Adaptive non-linear time-series estimation based on hidden Markov models

摘要

In this paper we propose maximum-likelihood (ML) estimation schemes for the parameters and states of ARMAX systems when the input is a finite-state Markov chain. Such models have applications in econometrics, speech processing, communication systems and neuro-biological signal processing. We derive the ML model estimates using the expectation maximization (EM) algorithm. We then develop two sequential or "online" estimation schemes: Recursive EM algorithm and a gradient based scheme.