Stochastic calculus, non-linear filtering, and the internal model principle: implications for articulatory speech recognition

A stochastic approach to modelling speech production and perception is discussed, based on Itô calculus. Speech is modelled by a system of non-linear stochastic differential equations evolving on a finite-dimensional state space, representing a partiallyobserved Markov process. The optimal non-linear filtering equations for the model are stated, and shown to exhibit a predictorcorrector structure, which mimics the structure of the original system. This is used to suggest a possible justification for the hypothesis that speakers and listeners make use of an “internal model” in producing and perceiving speech, and leads to a useful statistical framework for articulatory speech recognition.