A new maximum likelihood gradient algorithm for on-line hidden Markov model identification

Abstract

This paper presents a new algorithm for on-line identification of hidden Markov model (HMM) parameters. The scheme is gradient based, and provides parameter estimates which recursively maximise the likelihood function. It is therefore a recursive maximum likelihood (RML) algorithm, and it has optimal asymptotic properties. The only current on-line HMM identification algorithm with anything other than suboptimal rate of convergence is based on a prediction error (PE) cost function. As well as presenting a new algorithm, this paper also highlights and explains a counter-intuitive convergence problem for the current recursive PE (RPE) algorithm, when operating in low noise conditions. Importantly, this problem does not exist for the new RML algorithm. Simulation studies demonstrate the superior performance of the new algorithm. compared to current techniques.