Hidden Markov models

by Robert J. Elliott

The aim of this book is to present graduate students with a thorough survey of reference probability models and their applications to optimal estimation and control. These new and powerful methods are particularly useful in signal processing applications where signal models are only partially known and are in noisy environments. Well-known results, including Kalman filters and the Wonham filter, emerge as special cases. The authors begin with discrete time and discrete state spaces. From there, they proceed to cover continuous time, and progress from linear models to nonlinear models, and from completely known models to only partially known models. Readers are assumed to have a basic grounding in probability and systems theory, such as might be gained from the first year of graduate study, but otherwise this account is self-contained. Throughout, the authors have taken care to demonstrate engineering applications which show the usefulness of these methods.