Conditions for Existence of Second-Order and Third-Order Filters for Discrete Systems with Additive Noises

Mikhail Kamenshchikov
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Mikhail Kamenshchikov: Department of Nonlinear Dynamical Systems and Control Processes, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia

Mathematics, 2022, vol. 10, issue 3, 1-12

Abstract: The problem of constructing functional optimal observers (filters) for stochastic control systems with additive noises in discrete time are studied in this work. Under the assumption that there is no filter of the first order, necessary and sufficient conditions for the existence of filters of the second and third order are obtained in the canonical basis. Analytical expressions of the transfer function matrix from the input noise to the estimation error are presented. A numerical example is given to compare the performance of filters by the quadratic criterion in the steady state.

Keywords: discrete time functional filter; optimal unbiased estimation; steady state (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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