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Hidden Markov models (HMMs) are discrete-state, discrete-time, stochastic dynamical systems. They are often used to approximate systems with continuous state spaces operating in continuous time. In addition to introducing the basic ideas of HMMs and algorithms for using them, this book explains the derivations of the algorithms with enough supporting theory to enable readers to develop their own variants. The book also presents Kalman filtering as an extension of ideas from basic HMMs to models with continuous state spaces. Although applications of HMMs have become numerous (396,000 Google hits) since they emerged as the key technology for speech recognition in the 1980s, no introductory book on HMMs in general is available. This text aims to fill that gap. Hidden Markov Models and Dynamical Systems features illustrations that use the Lorenz system, laser data, and natural language data. The concluding chapter presents the application of HMMs to detecting sleep apnea in experimentally measured electrocardiograms. Algorithms are given in pseudocode in the text, and a working implementation of each algorithm is available on the accompanying website. Errata: https://archive.siam.org/books/ot107/ot107_err.pdf

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Andrew M. Fraser is a Technical Staff Member in the ISR division of the Los Alamos National Laboratory where he uses stochastic models in his work on signal analysis. He spent 15 years at Portland State University in Oregon serving on the faculties of both the Systems Science PhD Program and the Electrical and Computer Engineering Department before joining LANL in 2005. He earned a PhD in Physics from UT-Austin with a dissertation on the use of mutual information estimates in the analysis of chaotic time series. Before graduate school, he designed bipolar memory technology and products at Fairchild semiconductor. He is a member of SIAM and a Senior Member of the IEEE.

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