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

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 |

217 | |

225 | |