Implements the IKF-CG (Inverse Kalman Filter - Conjugate Gradient) algorithm for the one-interaction physical model with 1D output, different particle numbers for different time, and non-identity diagonal noise.
IKF_CG_particle_cell(param, kernel_type, delta_x_all, output, A_all_v,
sort_d_all_ix, sigma_2_vec, num_neighbors_vec,
tilde_nu, D, n_t_record, tol = 1e-6, maxIte = 1000)Returns a list containing:
A numeric vector of solved coefficients.
A numeric vector of residuals at each iteration.
An integer indicating the number of iterations performed.
A numeric vector containing model parameters. The first element is the log of beta (inverse range parameter), and the second element is the log of tau (variance ratio parameter).
A string specifying the covariance kernel type: "matern_5_2" or "exp".
A numeric vector of successive differences of sorted inputs.
A numeric vector of observations.
A numeric vector containing the non-zero entries in matrix A.
An integer vector of indices for sorting distances.
A numeric vector of variances for each time point.
An integer vector specifying number of neighbors for each observation.
A numeric value for numerical stabilization.
An integer specifying the dimension of observations.
An integer vector containing number of particles at each time point.
A numeric value specifying convergence tolerance (default: 1e-6).
An integer specifying maximum number of iterations (default: 1000).
Fang, X., & Gu, M. (2024). The inverse Kalman filter. arXiv:2407.10089.