Abstract

The standard hidden Markov model (HMM) and the hidden filter model assume local or state-conditioned stationarity for the modeled signal. In this work we generalize these models and develop the ‘trended HMM’ to allow the local, as well as the global (via a Markov chain), non-stationarity to be represented in the model. The mathematical structure of the trended HMM can be described by a discrete-time Markov process with its states associated with distinct regression functions on time, or alternatively by a ‘deterministic trend plus stationary residual’ time series with its parameters governed by the evolution of a Markov chain. The EM algorithm is applied to obtain closed-form re-estimation formulas for the model parameters. Compared with the types of HMMs developed in the past, the trended HMM is a more faithful and more structured representation of many classes of speech sounds whose production involves strong articulatory dynamics. As such, it is expected to be a more suitable model for use in speech processing applications.