Discrete Hidden Markov Model Bayesian Processors
2016
This chapter introduces the concept of discrete hidden Markov model (HMM) and illustrates their internal characteristics through a state‐space representation. It develops the concepts of Markov and hidden Markov chains and shows how they were related. Next, the chapter investigates properties of the HMM illustrating how the Bayesian concepts easily transfer over to this discrete representation. It investigates the three fundamental problems along with some variations: (1) the evaluation (simulation) problem; (2) the state estimation problem; and (3) the parameter estimation problem. A careful analysis of each led us to the popular Viterbi decoding technique and the specialized expectation‐maximization (EM) algorithm popularly called the Baum‐Welch technique. The chapter concludes with a case study to decode a transmitted coded sequence from data enhanced by a time‐reversal (T/R) processor and also considers applying the Viterbi algorithm to decode a message transmitted through a hostile environment with reverberations along with the processor and decoding algorithm.