Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Analysis of Algorithms of Numerical Implementations for the Wonham Filter Under Uncertainty in Measurements Noise Covariance

Author(s):

Alexey Vyacheslavovich Bosov

Doctor of Science in Technology, Principal Scientist, Institute of Informatics Problems,
Federal Research Center В«Computer Science and ControlВ» of the Russian Academy of Sciences
44/2 Vavilova Str., 119333, Moscow, Russia

abosov@ipiran.ru

Irina Anatol'evna Kudryavtseva

Ph.D., Associate Professor of the Department of Mathematical Cybernetics of Moscow Aviation Institute
(national research university)
4, Volokolamskoe shosse, Moscow, 125993, Russia

kudryavtseva.irina.a@gmail.com

Abstract:

The paper addresses the filtering a continuous-time Markov chain states that can be observed through linear measurements perturbed by a Wiener process. There is supposed the presence of uncertainty in the intensity of measurements noises. The problem is worked out under the assumption of unknown intensity but subject to its known upper bound. If there is no uncertainty in measurements the optimal solution is provided by the Wonham filter that doesn't ensure stable numerical implementations. The paper exposes that the Wonham filter shows robustness in the presence of uncertainty if model's parameters don't imply its divergent. It is detected that to cope with divergence tracking and handling trajectories aren't sufficient in the case of uncertainty. The more efficient way is to consider discretized approximations of the Wonham filter implemented for a discrete model that approximates the initial continuous-time measurements system. Such an approach perceptibly advantages if numerical implementations contain divergent trajectories. If there are no divergent trajectories, then the discretized filters give a slightly worse result but acceptable.

Keywords

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