Adaptive Nonlinear System Identification (eBook)

The Volterra and Wiener Model Approaches

Tokunbo Ogunfunmi (Autor)

eBook Download: PDF

2007 | 2007
XVI, 232 Seiten
Springer US (Verlag)
978-0-387-68630-1 (ISBN)

Infos

Focuses on System Identification applications of the adaptive methods presented. but which can also be applied to other applications of adaptive nonlinear processes.

Covers recent research results in the area of adaptive nonlinear system identification from the authors and other researchers in the field.

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Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches introduces engineers and researchers to the field of nonlinear adaptive system identification. The book includes recent research results in the area of adaptive nonlinear system identification and presents simple, concise, easy-to-understand methods for identifying nonlinear systems. These methods use adaptive filter algorithms that are well known for linear systems identification. They are applicable for nonlinear systems that can be efficiently modeled by polynomials.After a brief introduction to nonlinear systems and to adaptive system identification, the author presents the discrete Volterra model approach. This is followed by an explanation of the Wiener model approach. Adaptive algorithms using both models are developed. The performance of the two methods are then compared to determine which model performs better for system identification applications. Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches is useful to graduates students, engineers and researchers in the areas of nonlinear systems, control, biomedical systems and in adaptive signal processing.

Inhalt

PREFACE 7
ACKNOWLEDGEMENTS 10
CONTENTS 11
Chapter 1 INTRODUCTION TO NONLINEAR SYSTEMS 14
Why Study Nonlinear Systems? 14
1.1 Linear Systems 14
Introduction 14
( x x 16
x(t) t) t) 19
x(t 19
x( 19
t) 19
x( 19
x( 19
x( 19
x( 19
x( 19
x(t) 19
x( x( ) ) (t t ) dt (1.1) 1.1) 1.1) 19
1.2 Nonlinear Systems 24
1.3 Summary 30
Chapter 2 POLYNOMIAL MODELS OF NONLINEAR SYSTEMS 31
Orthogonal and Nonorthogonal Models 31
2.1 Nonlinear Orthogonal and Nonorthogonal Models 31
Introduction 31
2.2 Nonorthogonal Models Models Models 32
2.3 Orthogonal models 40
2.4 Summary 47
2.5 Appendix 2A (Sturm-Liouville System) 48
Chapter 3 VOLTERRA AND WIENER NONLINEAR MODELS 51
Introduction 51
3.1 Volterra Representation 52
3.2 Discrete Nonlinear Wiener Representation 57
h 72
k 72
h 72
k 72
h 72
k 72
k 72
h 72
k 72
k 72
k 72
k 72
h 72
k 72
k 72
k 72
k k k k k k k k k k k k k k k k k k 72
3.3 Detailed Nonlinear Wiener Model Representation 72
3.4 Delay Line Version of Nonlinear Wiener Model 77
3.5 The Nonlinear Hammerstein Model Representation 79
3.6 Summary 79
3.7 Appendix 3A 80
3.8 Appendix 3B 3B 82
3.9 Appendix 3C 3C 87
Chapter 4 NONLINEAR SYSTEM IDENTIFICATION METHODS 89
A brief survey of the available methods 89
4.1 Methods Based on Nonlinear Local Optimization 89
Introduction 89
4.2 Methods Based on Nonlinear Global Optimization 92
4.3 Neural Network Approaches 93
4.4 Summary 96
Chapter 5 INTRODUCTION TO ADAPTIVE SIGNAL PROCESSING 97
5.1 Wiener Filters for Optimum Linear Estimation 97
Introduction 97
5.2 Adaptive Filters (LMS-Based Algorithms) 104
5.3 Applications of Adaptive Filters 107
5.4 Least-Squares Method for Optimum Linear Estimation 109
5.5 Adaptive Filters (RLS-Based Algorithms) Algorithms) Algorithms) Algorithms) 119
5.6 Summary 125
5.7 Appendix 5A ABCD ( INVERSION) LEMMA: INVERSION OF [A+BCD] 125
Chapter 6 NONLINEAR ADAPTIVE SYSTEM IDENTIFICATION BASED ON VOLTERRA MODELS 127
Algorithms based on the Volterra and bilinear models 127
Introduction 127
6.1 LMS Algorithm for Truncated Volterra Series Model 128
6.2 LMS Adaptive Algorithms for Bilinear Models of Nonlinear Systems 130
6.3 RLS Algorithm for Truncated Volterra Series Model 133
6.4 RLS Algorithm for Bilinear Model 134
6.5 Computer Simulation Examples 135
6.6 Summary 140
Chapter 7 NONLINEAR ADAPTIVE SYSTEM IDENTIFICATION BASED ON WIENER MODELS ( PART 1) 141
Second-order least-mean-square (LMS)-based approach 141
Introduction 141
7.1 Second-Order System 142
7.2 Computer Simulation Examples 152
7.3 Summary 160
7.4 160
Appendix 160
7A: 160
The 160
Relation between 160
Autocorrelation 160
Matrix 160
and Cross-Correlation Matrix Matrix Matrix Matrix Matrix Matrix 160
7.5 Appendix 7B: General-Order Moments of Joint Gaussian Random Variables Variables Variables Variables Variables Variables Variables Variables Variables Variables Variables 162
Chapter 8 NONLINEAR ADAPTIVE SYSTEM IDENTIFICATION BASED ON WIENER MODELS ( PART 2) 170
Third-order least-mean-square (LMS)-based approach 170
Introduction 170
8.1 Third-Order System 170
8.2 Computer Simulation Results 181
8.3 Summary 185
8.4 185
APPENDIX 185
8A: 185
The Relation between 185
Autocorrelation 185
Matrix 185
, and Cross-Correlation Matrix 185
8.5 Appendix 8B: Inverse Matrix of the Cross-Correlation 193
Matrix 193
8.6 Appendix 8C: Verification of Equation 8.16 8.16 8.16 8.16 194
Chapter 9 NONLINEAR ADAPTIVE SYSTEM IDENTIFICATION BASED ON WIENER MODELS ( PART 3) 197
Other stochastic-gradient-based algorithms 197
Introduction 197
9.1 Nonlinear LMF Adaptation Algorithm 197
9.2 Transform Domain Nonlinear Wiener Adaptive Filter 198
9.3 Computer Simulation Examples 203
9.4 Summary 207
Chapter 10 NONLINEAR ADAPTIVE SYSTEM IDENTIFICATION BASED ON WIENER MODELS ( PART 4) 208
Least-squares based algorithms 208
Introduction 208
10.1 Standard RLS Nonlinear Wiener Adaptive Algorithm Algorithm Algorithm Algorithm Algorithm Algorithm Algorithm Algorithm Algorithm Algorithm Algorithm 209
10.2 Inverse QR Decomposition Nonlinear Wiener Adaptive Algorithm Algorithm Algorithm 210
10.3 Recursive OLS Volterra Adaptive Filtering 212
10.4 Computer Simulation Examples 217
10.5 Summary 221
Chapter 11 CONCLUSIONS, RECENT RESULTS, AND NEW DIRECTIONS 222
Summary 222
11.1 Conclusions 223
11.2 Recent Results and New Directions 223
REFERENCES 225
INDEX 233

Produkt-Details

• Erscheint lt. Verlag: 5.9.2007
• Reihe/Serie: Signals and Communication Technology
• Zusatzinfo: XVI, 232 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Grafik / Design
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Nachrichtentechnik
• Schlagworte: Adaptive Filters • Filter • nonlinear system • Nonlinear Systems • Performance • Signal Processing • System • System Identification • Volterra Model • Wiener Model
• ISBN-10: 0-387-68630-4 / 0387686304
• ISBN-13: 978-0-387-68630-1 / 9780387686301