Feedback particle filter for a continuous-time Markov chain

This paper concerns approximation of Wonham's filter for estimating a continuous-time Markov chain, with continuous measurements corrupted by noise. The approximation is a new manifestation of the feedback particle filter (FPF) [15], [14], [13], a control-oriented approach for nonlinear filtering. A complete characterization of the feedback mechanism that defines the FPF is obtained, which leads to tractable algorithms for the nonlinear filtering problem, even for large state spaces. Numerical examples illustrate the application of these techniques.