New finite-dimensional filters and smoothers for noisily observed Markov chains
Robert James Elliott · IEEE Transactions on Information Theory · 1993
New finite-dimensional filters and smoothers that are related to the Wonham filter of a noisily observed Markov chain are obtained. In particular, finite-dimensional, recursive filters and smoothers are given for the number of jumps from state i to state j, for the occupation time of state i, and for a stochastic integral related to the drift in the observations. These filters allow easy application of the EM algorithm for the estimation of the parameters of the Markov chain and observation process.>