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Bayesian Signal Processing: Classical, Modern and Particle Filtering Methods by James V. Candy

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9

DISCRETE HIDDEN MARKOV MODEL BAYESIAN PROCESSORS

9.1 INTRODUCTION

In this chapter we develop discrete (event) hidden Markov models. All of the Bayesian processors we have discussed are, in fact, hidden Markov processors, since the internal states are usually not measured directly and are therefore “hidden” by definition, but the distinguishing factor is the type of underlying process governing the sequence. In fact, the (state) transition matrix is a “probability” matrix with specific properties that distinguish it uniquely from other dynamic systems. These discrete representations of stochastic processes find enormous application in the speech, economics, biomedical, communications and music areas where coding approaches are prevalent. We discuss the development of the basic processor and investigate a case study in communications to demonstrate the design and application.

9.2 HIDDEN MARKOV MODELS

A discrete-time hidden Markov model (HMM) is a stochastic representation (model) of a process that can be used for simulation, modeling and estimation much the same as the state–space model is used for dynamic (physical) systems. These models are prevalent in acoustics, biosciences, climatology, control, communications, econometrics, text recognition, image processing, signal processing and speech processing [1]. Perhaps its distinguishing feature is that it is a “probabilistic model” in the sense that it is driven by internal probability distributions for both states and observations ...

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