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Article

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

1
Department of Nonlinear Dynamical Systems and Control Processes, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia
2
Laboratory of Terminal Control Systems, V. A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 117997 Moscow, Russia
3
Department of Engineering Cybernetics, National University of Science and Technology «MISiS», 119049 Moscow, Russia
Academic Editor: Leonid Piterbarg
Mathematics 2022, 10(3), 370; https://doi.org/10.3390/math10030370
Received: 12 December 2021 / Revised: 20 January 2022 / Accepted: 22 January 2022 / Published: 25 January 2022
(This article belongs to the Special Issue Stability Problems for Stochastic Models: Theory and Applications II)
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. View Full-Text
Keywords: discrete time functional filter; optimal unbiased estimation; steady state discrete time functional filter; optimal unbiased estimation; steady state
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MDPI and ACS Style

Kamenshchikov, M. Conditions for Existence of Second-Order and Third-Order Filters for Discrete Systems with Additive Noises. Mathematics 2022, 10, 370. https://doi.org/10.3390/math10030370

AMA Style

Kamenshchikov M. Conditions for Existence of Second-Order and Third-Order Filters for Discrete Systems with Additive Noises. Mathematics. 2022; 10(3):370. https://doi.org/10.3390/math10030370

Chicago/Turabian Style

Kamenshchikov, Mikhail. 2022. "Conditions for Existence of Second-Order and Third-Order Filters for Discrete Systems with Additive Noises" Mathematics 10, no. 3: 370. https://doi.org/10.3390/math10030370

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