Errors-in-Variables Methods in System Identification

  • Torsten Söderström

Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Torsten Söderström
    Pages 1-13
  3. Torsten Söderström
    Pages 15-47
  4. Torsten Söderström
    Pages 49-69
  5. Torsten Söderström
    Pages 71-88
  6. Torsten Söderström
    Pages 89-119
  7. Torsten Söderström
    Pages 121-133
  8. Torsten Söderström
    Pages 135-169
  9. Torsten Söderström
    Pages 171-195
  10. Torsten Söderström
    Pages 197-219
  11. Torsten Söderström
    Pages 221-236
  12. Torsten Söderström
    Pages 237-253
  13. Torsten Söderström
    Pages 255-267
  14. Torsten Söderström
    Pages 269-297
  15. Torsten Söderström
    Pages 299-401
  16. Torsten Söderström
    Pages 403-420
  17. Back Matter
    Pages 421-485

About this book


This book presents an overview of the different errors-in-variables (EIV) methods that can be used for system identification. Readers will explore the properties of an EIV problem. Such problems play an important role when the purpose is the determination of the physical laws that describe the process, rather than the prediction or control of its future behaviour. EIV problems typically occur when the purpose of the modelling is to get physical insight into a process. Identifiability of the model parameters for EIV problems is a non-trivial issue, and sufficient conditions for identifiability are given. The author covers various modelling aspects which, taken together, can find a solution, including the characterization of noise properties, extension to multivariable systems, and continuous-time models. The book finds solutions that are constituted of methods that are compatible with a set of noisy data, which traditional approaches to solutions, such as (total) least squares, do not find.

A number of identification methods for the EIV problem are presented. Each method is accompanied with a detailed analysis based on statistical theory, and the relationship between the different methods is explained. A multitude of methods are covered, including:
instrumental variables methods;
methods based on bias-compensation;
covariance matching methods; and 
prediction error and maximum-likelihood methods.

The book shows how many of the methods can be applied in either the time or the frequency domain and provides special methods adapted to the case of periodic excitation. It concludes with a chapter specifically devoted to practical aspects and user perspectives that will facilitate the transfer of the theoretical material to application in real systems.

Errors-in-Variables Methods in System Identification gives readers the possibility of recovering true system dynamics from noisy measurements, while solving over-determined systems of equations, making it suitable for statisticians and mathematicians alike. The book also acts as a reference for researchers and computer engineers because of its detailed exploration of EIV problems.    


Parameter Estimation Identification Methods Empirical Modelling EIV Problems Statistical System Identification

Authors and affiliations

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

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-75000-2
  • Online ISBN 978-3-319-75001-9
  • Series Print ISSN 0178-5354
  • Series Online ISSN 2197-7119
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