/// <summary>
/// Solves the navigation problem by the range-difference method (nonlinear method).
/// </summary>
/// <param name="A">Matrix of vectors { X, Y, Z }</param>
/// <param name="T">Vector of time</param>
/// <returns>Vector { X, Y, Z }</returns>
/// <param name="eps">Epsilon (0, 1)</param>
private static double[] RDM4(double[][] A, double[] T, double eps = 1e-8)
{
// Params
int count = A.GetLength(0);
double[] V = new double[count];
double[][] B;
double[] F, S;
// Roots
for (int i = 0; i < maxIterations; i++)
{
// Ax = b
B = RDMS.Left(A, T, V);
F = RDMS.Right(A, T, V);
S = Vector.Solve(B, F);
V = Vector.Add(V, S);
// Stop point
if (RDMS.Convergence(S, eps))
{
break;
}
}
// Vector { X, Y, Z }
return(Vector.Resize(V, 3));
}
// **************************************************************
// ALGORITHMS
// **************************************************************
// * RDM implementation for 5 (or more) time-synchronized
// receivers by solving a linearized system of equations [1].
// --------------------------------------------------------------
// * RDM implementation for 2, 3 and 4 time-synchronized
// receivers by solving a nonlinear system of equations [2,3].
//
//
// **************************************************************
// REFERENCES
// **************************************************************
// [1] I.V. Grin, R.A. Ershov, O.A. Morozov, V.R. Fidelman -
// "Evaluation of radio source’s coordinates based on solution
// of linearized system of equations by range-difference method"
// --------------------------------------------------------------
// [2] V.B. Burdin, V.A. Tyurin, S.A. Tyurin, V.M. Asiryan -
// "The estimation of target positioning by means of the
// range-difference method"
// --------------------------------------------------------------
// [3] E.P. Voroshilin, M.V. Mironov, V.A. Gromov -
// "The estimation of radio source positioning by means of the
// range-difference method using the multiposition passive
// satellite system"
// **************************************************************
/// <summary>
/// Solves the navigation problem by the range-difference method (linear method).
/// </summary>
/// <param name="A">Matrix of vectors { X, Y, Z }</param>
/// <param name="T">Vector of time</param>
/// <returns>Vector { X, Y, Z }</returns>
private static double[] RDM5(double[][] A, double[] T)
{
// Roots
double[][] B = RDMS.Left(A, T);
double[] F = RDMS.Right(A, T);
double[] S = Vector.Solve(B, F);
// Vector { X, Y, Z }
return(Vector.Resize(S, 3));
}
