Informatics and Applications2019, Volume 13, Issue 4, pp 68-75
NUMERICAL SCHEMES OF MARKOV JUMP PROCESS FILTERING GIVEN DISCRETIZED OBSERVATIONS I: ACCURACY CHARACTERISTICS
AbstractThe note is the initial in the series of the papers devoted to the numerical realization of the optimal state filtering of Markov jump processes given the indirect observations corrupted by the additive and/or multiplicative Wiener noises. This problem is solved by the time discretization of the observations with their subsequent processing.
Both the optimal and suboptimal estimations are expressed in terms of multiple integrals of the Gaussian densities with some mixing distributions. In the article, the author presents the investigation of various numerical integration schemes' influence on the accuracy of the approximating estimates. The problem turns into the characterization of distance between stochastic sequences generated by some recursions. The paper introduces a pseudometric describing the distance and presents a proposition determining the influence ofthe characteristic on both the local and global accuracy ofthe filtering estimate approximation.
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TitleNUMERICAL SCHEMES OF MARKOV JUMP PROCESS FILTERING GIVEN DISCRETIZED OBSERVATIONS I: ACCURACY CHARACTERISTICS
JournalInformatics and Applications
2019, Volume 13, Issue 4, pp 68-75
PublisherInstitute of Informatics Problems, Russian Academy of Sciences
Key wordsMarkov jump process; optimal filtering; additive and multiplicative observation noises; stochastic differential equation; analytical and numerical approximation
AuthorsA. V. Borisov
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