Informatics and Applications
2024, Volume 18, Issue 4, pp 10-18
FILTERING OF A CLASS OF MARKOV JUMP PROCESSES BY HETEROGENEOUS OBSERVATIONS WITH ADDITIVE NOISES
- A. V. Borisov
- Yu. N. Kurinov
- R. L. Smeliansky
Abstract
The paper is devoted to the optimal filtering problem of a class of Markov jump processes. The
estimated system state is a Markov jump process with a finite set of possible states representing the probabilistic
distributions. The available measurement information includes continuous and counting observations. The
continuous observation is a function of the system state corrupted by an independentWiener process. The counting
observation intensity also depends on the state. The filtering problem is to find the conditional mathematical
expectation of a scalar function of the state (a signal process) given the available observations. The required estimate
represents the solution to a system of the stochastic differential system. The paper also introduces an analog
of the Kushner–Stratonovich equation describing the temporal evolution of the state conditional distribution.
A numerical example illustrates the performance of the proposed filtering estimate. It presents the monitoring
of the quality state and numerical parameters of a communication channel given the oscillating observations of
round-trip time and the flow of the packet losses.
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[+] About this article
Title
FILTERING OF A CLASS OF MARKOV JUMP PROCESSES BY HETEROGENEOUS OBSERVATIONS WITH ADDITIVE NOISES
Journal
Informatics and Applications
2024, Volume 18, Issue 4, pp 10-18
Cover Date
2024-12-26
DOI
10.14357/19922264240402
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Markov jump process; stochastic differential observation system; observations with additive noises; Kushner–Stratonovich equation
Authors
A. V. Borisov  ,  , Yu. N. Kurinov , and R. L. Smeliansky
Author Affiliations
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
M. V. Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1,Moscow 119991, Russian Federation
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