Guaranteed root-mean-square estimates of the forecast of matrix observations under conditions of statistical uncertainty

We investigate the problem of linear estimation unknown mathematical expectations based on observations realizations random matrix sequences. Constructive methods have been developed for finding guaranteed RMS estimates non-stationary parameters average values It is shown that such are obtained either as solutions to boundary value problems systems differential equations or corresponding Cauchy problems. establish form and look errors quasi-minimax special forecast vector values. In presence small perturbations known matrices in model observations, found, their first approximation parameter method. Two test examples calculating root mean square given.