A hidden Markov model (HMM) encompasses a large class of stochastic process models and has been successfully applied to a number of scientific and engineering problems, including speech and other pattern recognition p...
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A hidden Markov model (HMM) encompasses a large class of stochastic process models and has been successfully applied to a number of scientific and engineering problems, including speech and other pattern recognition problems, and DNA sequence comparison. A hidden semi-Markov model (HSMM) is an extension of HMM, designed to remove the constant or geometric distributions of the state durations assumed in HMM. A larger class of practical problems can be appropriately modeled in the setting of HSMM. A major restriction is found, however, in both conventional HMM and HSMM, i.e., it is generally assumed that there exists at least one observation associated with every state that the hidden Markov chain takes on. We will remove this assumption and consider the following situations: (i) observation data may be missing for some intervals;and (ii) there are multiple observation streams that are not necessarily synchronous to each other and may have different "emission distributions" for the same state. We propose a new and computationally efficient forward-backward algorithm for HSMM with missing observations and multiple observation sequences. The required computational amount for the forward and backward variables is reduced to O(D), where D is the maximum allowed duration in a state. Finally, we will apply the extended HSMM to estimate the mobility model parameters for the Internet service provisioning in wireless networks. (C) 2002 Elsevier Science B.V. All rights reserved.
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