Optimal Filtering of Markov Jump Processes Given Observations with State-Dependent Noises: Exact Solution and Stable Numerical Schemesстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 7 июля 2020 г.
Аннотация:The paper is devoted to the optimal state filtering of the finite-state Markov jump processes,given indirect continuous-time observations corrupted by Wiener noise. The crucial feature isthat the observation noise intensity is a function of the estimated state, which breaks forthrightfiltering approaches based on the passage to the innovation process and Girsanov’s measure change.We propose an equivalent observation transform, which allows usage of the classical nonlinearfiltering framework. We obtain the optimal estimate as a solution to the discrete–continuous stochasticdifferential system with both continuous and counting processes on the right-hand side. For effectivecomputer realization, we present a new class of numerical algorithms based on the exact solution tothe optimal filtering given the time-discretized observation. The proposed estimate approximationsare stable, i.e., have non-negative components and satisfy the normalization condition. We provethe assertions characterizing the approximation accuracy depending on the observation systemparameters, time discretization step, the maximal number of allowed state transitions, and the appliedscheme of numerical integration.