FDD with Hidden Markov Models

Hidden Markov models provide a modeling framework when the state of a system can be inferred from some measured variables (observations) without direct knowledge of the state variables. It is a double stochastic process in the sense that both the observations and the states are stochastic [279, 484], The discussion focuses first on discrete-time Markov processes. Then, HMMs, their parameters, and the fundamental problems in developing an HMM are summarized. Finally, some applications are presented.

Discrete-Time Markov Processes

Consider a process that can be in any one of N distinct states S = {si, S2, • • • , Siv} at any time. The process state changes at regularly spaced times indexed by t, and the actual state at time t is denoted by qt. The evolving sequence of states are Q = {qi,q2, • ■ • ,qt} and qt belongs to one of the states in 5. A full probabilistic description of the process may necessitate specification of the current and some of the preceding states. A special case that is similar to state-space models requires only the immeCopyright © 2003 by Taylor & Francis Group, LLC

diate previous state. Called discrete-time, first order Markov chain, this special case is represented as P[qt — Sj|<7t-i = If the state transition probabilities from state i to state j are not time dependent

with the constraints

Was this article helpful?

0 0

Post a comment