Synthesis and analysis of an optimal filtering algorithm for discrete signals with anomalous noise

The paper examines the synthesis of a nonbiased filter which is optimal in the rms sense in the class of linear filters. The synthesis is carried out for the case of the reception of a multidimensional Gaussian Markovian signal on a background of a mixture of constant Gaussian noise and anomalous noise with a partial known a priori description. The synthesized filter is shown to be invariant to the matrix of anomalous-noise intensity. The optimality of a procedure for the exclusion of anomalous observations is demonstrated for a particular case.