ADAPTIVE ESTIMATION OF HMM TRANSITION-PROBABILITIES

This paper presents new schemes for recursive estimation of the stale transition probabilities for hidden Markov models (HMM's) via extended least squares (ELS) and recursive state prediction error (RSPE) metho ds. Local convergence analysis for the proposed RSPE algorithm is show n using the ordinary differential equation (ODE) approach developed fo r the more familiar recursive output prediction error (RPE) methods. T he presented scheme converges and is relatively well conditioned compa red with the previously proposed RPE scheme for estimating transition probabilities that perform poorly in low noise. The ELS algorithm pres ented in this paper is computationally of order N-2, which is less tha n the computational effort of order N-4 required to implement the RSPE (and previous RPE) scheme, where N is the number of Markov states. Bu ilding on earlier work, an algorithm for simultaneous estimation of th e state output mappings and the state transition probabilities that re quires less computational effort than earlier schemes is also presente d and discussed. Implementation aspects of the proposed algorithms are discussed, and simulation studies are prevented to illustrate converg ence and convergence rates.