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Author Söderström, Torsten, author.

Title Errors-in-variables methods in system identification / Torsten Söderström
Published Cham, Switzerland : Springer, 2018

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Description 1 online resource (xxvii, 485 pages) : illustrations (some color)
Series Communications and control engineering, 0178-5354
Communications and control engineering.
Contents Intro; Preface; Contents; Abbreviations; Notation; Notational Conventions; Summary of Assumptions; Assumptions on the System; Assumptions on the Noise; Assumptions on the Noise-free Input; Assumptions on the Experimental Conditions; Applicability; 1 Introduction; 1.1 Four Motivating Examples; 1.2 Outline of the Book; 1.3 Some Important Concepts in System Identification; 1.4 Some Notations; 1.5 Extensions and Bibliographical Notes; 2 The Static Case; 2.1 Line Fitting; 2.1.1 Some System Theoretic Considerations of Identifiability; 2.2 Confirmatory Factor Analysis; 2.2.1 The Modeling Part
2.2.2 Estimation Part2.3 The Frisch Scheme; 2.4 Extensions and Bibliographical Notes; 2.A Further Details; 2.A.1 Further Results for Line Fitting; 2.A.2 Consistency of the CFA Estimate; 3 The Errors-in-Variables Problem for Dynamic Systems; 3.1 The EIV Problem; 3.2 About Numerical Examples; 3.3 Two Special Cases; 3.4 Some Naïve Approaches; 3.4.1 Neglecting the Input Noise; 3.4.2 Estimating the Noise-Free Input Signal; 3.4.3 Rewriting the Model into Standard Form; 3.5 Extensions and Bibliographical Notes; 4 Identifiability Aspects; 4.1 Some General Aspects
4.2 Identifiability Analysis for Parametric Models4.3 Identifiability When Using Multiple Experiments; 4.4 Closed-Loop Operation; 4.5 Extensions and Bibliographical Notes; 5 Modeling Aspects; 5.1 Problem Statement and Notations; 5.2 Using Models with an Arbitrary Delay; 5.3 Continuous-Time EIV Models and Conversion to Discrete-Time; 5.4 Modeling the Noise Properties; 5.5 Frequency Domain Models; 5.6 Modeling the Total System; 5.7 Models for Multivariable Systems; 5.8 Classification of Estimators Based on Data Compression; 5.9 Model Order Determination; 5.9.1 Introduction
5.9.2 Some Approaches5.9.3 About the Rank Tests; 5.9.4 Discussion; 5.10 Extensions and Bibliographical Notes; 5.A Further Details; 5.A.1 Discrete-Time Model Approximation; 5.A.2 Analyzing Effects of Small Singular Values; 6 Elementary Methods; 6.1 The Least Squares Method; 6.2 The Instrumental Variable Method; 6.2.1 Description; 6.2.2 Consistency Analysis; 6.2.3 User Choices. Examples of Instrumental Vectors; 6.2.4 Instrumental Variable Methods Exploiting Higher-Order Statistics; 6.2.5 Other Instrumental Variable Techniques; 6.3 Extensions and Bibliographical Notes
7 Methods Based on Bias-Compensation7.1 The Basic Idea of Bias-Compensation; 7.2 The Bias-Eliminating Least Squares Method; 7.2.1 Introduction; 7.2.2 White Output Noise; 7.2.3 Correlated Output Noise; 7.3 The Frisch Scheme; 7.3.1 General Aspects; 7.3.2 White Output Noise; 7.3.3 Correlated Output Noise; 7.3.4 Using an Alternating Projection Algorithm; 7.4 The Generalized Instrumental Variable Method; 7.4.1 General Framework; 7.4.2 Various Examples; 7.4.3 GIVE Identification of MIMO Models; 7.5 Extensions and Bibliographical Notes; 7.5.1 BELS; 7.5.2 The Frisch Scheme; 7.5.3 GIVE
Summary 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
Bibliography Includes bibliographical references and index
Notes Online resource; title from PDF title page (SpringerLink, viewed April 11, 2018)
Subject Errors-in-variables models.
System identification.
Cybernetics & systems theory.
Communications engineering -- telecommunications.
Network hardware.
Probability & statistics.
Automatic control engineering.
MATHEMATICS -- General.
Errors-in-variables models
System identification
Form Electronic book
ISBN 9783319750019
3319750011