public GPSINSFilter(TimeSpan startTime, Vector3 startPos, Vector3 startVelocity, Quaternion orientation,
SensorSpecifications sensorSpecifications)
{
_startTime = startTime;
_orientation = orientation;
_sensorSpecifications = sensorSpecifications;
X0 = Matrix.Create(new double[n, 1]
{
{ startPos.X }, { startPos.Y }, { startPos.Z }, // Position
{ startVelocity.X }, { startVelocity.Y }, { startVelocity.Z }, // Velocity
{ _orientation.X }, { _orientation.Y }, { _orientation.Z }, { _orientation.W }, // Quaternion
});
// Make sure we don't reference the same object, but rather copy its values.
// It is possible to set PostX0 to a different state than X0, so that the initial guess
// of state is wrong.
PostX0 = X0.Clone();
// We use a very low initial estimate for error covariance, meaning the filter will
// initially trust the model more and the sensors/observations less and gradually adjust on the way.
// Note setting this to zero matrix will cause the filter to infinitely distrust all observations,
// so always use a close-to-zero value instead.
// Setting it to a diagnoal matrix of high values will cause the filter to trust the observations more in the beginning,
// since we say that we think the current PostX0 estimate is unreliable.
PostP0 = 0.001 * Matrix.Identity(n, n);
// Determine standard deviation of estimated process and observation noise variance
// Process noise (acceleromters, gyros, etc..)
_stdDevW = new Vector(new double[n]
{
_sensorSpecifications.AccelerometerStdDev.Forward,
_sensorSpecifications.AccelerometerStdDev.Right,
_sensorSpecifications.AccelerometerStdDev.Up,
0, 0, 0, 0, 0, 0, 0
});
// Observation noise (GPS inaccuarcy etc..)
_stdDevV = new Vector(new double[m]
{
_sensorSpecifications.GPSPositionStdDev.X,
_sensorSpecifications.GPSPositionStdDev.Y,
_sensorSpecifications.GPSPositionStdDev.Z,
// 0.001000, 0.001000, 0.001000,
// 1000, 1000, 1000,
_sensorSpecifications.GPSVelocityStdDev.X,
_sensorSpecifications.GPSVelocityStdDev.Y,
_sensorSpecifications.GPSVelocityStdDev.Z,
});
I = Matrix.Identity(n, n);
_zeroMM = Matrix.Zeros(m);
_rand = new GaussianRandom();
_prevEstimate = GetInitialEstimate(X0, PostX0, PostP0);
}
public static double[] cameraTransform(double PointX, double PointY, double PointZ)
{
// From http://en.wikipedia.org/wiki/3D_projection#Perspective_projection :
//
// Point(X|Y|X) a{x,y,z} The point in 3D space that is to be projected.
// Cube.Camera(X|Y|X) c{x,y,z} The location of the camera.
// Cube.Theta(X|Y|X) θ{x,y,z} The rotation of the camera. When c{x,y,z}=<0,0,0>, and 0{x,y,z}=<0,0,0>, the 3D vector <1,2,0> is projected to the 2D vector <1,2>.
// Cube.Viewer(X|Y|X) e{x,y,z} The viewer's position relative to the display surface.
// Bsub(X|Y) b{x,y} The 2D projection of a.
//
// "First, we define a point DsubXYZ as a translation of point a{x,y,z} into a coordinate system defined by
// c{x,y,z}. This is achieved by subtracting c{x,y,z} from a{x,y,z} and then applying a vector rotation matrix
// using -θ{x,y,z} to the result. This transformation is often called a camera transform (note that these
// calculations assume a left-handed system of axes)."
MathNet.Numerics.LinearAlgebra.Matrix convMat1, convMat2, convMat3, convMat4, convMat41, convMat42, DsubXYZ;
double CosThetaX = Math.Cos(Camera.RotationX); double SinThetaX = Math.Sin(Camera.RotationX);
double CosThetaY = Math.Cos(Camera.RotationY); double SinThetaY = Math.Sin(Camera.RotationY);
double CosThetaZ = Math.Cos(Camera.RotationZ); double SinThetaZ = Math.Sin(Camera.RotationZ);
convMat1 = new MathNet.Numerics.LinearAlgebra.Matrix(new double[][] {
new double[] { 1, 0, 0 },
new double[] { 0, CosThetaX, ((-1)*(SinThetaX)) },
new double[] { 0, SinThetaX, CosThetaX }
});
convMat2 = new MathNet.Numerics.LinearAlgebra.Matrix(new double[][] {
new double[] { CosThetaY, 0, SinThetaY },
new double[] { 0, 1, 0 },
new double[] { ((-1)*(SinThetaY)), 0, CosThetaY }
});
convMat3 = new MathNet.Numerics.LinearAlgebra.Matrix(new double[][] {
new double[] { CosThetaZ, ((-1)*(SinThetaZ)), 0 },
new double[] { SinThetaZ, CosThetaZ, 0 },
new double[] { 0, 0, 1 }
});
convMat41 = new MathNet.Numerics.LinearAlgebra.Matrix(new double[][] {
new double[] { PointX },
new double[] { PointY },
new double[] { PointZ }
});
convMat42 = new MathNet.Numerics.LinearAlgebra.Matrix(new double[][] {
new double[] { Camera.X },
new double[] { Camera.Y },
new double[] { Camera.Z }
});
convMat4 = convMat41.Clone();
convMat4.Subtract(convMat42);
DsubXYZ = ((convMat1.Multiply(convMat2)).Multiply(convMat3)).Multiply(convMat4);
double[] returnVals = new double[3];
returnVals[0] = DsubXYZ[0, 0]; returnVals[1] = DsubXYZ[1, 0]; returnVals[2] = DsubXYZ[2, 0];
return returnVals;
}
public GPSINSFilter(TimeSpan startTime, Vector3 startPos, Vector3 startVelocity, Quaternion orientation,
SensorSpecifications sensorSpecifications)
{
_startTime = startTime;
_orientation = orientation;
_sensorSpecifications = sensorSpecifications;
X0 = Matrix.Create(new double[n,1]
{
{startPos.X}, {startPos.Y}, {startPos.Z}, // Position
{startVelocity.X}, {startVelocity.Y}, {startVelocity.Z}, // Velocity
{_orientation.X}, {_orientation.Y}, {_orientation.Z}, {_orientation.W}, // Quaternion
});
// Make sure we don't reference the same object, but rather copy its values.
// It is possible to set PostX0 to a different state than X0, so that the initial guess
// of state is wrong.
PostX0 = X0.Clone();
// We use a very low initial estimate for error covariance, meaning the filter will
// initially trust the model more and the sensors/observations less and gradually adjust on the way.
// Note setting this to zero matrix will cause the filter to infinitely distrust all observations,
// so always use a close-to-zero value instead.
// Setting it to a diagnoal matrix of high values will cause the filter to trust the observations more in the beginning,
// since we say that we think the current PostX0 estimate is unreliable.
PostP0 = 0.001*Matrix.Identity(n, n);
// Determine standard deviation of estimated process and observation noise variance
// Process noise (acceleromters, gyros, etc..)
_stdDevW = new Vector(new double[n]
{
_sensorSpecifications.AccelerometerStdDev.Forward,
_sensorSpecifications.AccelerometerStdDev.Right,
_sensorSpecifications.AccelerometerStdDev.Up,
0, 0, 0, 0, 0, 0, 0
});
// Observation noise (GPS inaccuarcy etc..)
_stdDevV = new Vector(new double[m]
{
_sensorSpecifications.GPSPositionStdDev.X,
_sensorSpecifications.GPSPositionStdDev.Y,
_sensorSpecifications.GPSPositionStdDev.Z,
// 0.001000, 0.001000, 0.001000,
// 1000, 1000, 1000,
_sensorSpecifications.GPSVelocityStdDev.X,
_sensorSpecifications.GPSVelocityStdDev.Y,
_sensorSpecifications.GPSVelocityStdDev.Z,
});
I = Matrix.Identity(n, n);
_zeroMM = Matrix.Zeros(m);
_rand = new GaussianRandom();
_prevEstimate = GetInitialEstimate(X0, PostX0, PostP0);
}
/// <summary>LU Decomposition</summary>
/// <param name="A"> Rectangular matrix
/// </param>
/// <returns> Structure to access L, U and piv.
/// </returns>
public LUDecomposition(Matrix A)
{
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
LU = (Matrix)A.Clone();
piv = new int[m];
for (int i = 0; i < m; i++)
{
piv[i] = i;
}
pivsign = 1;
//double[] LUrowi;
double[] LUcolj = new double[m];
// Outer loop.
for (int j = 0; j < n; j++)
{
// Make a copy of the j-th column to localize references.
for (int i = 0; i < m; i++)
{
LUcolj[i] = LU[i, j];
}
// Apply previous transformations.
for (int i = 0; i < m; i++)
{
//LUrowi = LU[i];
// Most of the time is spent in the following dot product.
int kmax = System.Math.Min(i, j);
double s = 0.0;
for (int k = 0; k < kmax; k++)
{
s += LU[i, k] * LUcolj[k];
}
LU[i, j] = LUcolj[i] -= s;
}
// Find pivot and exchange if necessary.
int p = j;
for (int i = j + 1; i < m; i++)
{
if (System.Math.Abs(LUcolj[i]) > System.Math.Abs(LUcolj[p]))
{
p = i;
}
}
if (p != j)
{
for (int k = 0; k < n; k++)
{
double t = LU[p, k]; LU[p, k] = LU[j, k]; LU[j, k] = t;
}
int k2 = piv[p]; piv[p] = piv[j]; piv[j] = k2;
pivsign = -pivsign;
}
// Compute multipliers.
if (j < m & LU[j, j] != 0.0)
{
for (int i = j + 1; i < m; i++)
{
LU[i, j] /= LU[j, j];
}
}
}
}
public GPSFilter2D(GPSObservation startState)
{
X0 = Matrix.Create(new double[n, 1]
{
{ startState.Position.X }, { startState.Position.Y }, { startState.Position.Z },
// Position
{ 0 }, { 0 }, { 0 }, // Velocity
{ 0 }, { 0 }, { 0 }, // Acceleration
});
PostX0 = X0.Clone();
/* Matrix.Create(new double[n, 1]
* {
* {startState.Position.X}, {startState.Position.Y}, {startState.Position.Z}, // Position
* {1}, {0}, {0}, // Velocity
* {0}, {1}, {0}, // Acceleration
* });*/
// Start by assuming no covariance between states, meaning position, velocity, acceleration and their three XYZ components
// have no correlation and behave independently. This not entirely true.
PostP0 = Matrix.Identity(n, n);
// Refs:
// http://www.romdas.com/technical/gps/gps-acc.htm
// http://www.sparkfun.com/datasheets/GPS/FV-M8_Spec.pdf
// http://onlinestatbook.com/java/normalshade.html
// Assuming GPS Sensor: FV-M8
// Cold start: 41s
// Hot start: 1s
// Position precision: 3.3m CEP (horizontal circle, half the points within this radius centred on truth)
// Position precision (DGPS): 2.6m CEP
// const float coVarQ = ;
// _r = covarianceR;
// Determine standard deviation of estimated process and observation noise variance
// Position process noise
_stdDevW = Vector.Zeros(n); //(float)Math.Sqrt(_q);
_rand = new GaussianRandom();
// Circle Error Probable (50% of the values are within this radius)
// const float cep = 3.3f;
// GPS position observation noise by standard deviation [meters]
// Assume gaussian distribution, 2.45 x CEP is approx. 2dRMS (95%)
// ref: http://www.gmat.unsw.edu.au/snap/gps/gps_survey/chap2/243.htm
// Found empirically by http://onlinestatbook.com/java/normalshade.html
// using area=0.5 and limits +- 3.3 meters
_stdDevV = new Vector(new double[m]
{
0,
ObservationNoiseStdDevY,
0,
// 0,
// 0,
// 0,
// 0,
// 0,
// 0,
// 0,
});
//Vector.Zeros(Observations);
//2, 2, 4.8926f);
H = Matrix.Identity(m, n);
I = Matrix.Identity(n, n);
Q = new Matrix(n, n);
R = Matrix.Identity(m, m);
_prevEstimate = GetInitialEstimate(X0, PostX0, PostP0);
}
/// <summary>Construct the singular value decomposition.</summary>
/// <remarks>Provides access to U, S and V.</remarks>
/// <param name="Arg">Rectangular matrix</param>
public SingularValueDecomposition(Matrix Arg)
{
transpose = (Arg.RowCount < Arg.ColumnCount);
// Derived from LINPACK code.
// Initialize.
Matrix A = (Matrix)Arg.Clone();
if (transpose)
{
A.Transpose();
}
m = A.RowCount;
n = A.ColumnCount;
int nu = System.Math.Min(m, n);
s = new double[System.Math.Min(m + 1, n)];
U = new Matrix(m, nu);
V = new Matrix(n, n);
double[] e = new double[n];
double[] work = new double[m];
bool wantu = true;
bool wantv = true;
// Reduce A to bidiagonal form, storing the diagonal elements
// in s and the super-diagonal elements in e.
int nct = System.Math.Min(m - 1, n);
int nrt = System.Math.Max(0, System.Math.Min(n - 2, m));
for (int k = 0; k < System.Math.Max(nct, nrt); k++)
{
if (k < nct)
{
// Compute the transformation for the k-th column and
// place the k-th diagonal in s[k].
// Compute 2-norm of k-th column without under/overflow.
s[k] = 0;
for (int i = k; i < m; i++)
{
s[k] = Fn.Hypot(s[k], A[i, k]);
}
if (s[k] != 0.0)
{
if (A[k, k] < 0.0)
{
s[k] = -s[k];
}
for (int i = k; i < m; i++)
{
A[i, k] /= s[k];
}
A[k, k] += 1.0;
}
s[k] = -s[k];
}
for (int j = k + 1; j < n; j++)
{
if ((k < nct) & (s[k] != 0.0))
{
// Apply the transformation.
double t = 0;
for (int i = k; i < m; i++)
{
t += A[i, k] * A[i, j];
}
t = (-t) / A[k, k];
for (int i = k; i < m; i++)
{
A[i, j] += t * A[i, k];
}
}
// Place the k-th row of A into e for the
// subsequent calculation of the row transformation.
e[j] = A[k, j];
}
if (wantu & (k < nct))
{
// Place the transformation in U for subsequent back
// multiplication.
for (int i = k; i < m; i++)
{
U[i, k] = A[i, k];
}
}
if (k < nrt)
{
// Compute the k-th row transformation and place the
// k-th super-diagonal in e[k].
// Compute 2-norm without under/overflow.
e[k] = 0;
for (int i = k + 1; i < n; i++)
{
e[k] = Fn.Hypot(e[k], e[i]);
}
if (e[k] != 0.0)
{
if (e[k + 1] < 0.0)
{
e[k] = -e[k];
}
for (int i = k + 1; i < n; i++)
{
e[i] /= e[k];
}
e[k + 1] += 1.0;
}
e[k] = -e[k];
if ((k + 1 < m) & (e[k] != 0.0))
{
// Apply the transformation.
for (int i = k + 1; i < m; i++)
{
work[i] = 0.0;
}
for (int j = k + 1; j < n; j++)
{
for (int i = k + 1; i < m; i++)
{
work[i] += e[j] * A[i, j];
}
}
for (int j = k + 1; j < n; j++)
{
double t = (-e[j]) / e[k + 1];
for (int i = k + 1; i < m; i++)
{
A[i, j] += t * work[i];
}
}
}
if (wantv)
{
// Place the transformation in V for subsequent
// back multiplication.
for (int i = k + 1; i < n; i++)
{
V[i, k] = e[i];
}
}
}
}
// Set up the final bidiagonal matrix or order p.
int p = System.Math.Min(n, m + 1);
if (nct < n)
{
s[nct] = A[nct, nct];
}
if (m < p)
{
s[p - 1] = 0.0;
}
if (nrt + 1 < p)
{
e[nrt] = A[nrt, p - 1];
}
e[p - 1] = 0.0;
// If required, generate U.
if (wantu)
{
for (int j = nct; j < nu; j++)
{
for (int i = 0; i < m; i++)
{
U[i, j] = 0.0;
}
U[j, j] = 1.0;
}
for (int k = nct - 1; k >= 0; k--)
{
if (s[k] != 0.0)
{
for (int j = k + 1; j < nu; j++)
{
double t = 0;
for (int i = k; i < m; i++)
{
t += U[i, k] * U[i, j];
}
t = (-t) / U[k, k];
for (int i = k; i < m; i++)
{
U[i, j] += t * U[i, k];
}
}
for (int i = k; i < m; i++)
{
U[i, k] = -U[i, k];
}
U[k, k] = 1.0 + U[k, k];
for (int i = 0; i < k - 1; i++)
{
U[i, k] = 0.0;
}
}
else
{
for (int i = 0; i < m; i++)
{
U[i, k] = 0.0;
}
U[k, k] = 1.0;
}
}
}
// If required, generate V.
if (wantv)
{
for (int k = n - 1; k >= 0; k--)
{
if ((k < nrt) & (e[k] != 0.0))
{
for (int j = k + 1; j < nu; j++)
{
double t = 0;
for (int i = k + 1; i < n; i++)
{
t += V[i, k] * V[i, j];
}
t = (-t) / V[k + 1, k];
for (int i = k + 1; i < n; i++)
{
V[i, j] += t * V[i, k];
}
}
}
for (int i = 0; i < n; i++)
{
V[i, k] = 0.0;
}
V[k, k] = 1.0;
}
}
// Main iteration loop for the singular values.
int pp = p - 1;
int iter = 0;
double eps = System.Math.Pow(2.0, -52.0);
while (p > 0)
{
int k, kase;
// Here is where a test for too many iterations would go.
// This section of the program inspects for
// negligible elements in the s and e arrays. On
// completion the variables kase and k are set as follows.
// kase = 1 if s(p) and e[k-1] are negligible and k<p
// kase = 2 if s(k) is negligible and k<p
// kase = 3 if e[k-1] is negligible, k<p, and
// s(k), ..., s(p) are not negligible (qr step).
// kase = 4 if e(p-1) is negligible (convergence).
for (k = p - 2; k >= -1; k--)
{
if (k == -1)
{
break;
}
if (System.Math.Abs(e[k]) <= eps * (System.Math.Abs(s[k]) + System.Math.Abs(s[k + 1])))
{
e[k] = 0.0;
break;
}
}
if (k == p - 2)
{
kase = 4;
}
else
{
int ks;
for (ks = p - 1; ks >= k; ks--)
{
if (ks == k)
{
break;
}
double t = (ks != p?System.Math.Abs(e[ks]):0.0) + (ks != k + 1?System.Math.Abs(e[ks - 1]):0.0);
if (System.Math.Abs(s[ks]) <= eps * t)
{
s[ks] = 0.0;
break;
}
}
if (ks == k)
{
kase = 3;
}
else if (ks == p - 1)
{
kase = 1;
}
else
{
kase = 2;
k = ks;
}
}
k++;
// Perform the task indicated by kase.
switch (kase)
{
// Deflate negligible s(p).
case 1:
{
double f = e[p - 2];
e[p - 2] = 0.0;
for (int j = p - 2; j >= k; j--)
{
double t = Fn.Hypot(s[j], f);
double cs = s[j] / t;
double sn = f / t;
s[j] = t;
if (j != k)
{
f = (-sn) * e[j - 1];
e[j - 1] = cs * e[j - 1];
}
if (wantv)
{
for (int i = 0; i < n; i++)
{
t = cs * V[i, j] + sn * V[i, p - 1];
V[i, p - 1] = (-sn) * V[i, j] + cs * V[i, p - 1];
V[i, j] = t;
}
}
}
}
break;
// Split at negligible s(k).
case 2:
{
double f = e[k - 1];
e[k - 1] = 0.0;
for (int j = k; j < p; j++)
{
double t = Fn.Hypot(s[j], f);
double cs = s[j] / t;
double sn = f / t;
s[j] = t;
f = (-sn) * e[j];
e[j] = cs * e[j];
if (wantu)
{
for (int i = 0; i < m; i++)
{
t = cs * U[i, j] + sn * U[i, k - 1];
U[i, k - 1] = (-sn) * U[i, j] + cs * U[i, k - 1];
U[i, j] = t;
}
}
}
}
break;
// Perform one qr step.
case 3:
{
// Calculate the shift.
double scale = System.Math.Max(System.Math.Max(System.Math.Max(System.Math.Max(System.Math.Abs(s[p - 1]), System.Math.Abs(s[p - 2])), System.Math.Abs(e[p - 2])), System.Math.Abs(s[k])), System.Math.Abs(e[k]));
double sp = s[p - 1] / scale;
double spm1 = s[p - 2] / scale;
double epm1 = e[p - 2] / scale;
double sk = s[k] / scale;
double ek = e[k] / scale;
double b = ((spm1 + sp) * (spm1 - sp) + epm1 * epm1) / 2.0;
double c = (sp * epm1) * (sp * epm1);
double shift = 0.0;
if ((b != 0.0) | (c != 0.0))
{
shift = System.Math.Sqrt(b * b + c);
if (b < 0.0)
{
shift = -shift;
}
shift = c / (b + shift);
}
double f = (sk + sp) * (sk - sp) + shift;
double g = sk * ek;
// Chase zeros.
for (int j = k; j < p - 1; j++)
{
double t = Fn.Hypot(f, g);
double cs = f / t;
double sn = g / t;
if (j != k)
{
e[j - 1] = t;
}
f = cs * s[j] + sn * e[j];
e[j] = cs * e[j] - sn * s[j];
g = sn * s[j + 1];
s[j + 1] = cs * s[j + 1];
if (wantv)
{
for (int i = 0; i < n; i++)
{
t = cs * V[i, j] + sn * V[i, j + 1];
V[i, j + 1] = (-sn) * V[i, j] + cs * V[i, j + 1];
V[i, j] = t;
}
}
t = Fn.Hypot(f, g);
cs = f / t;
sn = g / t;
s[j] = t;
f = cs * e[j] + sn * s[j + 1];
s[j + 1] = (-sn) * e[j] + cs * s[j + 1];
g = sn * e[j + 1];
e[j + 1] = cs * e[j + 1];
if (wantu && (j < m - 1))
{
for (int i = 0; i < m; i++)
{
t = cs * U[i, j] + sn * U[i, j + 1];
U[i, j + 1] = (-sn) * U[i, j] + cs * U[i, j + 1];
U[i, j] = t;
}
}
}
e[p - 2] = f;
iter = iter + 1;
}
break;
// Convergence.
case 4:
{
// Make the singular values positive.
if (s[k] <= 0.0)
{
s[k] = (s[k] < 0.0?-s[k]:0.0);
if (wantv)
{
for (int i = 0; i <= pp; i++)
{
V[i, k] = -V[i, k];
}
}
}
// Order the singular values.
while (k < pp)
{
if (s[k] >= s[k + 1])
{
break;
}
double t = s[k];
s[k] = s[k + 1];
s[k + 1] = t;
if (wantv && (k < n - 1))
{
for (int i = 0; i < n; i++)
{
t = V[i, k + 1]; V[i, k + 1] = V[i, k]; V[i, k] = t;
}
}
if (wantu && (k < m - 1))
{
for (int i = 0; i < m; i++)
{
t = U[i, k + 1]; U[i, k + 1] = U[i, k]; U[i, k] = t;
}
}
k++;
}
iter = 0;
p--;
}
break;
}
}
// (vermorel) transposing the results if needed
if (transpose)
{
// swaping U and V
Matrix T = V;
V = U;
U = T;
}
}
LUDecomposition(
Matrix A
)
{
// TODO: it is usually considered as a poor practice to execute algorithms within a constructor.
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
LU = A.Clone();
_rowCount = A.RowCount;
_columnCount = A.ColumnCount;
piv = new int[_rowCount];
for (int i = 0; i < _rowCount; i++)
{
piv[i] = i;
}
pivsign = 1;
//double[] LUrowi;
double[] LUcolj = new double[_rowCount];
// Outer loop.
for (int j = 0; j < _columnCount; j++)
{
// Make a copy of the j-th column to localize references.
for (int i = 0; i < LUcolj.Length; i++)
{
LUcolj[i] = LU[i][j];
}
// Apply previous transformations.
for (int i = 0; i < LUcolj.Length; i++)
{
//LUrowi = LU[i];
// Most of the time is spent in the following dot product.
int kmax = Math.Min(i, j);
double s = 0.0;
for (int k = 0; k < kmax; k++)
{
s += LU[i][k] * LUcolj[k];
}
LU[i][j] = LUcolj[i] -= s;
}
// Find pivot and exchange if necessary.
int p = j;
for (int i = j + 1; i < LUcolj.Length; i++)
{
if (Math.Abs(LUcolj[i]) > Math.Abs(LUcolj[p]))
{
p = i;
}
}
if (p != j)
{
for (int k = 0; k < _columnCount; k++)
{
double t = LU[p][k]; LU[p][k] = LU[j][k]; LU[j][k] = t;
}
int k2 = piv[p]; piv[p] = piv[j]; piv[j] = k2;
pivsign = -pivsign;
}
// Compute multipliers.
if ((j < _rowCount) && (LU[j][j] != 0.0))
{
for (int i = j + 1; i < _rowCount; i++)
{
LU[i][j] /= LU[j][j];
}
}
}
InitOnDemandComputations();
}
public GPSFilter2D(GPSObservation startState)
{
X0 = Matrix.Create(new double[n,1]
{
{startState.Position.X}, {startState.Position.Y}, {startState.Position.Z},
// Position
{0}, {0}, {0}, // Velocity
{0}, {0}, {0}, // Acceleration
});
PostX0 = X0.Clone();
/* Matrix.Create(new double[n, 1]
{
{startState.Position.X}, {startState.Position.Y}, {startState.Position.Z}, // Position
{1}, {0}, {0}, // Velocity
{0}, {1}, {0}, // Acceleration
});*/
// Start by assuming no covariance between states, meaning position, velocity, acceleration and their three XYZ components
// have no correlation and behave independently. This not entirely true.
PostP0 = Matrix.Identity(n, n);
// Refs:
// http://www.romdas.com/technical/gps/gps-acc.htm
// http://www.sparkfun.com/datasheets/GPS/FV-M8_Spec.pdf
// http://onlinestatbook.com/java/normalshade.html
// Assuming GPS Sensor: FV-M8
// Cold start: 41s
// Hot start: 1s
// Position precision: 3.3m CEP (horizontal circle, half the points within this radius centred on truth)
// Position precision (DGPS): 2.6m CEP
// const float coVarQ = ;
// _r = covarianceR;
// Determine standard deviation of estimated process and observation noise variance
// Position process noise
_stdDevW = Vector.Zeros(n); //(float)Math.Sqrt(_q);
_rand = new GaussianRandom();
// Circle Error Probable (50% of the values are within this radius)
// const float cep = 3.3f;
// GPS position observation noise by standard deviation [meters]
// Assume gaussian distribution, 2.45 x CEP is approx. 2dRMS (95%)
// ref: http://www.gmat.unsw.edu.au/snap/gps/gps_survey/chap2/243.htm
// Found empirically by http://onlinestatbook.com/java/normalshade.html
// using area=0.5 and limits +- 3.3 meters
_stdDevV = new Vector(new double[m]
{
0,
ObservationNoiseStdDevY,
0,
// 0,
// 0,
// 0,
// 0,
// 0,
// 0,
// 0,
});
//Vector.Zeros(Observations);
//2, 2, 4.8926f);
H = Matrix.Identity(m, n);
I = Matrix.Identity(n, n);
Q = new Matrix(n, n);
R = Matrix.Identity(m, m);
_prevEstimate = GetInitialEstimate(X0, PostX0, PostP0);
}
LUDecomposition(Matrix a)
{
/* TODO: it is usually considered as a poor practice to execute algorithms within a constructor */
/* Use a "left-looking", dot-product, Crout/Doolittle algorithm. */
_lu = a.Clone();
_rowCount = a.RowCount;
_columnCount = a.ColumnCount;
_pivot = new int[_rowCount];
for (int i = 0; i < _rowCount; i++)
{
_pivot[i] = i;
}
_pivotSign = 1;
////double[] LUrowi;
double[] LUcolj = new double[_rowCount];
/* Outer loop */
for (int j = 0; j < _columnCount; j++)
{
/* Make a copy of the j-th column to localize references */
for (int i = 0; i < LUcolj.Length; i++)
{
LUcolj[i] = _lu[i][j];
}
/* Apply previous transformations */
for (int i = 0; i < LUcolj.Length; i++)
{
////LUrowi = LU[i];
/* Most of the time is spent in the following dot product */
int kmax = Math.Min(i, j);
double s = 0.0;
for (int k = 0; k < kmax; k++)
{
s += _lu[i][k] * LUcolj[k];
}
_lu[i][j] = LUcolj[i] -= s;
}
/* Find pivot and exchange if necessary */
int p = j;
for (int i = j + 1; i < LUcolj.Length; i++)
{
if (Math.Abs(LUcolj[i]) > Math.Abs(LUcolj[p]))
{
p = i;
}
}
if (p != j)
{
for (int k = 0; k < _columnCount; k++)
{
double t = _lu[p][k];
_lu[p][k] = _lu[j][k];
_lu[j][k] = t;
}
int k2 = _pivot[p];
_pivot[p] = _pivot[j];
_pivot[j] = k2;
_pivotSign = -_pivotSign;
}
/* Compute multipliers */
if ((j < _rowCount) && (_lu[j][j] != 0.0))
{
for (int i = j + 1; i < _rowCount; i++)
{
_lu[i][j] /= _lu[j][j];
}
}
}
InitOnDemandComputations();
}
