Second Order Hidden Markov Models with States Depending on Observations

摘要

Second order hidden Markov models (HMMs) have been used for a long time in pattern recognition,especially in speech recognition.In the standard second order HMM,the probability of a transition between two states at time t depends on the states in which the process was at time t-1 and t2.but has nothing to do with the previous observation. This paper presents a new type of second order HMMs in which the probability of a transition between two states at timeot only depends the states at time t1 and t-2 but also depends on the previous observation,moreover,the observation symbol probability is not dependent only on current state but also on the previous state,and the state sequence is still a second order Markov chain.Several new algorithms are given for the three basic problems of interest,including probability evaluation,optimal state sequence and parameter estimation.