Informatics and Applications
2021, Volume 15, Issue 2, pp 12-19
FILTERING OF MARKOV JUMP PROCESSES GIVEN COMPOSITE OBSERVATIONS I: EXACT SOLUTION
- A. V. Borisov
- D. Kh. Kazanchyan
Abstract
The first part of the series is devoted to the optimal filtering of the finite-state Markov jump processes (MJP) given the ensemble of the diffusion and counting observations. The noise intensity in the observable diffusion depends on the estimated MJP state. The special equivalent observation transformation converts them into the collection of the diffusion process of unit intensity, counting processes, and indirect measurements performed at some nonrandom discrete instants. The considered filtering estimate is expressed as a solution to the discrete-continuous stochastic differential system with the transformed observations on the right-hand side. The identifiability condition, under which MJP state can be reconstructed from indirect noisy observations precisely, is presented.
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[+] About this article
Title
FILTERING OF MARKOV JUMP PROCESSES GIVEN COMPOSITE OBSERVATIONS I: EXACT SOLUTION
Journal
Informatics and Applications
2021, Volume 15, Issue 2, pp 12-19
Cover Date
2021-06-30
DOI
10.14357/19922264210202
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Markov jump process; optimal filtering; multiplicative observation noises; stochastic differential equation; continuous and counting observations; identifiability condition
Authors
A. V. Borisov  ,  ,  ,  and D. Kh. Kazanchyan
Author Affiliations
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Moscow Aviation Institute (National Research University), 4 Volokolamskoe Shosse, Moscow 125080, Russian Federation
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
Moscow Center for Fundamental and Applied Mathematics, M.V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
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