# Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches

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

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 Copyright

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