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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
A. Nemura and E. Klekis, Estimation of Parameters and States of Systems with Jump-like Varying Properties (Mokslas, Vil’nyus, 1988) [in Russian].
V. A. Bukhalev, Recognition, Estimation and Control in Systems with a Random Hopping Structure (Nauka, Moscow, 1996) [in Russian].
A. V. Borisov and A. I. Stefanovich, “Optimal state filtering of controllable systems with random structure,” J. Comput. Syst. Sci. Int. 46, 348 (2007).
A. Bain and D. Crisan, Fundamentals of Stochastic Filtering (Springer, New York, 2009).
A. V. Bosov and A. R. Pankov, “Conditionally minimax filtering in a system with switching observation channels,” Automation and Remote Control 56, 835–843 (1995).
E. A. Rudenko, “Analytical-numerical approximations of the optimal recurrent logical–dynamical low order filter-predictor,” J. Comput. Syst. Sci. Int. 54, 691 (2015).
E. A. Rudenko, “Finite-dimensional recurrent algorithms for optimal nonlinear logical–dynamical filtering,” J. Comput. Syst. Sci. Int. 55, 36 (2016).
E. A. Rudenko, “Optimal recurrent logical-dynamical finite memory filter,” J. Comput. Syst. Sci. Int. 56, 607 (2017).
I. A. Kudryavtseva, E. A. Rudenko, and K. A. Rybakov, “Software for optimal state estimation in stochastic dynamical systems,” Inform. Telekommun. Tekhnol., No. 43, 23–28 (2019).
A. P. Trifonov and Yu. S. Shinakov, Joint Discrimination of Signals and Assessment of their Parameters against the Background of Interference (Radio Svyaz’, Moscow, 1986) [in Russian].
V. S. Pugachev and I. N. Sinitsyn, Stochastic Systems Theory (Logos, Moscow, 2004) [in Russian].
A. N. Shiryaev, Probability (Nauka, Moscow, 1980) [in Russian].
E. A. Rudenko, “Optimal nonlinear recurrent finite memory filter,” J. Comput. Syst. Sci. Int. 57, 43 (2018).
E. A. Rudenko, “Autonomous path estimation for a descent vehicle using recursive gaussian filters,” J. Comput. Syst. Sci. Int. 57, 695 (2018).
Funding
This study was supported by the Russian Foundation for Basic Research, project no. 18-08-00128-a.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by A. Mazurov
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064230720060118