Algorithms of Third-Order Hidden Markov Model and Its Relationship with First-Order Hidden Markov Model

In order to consider more statistical characteristics,a class of third-order hidden Markov model is proposed.In this model,both state transition and output observation depend on the current state and on the two preceding states as well.Three algorithms of the third-order hidden Markov model are studied and derived,including the forward-backward algorithm for observation sequence evaluation,the Viterbi algorithm for determining the optimal state sequence,and the Baum-Welch algorithm for training the third-order hidden Markov model.A first-order hidden Markov model equivalent to the third-order hidden Markov model is constructed.A theorem of their equivalence is proposed and proved.This study contributes to the algorithmic theory of the hidden Markov model,and provides a better method to practical applications.