Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches

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Springer Science & Business Media, Sep 5, 2007 - Science - 232 pages
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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.

 

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Contents

Introduction to Nonlinear System
1
12 Nonlinear Systems
11
13 Summary
17
Polynomial models of nonlinear system
19
22 Nonorthogonal Models
20
23 Orthogonal models
28
24 Summary
35
25 Appendix 2A SturmLiouville System
36
63 RLS Algorithm for Truncated Volterra Series Model
121
64 RLS Algorithm for Bilinear Model
122
65 Computer Simulation Examples
123
66 Summary
128
Nonlinear adaptive system identification based in wiener models part 1
129
71 SecondOrder System
130
72 Computer Simulation Examples
140
73 Summary
148

Volterra and wiener nonlinear models
39
31 Volterra Representation
40
32 Discrete Nonlinear Wiener Representation
45
33 Detailed Nonlinear Wiener Model Representation
60
34 Delay Line Version of Nonlinear Wiener Model
65
35 The Nonlinear Hammerstein Model Representation
67
37 Appendix 3A
68
38 Appendix 3B
70
39 Appendix 3C
75
Nonlinear system identification methods
77
42 Methods Based on Nonlinear Global Optimization
80
43 Neural Network Approaches
81
44 Summary
84
Introduction to adaptive signal processing
85
52 Adaptive Filters LMSBased Algorithms
92
53 Applications of Adaptive Filters
95
54 LeastSquares Method for Optimum Linear Estimation
97
55 Adaptive Filters RLSBased Algorithms
107
56 Summary
113
Nonlinear adaptive system identification based on volterra models
115
61 LMS Algorithm for Truncated Volterra Series Model
116
62 LMS Adaptive Algorithms for Bilinear Models of Nonlinear Systems
118
GeneralOrder Moments of Joint Gaussian Random Variables
150
Nonlinear adaptive system identification based on wiener models part 2
158
82 Computer Simulation Results
170
83 Summary
174
Inverse Matrix of the CrossCorrelation Matrix Rw
182
Verification of Equation 816
183
Nonlinear adaptive system identification based on wiemer
187
92 Transform Domain Nonlinear Wiener Adaptive Filter
188
93 Computer Simulation Examples
193
94 Summary
197
Nonlinear adaptive system identification based on winer model part 4
198
101 Standard RLS Nonlinear Wiener Adaptive Algorithm
200
102 Inverse QR Decomposition Nonlinear Wiener Adaptive Algorithm
201
103 Recursive OLS Volterra Adaptive Filtering
203
104 Computer Simulation Examples
208
105 Summary
212
Conclusion recent result and new directions
213
111 Conclusions
214
References
217
Index
225
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