Hidden Markov Models

Estimation and Control

  • Robert J. Elliott
  • John B. Moore
  • Lakhdar Aggoun

Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 29)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Introduction

    1. Front Matter
      Pages 1-1
  3. Discrete-Time HMM Estimation

  4. Continuous-Time HMM Estimation

    1. Front Matter
      Pages 195-195
  5. Two-Dimensional HMM Estimation

    1. Front Matter
      Pages 235-235
  6. HMM Optimal Control

    1. Front Matter
      Pages 271-271
  7. Back Matter
    Pages 351-377

About this book


As more applications are found, interest in Hidden Markov Models continues to grow. Following comments and feedback from colleagues, students and other working with Hidden Markov Models the corrected 3rd printing of this volume contains clarifications, improvements and some new material, including results on smoothing for linear Gaussian dynamics.

In Chapter 2 the derivation of the basic filters related to the Markov chain are each presented explicitly, rather than as special cases of one general filter. Furthermore, equations for smoothed estimates are given. The dynamics for the Kalman filter are derived as special cases of the authors’ general results and new expressions for a Kalman smoother are given. The Chapters on the control of Hidden Markov Chains are expanded and clarified. The revised Chapter 4 includes state estimation for discrete time Markov processes and Chapter 12 has a new section on robust control.


93E11, 93E20, 60G35, 60H30 EM algorithm Hidden Markov chains filtering parameter estimation stochastic control Brownian motion dynamics equation hidden Markov model Markov chain Markov model Markov process optimal control Parameter Rang

Authors and affiliations

  • Robert J. Elliott
    • 1
  • John B. Moore
    • 2
  • Lakhdar Aggoun
    • 3
  1. 1.Haskayne School of Business Scurfield HallUniversity of CalgaryCalgaryCanada
  2. 2.Department of Systems Engineering and Cooperative Research Centre for Robust and Adaptive Systems Research School of Physical Sciences and EngineeringAustralian National UniversityCanberraAustralia
  3. 3.Department of Mathematics and Statistics College of ScienceSultan Qaboos UniversitySultanate of Oman

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media, LLC 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94364-0
  • Online ISBN 978-0-387-84854-9
  • Series Print ISSN 0172-4568
  • Buy this book on publisher's site
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