Extended Viterbi Algorithm for Hidden Markov Process: A Transient/Steady Probabilities Approach

In this paper an extended Viterbi algorithm is presented for first-order hidden Markov processes, with the help of a dummy combined state sequence. For this, the Markov switching’s transient probabilities and steady probabilities are studied separately. The algorithm gives a maximum likelihood estimate for the state sequence of a hidden Markov process. Comparing with the standard Viterbi algorithm, this method gives a higher maximum likelihood, and also picks up the state switching earlier, which is particularly important for the out of sample applications. The theory of this method is discussed in this paper and then a sample of a series of experiment is presented to illustrate the theory. A quantitative comparison is also given between this method and the standard Viterbi algorithm.