Solution of Robust Stochastic Discrete Filtering Problem Based on Minimax Functional Criterion

Currently, the solution to the vast majority of problems of assessing the state of discrete stochastic systems operating in stochastic environments is carried out using algorithms developed on the basis of the discrete Kalman filter. The main disadvantage of such estimation schemes is the need for an accurate a priori description of the probabilistic characteristics of the noise of the object and the interference of its observer, the absence of which leads to divergence of the filtering process. All known modifications of the Kalman filtering scheme ensure the stability of the estimation process only for some special cases, leaving the problem of an a priori description of the operating conditions of real systems as a whole unresolved. In this regard, the paper considers an alternative approach to the synthesis of a stable (robust) stochastic estimation scheme based on the choice of a matrix filtering coefficient from the optimization condition of a minimax functional criterion determined by the most unfavorable class of probabilistic distributions noise of the object and its observer. An advantageous feature of the proposed filter, in addition to its robust properties, is a significantly smaller dimension compared to the Kalman scheme, equal to the dimension of the object, which sharply reduces the amount of computational costs in the practical implementation of the filter. The results of a numerical experiment illustrating the effectiveness of the considered approach are presented.