On-line estimation and identification of HMMs with grouped state values

This paper presents a signal-processing scheme for the class of lumpable or weakly lumpable hidden Markov models (HMMs) which have state values clustered into groups. Attention is focused not only on state estimation for known models but also on on-line model identification. The approach taken employs a new technique whereby separate state estimators are used for each group of state values. The state estimator for each group estimates the discrete states in that group together with an associated flag state which represents all the other groups. The result is that the computational complexity is greatly reduced. Hidden Markov model parameters associated with lumpable or weakly lumpable Markov chains can be identified on-line using available techniques such as the recursive prediction error (RPE) approach taken in this paper. These techniques estimate the transition probabilities and discrete state values of the Markov chain on-line. Other parameters, such as the noise density associated with the observations, can also be identified.