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. 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.