Quasicontinuous state hidden Markov models incorporating state histories

The Markovity assumed in conventional hidden Markov models (HMMs) does not necessarily match the statistical structure of many real signals, since many signals have long-term dependencies. In this paper, we generalize the concept of the HMM state to include the history of states or previous models leading to a state, while still limiting the number of basic states to a finite number. This expanded state is efficiently represented using real-numbered states, the fractional part representing the history. State sequence estimation is accomplished using an extension of the Viterbi algorithm. Parameters estimation for state transition probabilities and output distributions is presented.