On adaptive HMM state estimation

New online adaptive hidden Markov model (HMM) state estimation schemes are developed, based on extended least squares (ELS) concepts and recursive prediction error (RPE) methods. The best of the new schemes exploit the idempotent nature of Markov chains and work with a least squares prediction error index, using a posterior estimates, more suited to Markov models than traditionally used in identification of linear systems. These new schemes learn the set of N Markov chain states, and the a posteriori probability of being in each of the states at each time instant. They are designed to achieve the strengths, in terms of computational effort and convergence rates, of each of the two classes of earlier proposed adaptive HMM schemes without the weaknesses of each in these areas. The computational effort is of order N. Implementation aspects of the proposed algorithms are discussed, and simulation studies are presented to illustrate convergence rates in comparison to earlier proposed online schemes