Abstract
A Hidden Markov Model (HMM) is composed of two processes, a Markov chain whose evolution is hidden and an emission process that is observable. The resolution of fundamental problems in HMM is based on the computation of the probability of an observed emission sequence using all possible corresponding hidden sequences. In this paper, we assume that the Markov chain is not completely hidden and we know one or two states at fixed times during the evolution interval time. The obtained HMM is then partially hidden. Principally we interest to the computation of the probability of an observed emission sequence given that the Markov chain goes through one or two fixed states at fixed times. Mainly we resolve the likelihood and decoding problems by developing formulas for forward and backward probabilities and the related Viterbi algorithm, assuming that we have some precise information at fixed times. Numerical examples are studied to show the smooth running of the proposed partially HMM.
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