Filtering in Stochastic Systems: Analysis for the case of continuous observations with memory of arbitrary multiplicity

Abstract

We consider stochastic systems with continuous time over observations with memory in the presence of an anomalous noise. The paper is devoted to analysis of some properties of an optimal unbiased in mean-square sense filter. In the case of anomalous noises action in the observation channel with memory, we have proved insensitivity of the filter to inaccurate knowledge of the matrix of anomalous noise intensity and its equivalence to a truncated filter constructed only over non-anomalous components of an observation vector.