Estimation of the matrices of parameters and covariations of the perturbation vectors in multidimensional discrete-time dynamic systems under special structure of the unknown covariance matrices

For the multidimensional linear dynamic system obeying a difference equation with an unknown covariance matrix of the vector of random perturbations having dependent components, consideration was given to estimation of the matrix of system parameters and the covariance matrix represented by a linear combination of the given symmetrical matrices. The family of joint probability densities of the observation vector was factorized, and the sufficient statistics was determined. For the estimates of the maximum likelihood of the system parameter matrices and the estimates of the coefficients of expansion of the covariance matrix, equations were presented. Developed was a recurrent procedure for joint estimation of the system parameter matrices and the covariance matrix with arrival of observations.