EXACT ADAPTIVE FILTERS FOR MARKOV-CHAINS OBSERVED IN GAUSSIAN-NOISE

A discrete time, finite state Markov chain is observed through a real or vector valued function whose values are corrupted by Gaussian noise. By introducing a new measure exact, unnormalized, recursive estimates and smoothers are obtained for the state of the Markov chain, for the number of jumps from one state to another, for the occupation time in any state, and for processes related to the observation parameters. Using the EM algorithm these allow estimates of all the parameters of the model to be revised, including the variance of the Gaussian noise in the observations. The filters are, therefore, adaptive or ''self-tuning''.