魯棒自適應濾波原理、算法及應用

第 1 章 魯棒自適應濾波概述···············································································.1
1.1 背景和意義 ··························································································.1
1.2 國內外研究現狀和發展態勢 ·····································································.2
1.2.1 α-SDM 研究及其應用 ····································································.2
1.2.2 自適應濾波原理及其典型應用·························································.3
1.2.3 自適應濾波算法的研究進展····························································.5
1.2.4 基於核方法的非線性自適應濾波算法················································.8
1.3 本書章節安排 ·······················································································.9
第 2 章 非高斯環境下的自適應濾波理論基礎··························································10
2.1 α 穩定分布模型·····················································································10
2.1.1 α 穩定分布特征函數······································································10
2.1.2 α 穩定分布的重要性質···································································16
2.2 相關熵 ································································································18
2.2.1 相關熵的概念 ··············································································18
2.2.2 相關熵的性質 ··············································································19
2.2.3 廣義相關熵的概念 ········································································23
2.2.4 廣義相關熵的性質 ········································································24
2.3 常用的優化方法 ····················································································27
2.3.1 梯度法 ·······················································································27
2.3.2 牛頓遞歸法 ·················································································28
2.4 核自適應濾波算法 ·················································································29
2.4.1 Mercer 核函數··············································································29
2.4.2 重構核希爾伯特空間（RKHS）·······················································30
2.4.3 特征空間 ····················································································30
2.4.4 基於高斯核函數的自適應濾波算法···················································31
2.4.5 自適應濾波算法的性能指標····························································31
2.5 本章小結 ·····························································································34
第 3 章 仿射投影類自適應濾波算法······································································35
3.1 歸一化最小均方（NLMS）算法································································35
3.1.1 LMS 算法原理 ·············································································35
3.1.2 NLMS 算法原理···········································································37
3.2 仿射投影（AP）算法 ·············································································38
3.2.1 AP 算法原理 ···············································································39
魯棒自適應濾波原理、算法及應用 ·VI·
3.2.2 AP 算法的計算復雜度 ···································································40
3.2.3 快速 AP 算法——基於原始權重向量更新的快速近似方法 ·····················41
3.3 仿射投影符號算法（APSA） ···································································42
3.3.1 APSA 算法原理············································································42
3.3.2 APSA 算法均方穩定性分析·····························································44
3.4 仿射投影廣義最大相關熵（APGMC）算法 ·················································47
3.4.1 廣義最大相關熵準則·····································································47
3.4.2 APGMC 算法原理·········································································48
3.4.3 APGMC 算法計算復雜度分析··························································51
3.4.4 均方收斂穩定性分析·····································································51
3.4.5 其他魯棒 AP 類算法······································································52
3.5 基於數據復用方法的 GMC 算法································································56
3.5.1 數據復用最大相關熵（DR-MCC）算法 ·············································57
3.5.2 數據復用廣義最大相關熵（DR-GMC）算法·······································57
3.5.3 隨機數據復用廣義最大相關熵（RDR-GMC）算法·······························58
3.5.4 隨機牛頓遞歸數據復用廣義最大相關熵算法·······································61
3.6 面向稀疏系統辨識的仿射投影類算法 ·························································66
3.6.1 通用稀疏系統辨識 ········································································66
3.6.2 塊/聚集型稀疏系統辨識 ·································································77
3.7 仿射投影類算法的實驗仿真與分析 ····························································84
3.7.1 面向 APSA 算法的實驗仿真與分析···················································84
3.7.2 面向 APGMC 算法的實驗仿真與分析················································89
3.7.3 面向數據復用算法的實驗仿真與分析················································92
3.7.4 面向塊/聚集型稀疏系統辨識算法的實驗仿真與分析·····························97
第 4 章 基於最小二乘架構的魯棒自適應濾波算法·················································.103
4.1 遞歸最小二乘算法 ··············································································.103
4.1.1 最小二乘問題 ···········································································.103
4.1.2 遞歸最小二乘算法 ·····································································.105
4.1.3 遞歸最小 p 次冪算法··································································.107
4.2 不動點廣義最大相關熵算法 ··································································.110
4.2.1 概要 ·······················································································.110
4.2.2 FP-GMC 算法原理 ·····································································.110
4.2.3 FP-GMC 算法收斂性分析 ····························································.112
4.2.4 FP-GMC 算法的在線形式 ····························································.115
4.2.5 自適應凸組合遞歸廣義最大相關熵（AC-RGMC）算法······················.120
4.3 面向二階 Volterra 濾波的 RGMC 算法······················································.124
4.3.1 二階 Volterra 濾波器概述·····························································.124
4.3.2 面向 SOV 濾波器的基本 RGMC 算法 ·············································.125
目 錄 ·VII·
4.3.3 具有可變遺忘因子的 RGMC 算法··················································.126
4.4 線性約束條件下的魯棒遞歸自適應濾波算法 ·············································.129
4.4.1 遞歸約束廣義最大相關熵（RCGMC）算法·····································.130
4.4.2 RCGMC 算法性能分析 ·······························································.134
4.4.3 RCGMC 算法的低計算復雜度方法 ················································.140
4.4.4 其他遞歸類約束算法··································································.144
4.5 RLS 型自適應濾波算法的實驗仿真與分析················································.150
4.5.1 面向 RGMC 算法的實驗仿真與分析···············································.150
4.5.2 面向 SOV 濾波器算法的實驗仿真與分析 ········································.160
4.5.3 面向 RCGMC 算法的實驗仿真與分析·············································.164
第 5 章 魯棒核自適應濾波算法·········································································.171
5.1 核最小均方算法 ·················································································.172
5.2 核最小 p 次冪算法 ··············································································.174
5.2.1 核最小 p 次冪算法基本原理·························································.175
5.2.2 投影核最小 p 次冪算法·······························································.176
5.2.3 PKLMP 算法的收斂性分析 ··························································.180
5.2.4 PKLMP 算法的改進 ···································································.185
5.3 基於數據復用方法的歸一化核最大相關熵算法··········································.188
5.3.1 核數據復用最大相關熵算法·························································.188
5.3.2 核數據復用廣義最大相關熵算法···················································.191
5.4 帶有反饋機制的核自適應濾波算法 ·························································.194
5.4.1 具有單時滯反饋結構的核最小均方（SF-KLMS）算法 ·······················.195
5.4.2 具有單時滯反饋結構的核廣義最大相關熵（SF-KGMC）算法 ·············.201
5.4.3 具有多時滯反饋結構的非線性遞歸核自適應濾波算法························.208
5.4.4 基於隨機傅裏葉特征的 NR-KNLMS-MF 算法 ··································.215
5.5 基於遞歸方法的核自適應濾波算法 ·························································.219
5.5.1 核遞歸最小二乘算法··································································.219
5.5.2 核遞歸最大相關熵算法·······························································.221
5.5.3 具有加權輸出信息的 KRMC 算法··················································.223
5.5.4 核遞歸廣義最大相關熵算法·························································.225
5.5.5 具有投影加權輸出信息的 KRGMC 算法 ·········································.228
5.6 核自適應濾波算法實驗仿真與分析 ·························································.230
5.6.1 面向 PKLMP 算法的實驗仿真與分析 ·············································.230
5.6.2 面向 KDNR-GMC 算法的實驗仿真與分析·······································.241
5.6.3 面向反饋 KAF 算法的實驗仿真與分析 ···········································.246
5.6.4 面向遞歸 KAF 算法的實驗仿真與分析 ···········································.253
參考文獻 ·······································································································.259