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(); }