Adaptive nonlinear system identification : the volterra and wiener model approaches

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.

Preface	p. vii
Acknowledgements	p. xi
1 Introduction to Nonlinear Systems	p. 1
1.1 Linear Systems	p. 1
1.2 Nonlinear Systems	p. 11
1.3 Summary	p. 17
2 Polynomial Models of Nonlinear Systems	p. 19
2.1 Nonlinear Orthogonal and Nonorthogonal Models	p. 19
2.2 Nonorthogonal Models	p. 20
2.3 Orthogonal Models	p. 28
2.4 Summary	p. 35
2.5 Appendix 2A (Sturm-Liouville System)	p. 36
3 Volterra and Wiener Nonlinear Models	p. 39
3.1 Volterra Respresentation	p. 40
3.2 Discrete Nonlinear Wiener Representation	p. 45
3.3 Detailed Nonlinear Wiener Model Representation	p. 60
3.4 Delay Line Version of Nonlinear Wiener Model	p. 65
3.5 The Nonlinear Hammerstein Model Representation	p. 67
3.6 Summary	p. 67
3.7 Appendix 3A	p. 68
3.8 Appendix 3B	p. 70
3.9 Appendix 3C	p. 75
4 Nonlinear System Identification Methods	p. 77
4.1 Methods Based on Nonlinear Local Optimization	p. 77
4.2 Methods Based on Nonlinear Global Optimization	p. 80
4.3 The Need for Adaptive Methods	p. 81
4.4 Summary	p. 84
5 Introduction to Adaptive Signal Processing	p. 85
5.1 Weiner Filters for Optimum Linear Estimation	p. 85
5.2 Adaptive Filters (LMS-Based Algorithms)	p. 92
5.3 Applications of Adaptive Filters	p. 95
5.4 Least-Squares Method for Optimum Linear Estimation	p. 97
5.5 Adaptive Filters (RLS-Based Algorithms)	p. 107
5.6 Summary	p. 113
5.7 Appendix 5A	p. 113
6 Nonlinear Adaptive System Identification Based on Volterra Models	p. 115
6.1 LMS Algorithm for Truncated Volterra Series Model	p. 116
6.2 LMS Algorithm for Bilinear Model of Nonlinear Systems	p. 118
6.3 RLS Algorithm for Truncated Volterra Series Model	p. 121
6.4 RLS Algorithm for Bilinear Model	p. 122
6.5 Computer Simulation Examples	p. 123
6.6 Summary	p. 128
7 Nonlinear Adaptive System Identification Based on Wiener Models (Part 1)	p. 129
7.1 Second-Order System	p. 130
7.2 Computer Simulation Examples	p. 140
7.3 Summary	p. 148
7.4 Appendix 7A: Relation between Autocorrelation Matrix R[subscript xx], R[subscript xx] and Cross-Correlation Matrix R[subscript xx]	p. 148
7.5 Appendix 7B: General Order Moments of Joint Gaussian Random Variables	p. 150
8 Nonlinear Adaptive System Identification Based on Wiener Models (Part 2)	p. 159
8.1 Third-Order System	p. 159
8.2 Computer Simulation Examples	p. 170
8.3 Summary	p. 174
8.4 Appendix 8A: Relation Between Autocorrelation Matrix R[subscript xx], R[subscript xx] and Cross-Correlation Matrix R[subscript xx]	p. 174
8.5 Appendix 8B: Inverse Matrix of Cross-Correlation Matrix R[subscript xx]	p. 182
8.6 Appendix 8C: Verification of Equation 8.16	p. 183
9 Nonlinear Adaptive System Identification Based on Wiener Models (Part 3)	p. 187
9.1 Nonlinear LMF Adaptation Algorithm	p. 187
9.2 Transform Domain Nonlinear Wiener Adaptive Filter	p. 188
9.3 Computer Simulation Examples	p. 193
9.4 Summary	p. 197
10 Nonlinear Adaptive System Identification Based on Wiener Models (Part 4)	p. 199
10.1 Standard RLS Nonlinear Wiener Adaptive Algorithm	p. 200
10.2 Inverse QR Decomposition Nonlinear Wiener Filter Algorithm	p. 201
10.3 Recursive OLS Volterra Adaptive Filtering	p. 203
10.4 Computer Simulation Examples	p. 208
10.5 Summary	p. 212
11 Conclusions, Recent Results, and New Directions	p. 213
11.1 Conclusions	p. 214
11.2 Recent Results and New Directions	p. 214
References	p. 217
Index	p. 225

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