Reformulating the HMM as a trajectory model by imposing explicit relationships between static and dynamic feature vector sequences

In the present paper, a trajectory model, derived from a hidden Markov model (HMM) by imposing explicit relationships between static and dynamic feature vector sequences, is developed and evaluated. The derived model, named a trajectory HMM, can alleviate two limitations of the standard HMM, which are (i) piece-wise constant statistics within a state and (ii) conditional independence assumption of state output probabilities, without increasing the number of model parameters. In the present paper, a Viterbi-type training algorithm based on the maximum likelihood criterion is also derived. The performance of the trajectory HMM was evaluated both in speech recognition and synthesis. In a speaker-dependent continuous speech recognition experiment, the trajectory HMM achieved an error reduction over the corresponding standard HMM. Subjective listening test results showed that the introduction of the trajectory HMM improved the naturalness of synthetic speech.