Two-time-scale Wonham filters

This paper is concerned with a two-time-scale approximation of Wonham filters. A main feature is that the underlying hidden Markov chain has a large state space. To reduce computational complexity, we develop two-time-scale approach. Under time scale separation, we divide the state space of the Markov chain into a number of groups such that the chain jumps rapidly within each group and switches occasionally from one group to another. Such structure yields a limit Wonham filter preserving the main features of the filtering process, but has a much smaller dimension and therefore is easier to compute. Using the limit filter enables us to develop efficient approximations for the filters for hidden Markov chains. One of the main advantages of our approach is the substantial reduction of dimensionality.