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Filtering Problem for Discrete Volterra Equations with Combined Disturbances

Abstract A minimax filtering problem for discrete Volterra equations with combined noise models is considered. The combined models are defined as the sums of uncertain bounded deterministic functions and stochastic white noises. However, the corresponding variational problem turns out to be very difficult for direct solution. Therefore, simplified filtering algorithms are developed. The levels of nonoptimality for these simplified algorithms are introduced as the ratios of the filtering performances for the simplified and optimal estimators. In opposite to the original variational problem, these levels can be easily evaluated numerically. Thus, simple filtering algorithms with guaranteed performance are obtained. Numerical experiments confirm the efficiency of our approach.