Recurrent estimation of the observation parameters and covariances in multidimensional systems for covariances of a special structure (Q1882044)

This paper considers the problem of identification of a multidimensional discrete-time system described by a parameter matrix, provided that the components of the observation vector have unknown covariances. A procedure for recurrent recalculation of the optimal estimates of the system parameter matrix and unknown coefficients in the expansion of the covariance matrix of the output vector in the given basis upon the arrival of the current input-output pair is obtained. The estimates obtained here feature uniform optimality for all values of the unknown parameters. Recurrent formulas for simultaneous recalculation of the estimates of the parameter matrix and variance components are obtained.