b, c);
bRif = magneticCompensation(q, m_x, m_y, m_z);
double bx = bRif[0, 0];
double by = bRif[1, 0];
double bz = bRif[2, 0];
//Jacobian Computation
double j11 = (2 * a * a_x + 2 * b * a_y + 2 * c * a_z);
double j12 = (-2 * b * a_x + 2 * a * a_y + 2 * d * a_z);
double j13 = (-2 * c * a_x - 2 * d * a_y + 2 * a * a_z);
double j14 = (2 * d * a_x - 2 * c * a_y + 2 * b * a_z);
double j21 = (2 * b * a_x - 2 * a * a_y - 2 * d * a_z);
double j22 = (2 * a * a_x + 2 * b * a_y + 2 * c * a_z);
double j23 = (2 * d * a_x - 2 * c * a_y + 2 * b * a_z);
double j24 = (2 * c * a_x + 2 * d * a_y - 2 * a * a_z);
double j31 = (2 * c * a_x + 2 * d * a_y - 2 * a * a_z);
double j32 = (-2 * d * a_x + 2 * c * a_y - 2 * b * a_z);
double j33 = (2 * a * a_x + 2 * b * a_y + 2 * c * a_z);
double j34 = (-2 * b * a_x + 2 * a * a_y + 2 * d * a_z);
double j41 = (2 * a * m_x + 2 * b * m_y + 2 * c * m_z);
double j42 = (-2 * b * m_x + 2 * a * m_y + 2 * m_z * d);
double j43 = (-2 * c * m_x - 2 * d * m_y + 2 * a * m_z);
double j44 = (2 * d * m_x - 2 * c * m_y + 2 * b * m_z);
double j51 = (2 * b * m_x - 2 * a * m_y - 2 * d * m_z);
double j52 = (2 * a * m_x + 2 * b * m_y + 2 * c * m_z);
double j53 = (2 * d * m_x - 2 * c * m_y + 2 * b * m_z);
double j54 = (2 * c * m_x + 2 * d * m_y - 2 * a * m_z);
double j61 = (2 * c * m_x + 2 * d * m_y - 2 * a * m_z);
double j62 = (-2 * d * m_x + 2 * c * m_y - 2 * b * m_z);
double j63 = (2 * a * m_x + 2 * b * m_y + 2 * c * m_z);
double j64 = (-2 * b * m_x + 2 * a * m_y + 2 * d * m_z);
jacobian[0, 0] = j11;
jacobian[0, 1] = j12;
jacobian[0, 2] = j13;
jacobian[0, 3] = j14;
jacobian[1, 0] = j21;
jacobian[1, 1] = j22;
jacobian[1, 2] = j23;
jacobian[1, 3] = j24;
jacobian[2, 0] = j31;
jacobian[2, 1] = j32;
jacobian[2, 2] = j33;
jacobian[2, 3] = j34;
jacobian[3, 0] = j41;
jacobian[3, 1] = j42;
jacobian[3, 2] = j43;
jacobian[3, 3] = j44;
jacobian[4, 0] = j51;
jacobian[4, 1] = j52;
jacobian[4, 2] = j53;
jacobian[4, 3] = j54;
jacobian[5, 0] = j61;
jacobian[5, 1] = j62;
jacobian[5, 2] = j63;
jacobian[5, 3] = j64;
jacobian = -1 * jacobian;
//End Jacobian Computation
//DCM Rotation Matrix
R[0, 0] = d * d + a * a - b * b - c * c;
R[0, 1] = 2 * (a * b - c * d);
R[0, 2] = 2 * (a * c + b * d);
R[1, 0] = 2 * (a * b + c * d);
R[1, 1] = d * d + b * b - a * a - c * c;
R[1, 2] = 2 * (b * c - a * d);
R[2, 0] = 2 * (a * c - b * d);
R[2, 1] = 2 * (b * c + a * d);
R[2, 2] = d * d + c * c - b * b - a * a;
R[3, 3] = d * d + a * a - b * b - c * c;
R[3, 4] = 2 * (a * b - c * d);
R[3, 5] = 2 * (a * c + b * d);
R[4, 3] = 2 * (a * b + c * d);
R[4, 4] = d * d + b * b - a * a - c * c;
R[4, 5] = 2 * (b * c - a * d);
R[5, 3] = 2 * (a * c - b * d);
R[5, 4] = 2 * (b * c + a * d);
R[5, 5] = d * d + c * c - b * b - a * a;
R[3, 0] = 0;
R[3, 1] = 0;
R[3, 2] = 0;
R[4, 0] = 0;
R[4, 1] = 0;
R[4, 2] = 0;
R[5, 0] = 0;
R[5, 1] = 0;
R[5, 2] = 0;
R[0, 3] = 0;
R[0, 4] = 0;
R[0, 5] = 0;
R[1, 3] = 0;
R[1, 4] = 0;
R[1, 5] = 0;
R[2, 3] = 0;
R[2, 4] = 0;
R[2, 5] = 0;
//End DCM
//Reference Vector
y_e[0, 0] = 0;
y_e[1, 0] = 0;
y_e[2, 0] = 1;
y_e[3, 0] = bx;
y_e[4, 0] = by;
y_e[5, 0] = bz;
//Body frame Vector
y_b[0, 0] = a_x;
y_b[1, 0] = a_y;
y_b[2, 0] = a_z;
y_b[3, 0] = m_x;
y_b[4, 0] = m_y;
y_b[5, 0] = m_z;
//Gauss Newton Step
n = n_k - MatrixLibrary.Matrix.Inverse((MatrixLibrary.Matrix.Transpose(jacobian) * jacobian)) * MatrixLibrary.Matrix.Transpose(jacobian) * (y_e - R * y_b);
double normGauss = Math.Sqrt(n[0, 0] * n[0, 0] + n[1, 0] * n[1, 0] + n[2, 0] * n[2, 0] + n[3, 0] * n[3, 0]);
n /= normGauss;
//Console.Out.WriteLine(n + " "+ norm);
a = n[0, 0];
b = n[1, 0];
c = n[2, 0];
d = n[3, 0];
n_k[0, 0] = a;
n_k[1, 0] = b;
n_k[2, 0] = c;
n_k[3, 0] = d;
i++;
}
return(new MyQuaternion(d, a, b, c).getQuaternionAsVector());
}