Online identification of hidden Semi-Markov models

Abstract

Hidden Markov models (HMM) are a powerful tool in signal modelling. In an HMM, the probability that signal leaves a state is constant, and hence the duration that signal stays in each state has an exponential distribution. However, this exponential density is not appropriate for a large class of physical signals. Hence, a more sophisticated model, called hidden semiMarkov models (HSMM), are used where the state durations are modelled in some form. This paper presents new signal model for hidden semiMarkov models. This model is based on state duration dependant transition probabilities, where the state duration densities are modelled with parametric distribution functions. An adaptive algorithm for online identification of HSMMs based on our signal model is presented. This algorithm is based on the 'recursive prediction error' technique, where the parameter estimates are updated adaptively in a direction that maximizes the likelihood of parameter estimates. From the numerical results it is shown that the proposed algorithms can successfully estimate the true value of parameters. These results also show that our algorithm can adaptively track the parameter's changes in time.