Discrete-time Stochastic Systems

Estimation and Control

  • T. Söderström

Table of contents

  1. Front Matter
    Pages i-xxi
  2. T. Söderström
    Pages 1-6
  3. T. Söderström
    Pages 7-27
  4. T. Söderström
    Pages 29-58
  5. T. Söderström
    Pages 59-122
  6. T. Söderström
    Pages 123-135
  7. T. Söderström
    Pages 137-183
  8. T. Söderström
    Pages 223-243
  9. T. Söderström
    Pages 245-295
  10. T. Söderström
    Pages 297-317
  11. T. Söderström
    Pages 319-365
  12. Back Matter
    Pages 367-375

About this book


Discrete-time Stochastic Systems gives a comprehensive introduction to the estimation and control of dynamic stochastic systems and provides complete derivations of key results such as the basic relations for Wiener filtering. The book covers both state-space methods and those based on the polynomial approach. Similarities and differences between these approaches are highlighted. Some non-linear aspects of stochastic systems (such as the bispectrum and extended Kalman filter) are also introduced and analysed. The books chief features are as follows:

• inclusion of the polynomial approach provides alternative and simpler computational methods than simple reliance on state-space methods;

• algorithms for analysis and design of stochastic systems allow for ease of implementation and experimentation by the reader;

• the highlighting of spectral factorization gives appropriate emphasis to this key concept often overlooked in the literature;

• explicit solutions of Wiener problems are handy schemes, well suited for computations compared with more commonly available but abstract formulations;

• complex-valued models that are directly applicable to many problems in signal processing and communications.

Changes in the second edition include:

• additional information covering spectral factorisation and the innovations form;

• the chapter on optimal estimation being completely rewritten to focus on a posteriori estimates rather than maximum likelihood;

• new material on fixed lag smoothing and algorithms for solving Riccati equations are improved and more up to date;

• new presentation of polynomial control and new derivation of linear-quadratic-Gaussian control.

Discrete-time Stochastic Systems is primarily of benefit to students taking M.Sc. courses in stochastic estimation and control, electronic engineering and signal processing but may also be of assistance for self study and as a reference.


Markov chain Markov process Measure Probability theory Random variable actor algorithms communication information innovation stochastic process

Authors and affiliations

  • T. Söderström
    • 1
  1. 1.Department of Systems and Control, Information TechnologyUppsala UniversityUppsalaSweden

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag London Limited 2002
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-85233-649-3
  • Online ISBN 978-1-4471-0101-7
  • Series Print ISSN 1439-2232
  • Series Online ISSN 2510-3814
  • Buy this book on publisher's site
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