Wonham Filtering by Observations with Multiplicative Noises

We solve the optimal filtering problem for states of a homogeneous finite-state Markov jump process by indirect observations in the presence of Wiener noise. The key feature of this problem is that the noise intensities in observations depend on the unobserved state. The filtering estimate is repres...

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Bibliographic Details
Published in:	Automation and remote control Vol. 79; no. 1; pp. 39 - 50
Main Author:	Borisov, A. V.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 2018 Springer Nature B.V
Subjects:	CAE) and Design Calculus of Variations and Optimal Control; Optimization Computer-Aided Engineering (CAD Control Filtration Markov processes Martingales Mathematics Mathematics and Statistics Mechanical Engineering Mechatronics Robotics Systems Theory Topical Issue optimal nonlinear filtering right continuous filtration Markov jump process multiplicative noises in observations integral representation of a martingale
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Summary:	We solve the optimal filtering problem for states of a homogeneous finite-state Markov jump process by indirect observations in the presence of Wiener noise. The key feature of this problem is that the noise intensities in observations depend on the unobserved state. The filtering estimate is represented as a solution to some stochastic system with continuous and purely discontinuous martingales in the right-hand side. We discuss the theoretical results and present a numerical example that illustrates the properties of the obtained estimates.
ISSN:	0005-1179 1608-3032
DOI:	10.1134/S0005117918010046