Informatics and Applications
2020, Volume 14, Issue 2, pp 10-18
NUMERICAL SCHEMES OF MARKOV JUMP PROCESS FILTERING GIVEN DISCRETIZED OBSERVATIONS III: MULTIPLICATIVE NOISES CASE
Abstract
The paper presents the final part of investigations initialized in the papers Borisov, A. 2019. Numerical schemes of Markov jump process filtering given discretized observations I: Accuracy characteristics. Inform. Appl. 13(4):68-75 and Borisov, A. 2020. Numerical schemes of Markov jump process filtering given discretized observations II: Multiplicative noises case. Inform. Appl. 14(1):17-23. Relying on the theoretical results, this paper presents a numerical algorithm of the state filtering of homogeneous Markov jump processes (MJP) given indirect noisy continuous time observations discretized by time. The class of observation systems under consideration is restricted by ones with multiplicative noises: any additive payload component is absent in the observable signal, but the observation noise intensity is a function of the MJP state under estimation. To calculate the integrals in the estimate, the author uses the composite midpoint rule of the precision order 3, along with the composite midpoint rule for triangles of the precision order 4. The constructed numerical algorithms of filtering have the final precision of the orders 1 and 2.
[+] References (7)
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[+] About this article
Title
NUMERICAL SCHEMES OF MARKOV JUMP PROCESS FILTERING GIVEN DISCRETIZED OBSERVATIONS III: MULTIPLICATIVE NOISES CASE
Journal
Informatics and Applications
2020, Volume 14, Issue 2, pp 10-18
Cover Date
2020-06-30
DOI
10.14357/19922264200202
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Markov jump process; optimal filtering; additive and multiplicative observation noises; stochastic differential equation; analytical and numerical approximation
Authors
A. V. Borisov 
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
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