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Mean-Square Filtering Problem for Discrete Volterra Equations

Abstract The mean-square filtering problem for the discrete Volterra equations is a nontrivial task due to an enormous amount of operations required for the implementation of optimal filter. A difference equation of a moderate dimension is chosen as an approximate model for the original system. Then the reduced Kalman filter can be used as an approximate but efficient estimator. Using the duality theory of convex variational problems, a level of nonoptimality for the chosen filter is obtained. This level can be efficiently computed without exactly solving the full filtering problem.