Abstract:

It is wel-l known that HMM has been widely used in many fields. In this paper we will discuss a more general model, which is similar to Pairwise Markov Model ( PMM) proposed by Wojciech Pieczynski. Compared to HMM, the state process here is not necessarily aMarkov chain. So it has more general applications in image segmentation, speech signal processing, and etc. We will give a complete mathemat ical description for this model with discrete states and discrete observations, including modeling,state estimation and parameter estimat ion, which haven. t been studied before. Based on the method proposed here, we will get a recursive algorithm for the estimation of the state and the parameters.

Key words: change of measure, recursive parameter est imation, recursive state estimation, General Hidden Markov Model ( GHMM)