This book presents the design, analysis, and application of nonlinear adaptive filters with the goal of improving efficient performance (ie the convergence speed, steady-state error, and computational complexity). The authors present a nonlinear adaptive filter, which is an important part of nonlinear system and digital signal processing and can be applied to diverse fields such as communications, control power system, radar sonar, etc. The authors also present an efficient nonlinear filter model and robust adaptive filtering algorithm based on the local cost function of optimal criterion to overcome non-Gaussian noise interference. The authors show how these achievements provide new theories and methods for robust adaptive filtering of nonlinear and non-Gaussian systems. The book is written for the scientist and engineer who are not necessarily an expert in the specific nonlinear filtering field but who want to learn about the current research and application. The book is also written to accompany a graduate/PhD course in the area of nonlinear system and adaptive signal processing.
Author(s): Haiquan Zhao, Badong Chen
Publisher: Springer
Year: 2023
Language: English
Pages: 270
City: Cham
Preface
Acknowledgments
Contents
Abbreviations and Acronyms
Chapter 1: Adaptive Filter
1.1 Introduction
1.2 Linear Adaptive Filters
1.2.1 LMS Algorithm
1.2.2 Affine Projection Algorithm
1.2.3 Recursive Least-Squares Algorithm
1.2.4 Subband Algorithm
1.2.5 Kalman Filter
1.3 Nonlinear Adaptive Filters
1.3.1 Volterra Filter
1.3.2 FLANN Adaptive Filter
1.3.3 Spline Adaptive Filter
1.3.4 Kernel Adaptive Filter
1.4 Summary
References
Chapter 2: Volterra Adaptive Filter
2.1 Introduction
2.2 Volterra Filter Model
2.3 Pipelined Volterra Filter
2.4 Convex Combination of Volterra Filter
2.4.1 The Algorithm I
2.4.2 The Algorithm II
2.5 Robust Volterra Filtering Algorithm
2.6 The Volterra Expansion Model Based Filtered-x Logarithmic Continuous Least Mean p-Norm (VFxlogCLMP) Algorithm for Active N...
2.6.1 VFxlogLMP Algorithm
2.6.2 VFxlogCLMP Algorithm
2.6.3 Performance Analysis of the VFxlogCLMP Algorithm
2.6.4 EMSE Analysis
2.6.5 Convergence Condition of the VFxlogCLMP Algorithm
2.7 Diffusion Volterra Nonlinear Filtering Algorithm
2.7.1 Diffusion Least Mean Square (DLMS) Algorithm
2.7.2 Problem Formulation
2.7.3 The DV Filtering Algorithm
2.8 Simulation Results
2.8.1 Pipelined Volterra Filter
2.8.2 Convex Combination of Volterra Filter
2.8.3 Robust Volterra Filtering Algorithm
2.8.4 The VFxlogCLMP Algorithm for ANC Application
2.8.5 Diffusion Volterra Filtering Algorithm
2.9 Summary
References
Chapter 3: FLANN Adaptive Filter
3.1 Introduction
3.2 Neural Network Structures
3.2.1 MLP
3.2.2 ChNN
3.2.3 FLANN
3.2.4 LeNN
3.3 Recursive FLANN
3.3.1 Feedback FLANN Filter
3.3.2 Reduced Feedback FLANN Filter
3.3.3 Recursive FLANN Structure
3.3.3.1 A BIBO Stability Condition
3.4 Convex Combination of FLANN Filter
3.5 Random Fourier Filter
3.5.1 Random Fourier Feature
3.5.2 RF-LMS Algorithm
3.5.3 Cascaded RF-LMS (CRF-LMS) Algorithm
3.5.4 Mean Convergence Analysis
3.5.5 Computational Complexity
3.6 Nonlinear Active Noise Control
3.6.1 Robust Control Algorithms for NANC
3.6.1.1 FsLMP Algorithm
3.6.1.2 FsqLMP Algorithm
3.6.1.3 RFsLMS Algorithm
3.6.1.4 FsMCC Algorithm
3.6.1.5 RFF-FxMCC Algorithm
3.7 Nonlinear Channel Equalization
3.7.1 Communication Channel Equalization
3.7.2 Channel Equalization Using a Generalized NN Model
3.7.3 FLNN Equalizer
3.7.3.1 Adaptive Equalizer with FLNN Cascaded with Chebyshev Orthogonal Polynomial
3.7.3.2 Decision Feedback Equalizer Using the Combination of FIR and FLNN
3.8 Computer Simulation Examples
3.8.1 FLANN-Based NANC with Minimum Phase Secondary Path System
3.8.2 Random Fourier Filter-Based NANC
3.8.2.1 Projection Dimension and Memory Length of Random Fourier Filter
3.8.2.2 Real Example: Random Fourier Filter-Based Active Traction Substation Noise Control
3.8.3 Nonlinear Channel Equalization
3.8.3.1 Channel Equalization Using a Generalized NN Model
3.8.3.2 Adaptive Equalizer Based on the FLNN Cascaded with Chebyshev Orthogonal Polynomial Structure
3.8.3.3 Adaptive Decision Feedback Equalizer with the Combination of FIR Filter and FLANN
3.9 Summary
References
Chapter 4: Spline Adaptive Filter
4.1 Introduction
4.2 Spline Filter Model
4.2.1 Spline Adaptive Filter
4.2.2 Basic Spline Filter Algorithm
4.2.2.1 SAF-LMS Algorithm
4.2.2.2 SAF-NLMS Algorithm
4.2.2.3 SAF-SNLMS Algorithm
4.2.2.4 SAF-VSS-SNLMS Algorithm
4.3 Robust Spline Filtering Algorithm
4.3.1 SAF-MCC Algorithm
4.3.2 Performance Analysis
4.4 Applications
4.4.1 Active Noise Control Based on Spline Filter
4.4.1.1 FcGMCC Algorithm
4.4.1.2 Convergence Analysis
4.4.2 Echo Cancellation Based on Spline Filter
4.4.2.1 The Nonlinear Echo Canceler
4.4.2.2 The Architectures Proposed in
4.5 Computer Simulation Examples
4.5.1 Basic Spline Filter Algorithm Simulation
4.5.2 SAF-MCC Algorithm Simulation
4.5.3 Performance Analysis Simulation
4.5.4 Simulation of ANC
4.5.4.1 Performance of the FcGMCC Algorithm
4.5.5 Simulation of Echo Cancellation
4.6 Summary
References
Chapter 5: Kernel Adaptive Filters
5.1 Introduction
5.2 Kernel Adaptive Filters
5.2.1 Reproducing Kernel Hilbert Space
5.2.2 Kernel Least Mean Square
5.2.2.1 Kernel Selection
5.2.2.2 Step-Size Selection
5.2.2.3 Mean Square Convergence Analysis
5.2.3 Kernel Affine Projection Algorithms
5.2.3.1 Affine Projection Algorithms
5.2.3.2 Kernel Affine Projection Algorithms
5.2.4 Kernel Recursive Least Squares
5.3 Network Optimization
5.3.1 Sparsification Algorithms
5.3.1.1 Novelty Criterion
5.3.1.2 Approximate Linear Dependency
5.3.1.3 Surprise Criterion
5.3.2 Quantization Algorithms
5.3.2.1 On-Line Quantization
5.3.2.2 Off-Line Quantization
5.3.3 Kernel Approximation
5.3.3.1 Nyström Method
5.3.3.2 Random Fourier Feature Method
5.4 Computer Simulation Examples
5.4.1 Comparisons of Different KAFs
5.4.1.1 Mackey-Glass Chaotic Time Series Prediction
5.4.1.2 Nonlinear Channel Equalization
5.4.2 Comparisons of Network Optimization Methods
5.4.2.1 Relation Between Code Book Size and Performance
5.4.2.2 Comparison of Several Network Optimization Methods
5.4.2.3 KRLS with Different Sparsification Methods
5.4.2.4 Comparison of Different Quantization Methods
5.4.2.5 KRR with Different Quantization Methods
5.5 Summary
References
Index
