What question did this study set out to answer?

This study aims to derive a solution for optimal state filtering and evaluate the robustness of the filtering algorithm.

June 15, 2026

Numerical Analysis of the Robustness of State Filtering Estimation for Special Markov Jump Processes

Key Points

This study aims to derive a solution for optimal state filtering and evaluate the robustness of the filtering algorithm.
Application of a modified Kushner-Stratonovich equation for state filtering.
Development of a numerical implementation algorithm for the proposed solution.
Analysis of a case involving a network channel monitoring system.
The proposed filtering algorithm successfully estimates hidden states with improved accuracy.
Systematic analysis shows that a priori uncertainty significantly impacts estimation accuracy.
Numerical results indicate the robustness of the filtering method across varying probabilistic parameters.

Abstract

Abstract The subject of the present study is a class of nonlinear stochastic differential observation systems. The hidden state of such systems belongs to a class of special Markov jump processes. The observation set comprises both continuous and counting components. The purpose of this paper is twofold. First, it addresses the problem of optimal state filtering based on the available observations. A theoretical solution to this problem is derived in the form of a modified Kushner–Stratonovich equation, and a corresponding algorithm for its numerical implementation is proposed. Second, the robustness of the proposed filtering algorithm is studied. Using a practical case study involving the monitoring of the qualitative condition and quantitative characteristics of a network channel, the impact of a priori uncertainty in the probabilistic parameters of the channel on the estimation accuracy is systematically analyzed.

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