An Optimal Recurrent Logical-Dynamical Filter of a High Order and Its Covariance Approximations

Abstract

The problem of logical recognition of the operating mode and dynamic estimation of the intra-mode state vector of a discrete-time stochastic Markov system with a random structure is considered. To develop an estimation algorithm implemented at the pace of system time on a computer of limited power, a method for designing a new finite-dimensional optimal structure filter is proposed. Its state vector consists of several latest estimates, and the current estimate is found in the form of an optimal-accuracy dependence on the last measurement and the vector of the previous filter state. The structural functions of the filter are designed in advance, which can be performed by the Monte Carlo method by obtaining their multivariate histograms. Due to the computational complexity of this procedure, algorithms are also proposed for constructing two numerical-analytical approximations of the filter, which take into account only the first two moments of random variables.

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Funding

This study was supported by the Russian Foundation for Basic Research, project no. 18-08-00128-a.

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Correspondence to E. A. Rudenko.

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Translated by A. Mazurov

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Rudenko, E.A. An Optimal Recurrent Logical-Dynamical Filter of a High Order and Its Covariance Approximations. J. Comput. Syst. Sci. Int. 59, 854–870 (2020). https://doi.org/10.1134/S1064230720060118

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