Ogunfunmi Adaptive Nonlinear System Identification

The Volterra and Wiener Model Approaches
1. Auflage 2007
ISBN: 978-0-387-68630-1
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 232 Seiten

Reihe: Signals and Communication Technology

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.

Autoren/Hrsg.

Ogunfunmi, Tokunbo

Inhaltsverzeichnis

1;PREFACE;7
2;ACKNOWLEDGEMENTS;10
3;CONTENTS;11
4;Chapter 1 INTRODUCTION TO NONLINEAR SYSTEMS;14
4.1;Why Study Nonlinear Systems?;14
4.2;1.1 Linear Systems;14
4.3;Introduction;14
4.4;( x x;16
4.5;x(t) t) t);19
4.6;x(t;19
4.7;x(;19
4.8;t);19
4.9;x(;19
4.10;x(;19
4.11;x(;19
4.12;x(;19
4.13;x(;19
4.14;x(t);19
4.15;x( x( ) ) (t t ) dt (1.1) 1.1) 1.1);19
4.16;1.2 Nonlinear Systems;24
4.17;1.3 Summary;30
5;Chapter 2 POLYNOMIAL MODELS OF NONLINEAR SYSTEMS;31
5.1;Orthogonal and Nonorthogonal Models;31
5.2;2.1 Nonlinear Orthogonal and Nonorthogonal Models;31
5.3;Introduction;31
5.4;2.2 Nonorthogonal Models Models Models;32
5.5;2.3 Orthogonal models;40
5.6;2.4 Summary;47
5.7;2.5 Appendix 2A (Sturm-Liouville System);48
6;Chapter 3 VOLTERRA AND WIENER NONLINEAR MODELS;51
6.1;Introduction;51
6.2;3.1 Volterra Representation;52
6.3;3.2 Discrete Nonlinear Wiener Representation;57
6.4;h;72
6.5;k;72
6.6;h;72
6.7;k;72
6.8;h;72
6.9;k;72
6.10;k;72
6.11;h;72
6.12;k;72
6.13;k;72
6.14;k;72
6.15;k;72
6.16;h;72
6.17;k;72
6.18;k;72
6.19;k;72
6.20;k k k k k k k k k k k k k k k k k k;72
6.21;3.3 Detailed Nonlinear Wiener Model Representation;72
6.22;3.4 Delay Line Version of Nonlinear Wiener Model;77
6.23;3.5 The Nonlinear Hammerstein Model Representation;79
6.24;3.6 Summary;79
6.25;3.7 Appendix 3A;80
6.26;3.8 Appendix 3B 3B;82
6.27;3.9 Appendix 3C 3C;87
7;Chapter 4 NONLINEAR SYSTEM IDENTIFICATION METHODS;89
7.1;A brief survey of the available methods;89
7.2;4.1 Methods Based on Nonlinear Local Optimization;89
7.3;Introduction;89
7.4;4.2 Methods Based on Nonlinear Global Optimization;92
7.5;4.3 Neural Network Approaches;93
7.6;4.4 Summary;96
8;Chapter 5 INTRODUCTION TO ADAPTIVE SIGNAL PROCESSING;97
8.1;5.1 Wiener Filters for Optimum Linear Estimation;97
8.2;Introduction;97
8.3;5.2 Adaptive Filters (LMS-Based Algorithms);104
8.4;5.3 Applications of Adaptive Filters;107
8.5;5.4 Least-Squares Method for Optimum Linear Estimation;109
8.6;5.5 Adaptive Filters (RLS-Based Algorithms) Algorithms) Algorithms) Algorithms);119
8.7;5.6 Summary;125
8.8;5.7 Appendix 5A ABCD ( INVERSION) LEMMA: INVERSION OF [A+BCD];125
9;Chapter 6 NONLINEAR ADAPTIVE SYSTEM IDENTIFICATION BASED ON VOLTERRA MODELS;127
9.1;Algorithms based on the Volterra and bilinear models;127
9.2;Introduction;127
9.3;6.1 LMS Algorithm for Truncated Volterra Series Model;128
9.4;6.2 LMS Adaptive Algorithms for Bilinear Models of Nonlinear Systems;130
9.5;6.3 RLS Algorithm for Truncated Volterra Series Model;133
9.6;6.4 RLS Algorithm for Bilinear Model;134
9.7;6.5 Computer Simulation Examples;135
9.8;6.6 Summary;140
10;Chapter 7 NONLINEAR ADAPTIVE SYSTEM IDENTIFICATION BASED ON WIENER MODELS ( PART 1);141
10.1;Second-order least-mean-square (LMS)-based approach;141
10.2;Introduction;141
10.3;7.1 Second-Order System;142
10.4;7.2 Computer Simulation Examples;152
10.5;7.3 Summary;160
10.6;7.4;160
10.7;Appendix;160
10.8;7A:;160
10.9;The;160
10.10;Relation between;160
10.11;Autocorrelation;160
10.12;Matrix;160
10.13;and Cross-Correlation Matrix Matrix Matrix Matrix Matrix Matrix;160
10.14;7.5 Appendix 7B: General-Order Moments of Joint Gaussian Random Variables Variables Variables Variables Variables Variables Variables Variables Variables Variables Variables;162
11;Chapter 8 NONLINEAR ADAPTIVE SYSTEM IDENTIFICATION BASED ON WIENER MODELS ( PART 2);170
11.1;Third-order least-mean-square (LMS)-based approach;170
11.2;Introduction;170
11.3;8.1 Third-Order System;170
11.4;8.2 Computer Simulation Results;181
11.5;8.3 Summary;185
11.6;8.4;185
11.7;APPENDIX;185
11.8;8A:;185
11.9;The Relation between;185
11.10;Autocorrelation;185
11.11;Matrix;185
11.12;, and Cross-Correlation Matrix;185
11.13;8.5 Appendix 8B: Inverse Matrix of the Cross-Correlation;193
11.14;Matrix;193
11.15;8.6 Appendix 8C: Verification of Equation 8.16 8.16 8.16 8.16;194
12;Chapter 9 NONLINEAR ADAPTIVE SYSTEM IDENTIFICATION BASED ON WIENER MODELS ( PART 3);197
12.1;Other stochastic-gradient-based algorithms;197
12.2;Introduction;197
12.3;9.1 Nonlinear LMF Adaptation Algorithm;197
12.4;9.2 Transform Domain Nonlinear Wiener Adaptive Filter;198
12.5;9.3 Computer Simulation Examples;203
12.6;9.4 Summary;207
13;Chapter 10 NONLINEAR ADAPTIVE SYSTEM IDENTIFICATION BASED ON WIENER MODELS ( PART 4);208
13.1;Least-squares based algorithms;208
13.2;Introduction;208
13.3;10.1 Standard RLS Nonlinear Wiener Adaptive Algorithm Algorithm Algorithm Algorithm Algorithm Algorithm Algorithm Algorithm Algorithm Algorithm Algorithm;209
13.4;10.2 Inverse QR Decomposition Nonlinear Wiener Adaptive Algorithm Algorithm Algorithm;210
13.5;10.3 Recursive OLS Volterra Adaptive Filtering;212
13.6;10.4 Computer Simulation Examples;217
13.7;10.5 Summary;221
14;Chapter 11 CONCLUSIONS, RECENT RESULTS, AND NEW DIRECTIONS;222
14.1;Summary;222
14.2;11.1 Conclusions;223
14.3;11.2 Recent Results and New Directions;223
15;REFERENCES;225
16;INDEX;233