Hidden Markov models with states depending on observations

In the standard hidden Markov model, the current state depends only on the immediately preceding state, but has nothing to do with the immediately preceding observation. This paper presents a new type of hidden Markov models in which the current state depends both on the immediately preceding state and the immediately preceding observation, and the state sequence is still a Markov chain. Several new algorithms are given and simulated for the three basic problems of interest, including probability evaluation, optimal state sequence and parameter estimation. One example of its initial applications shows that the new model may outperform the standard model in some circumstance.