本文選題：自適應濾波算法 + 仿射投影算法��； 參考：《重慶郵電大學》2015年碩士論文

【摘要】：自適應濾波器在工程實踐中應用廣泛，如系統(tǒng)辨識、信道均衡、干擾消除、線性與非線性預測等。常見的自適應濾波算法有最小均方算法(Least Mean Square,LMS)與最小二乘算法(Recursive Least Square, RLS)。LMS算法計算復雜度低，但收斂速度緩慢。RLS與其相反，即收斂速度快，但計算復雜度高。為提高LMS的收斂速度，常用仿射投影算法(Affine Projection Algorithm, APA)替代LMS以提高算法收斂速度。但標準APA算法有兩個主要缺點：1.大步長或小正則因子APA算法收斂速度快，但穩(wěn)態(tài)誤差高；小步長或大正則因子APA算法穩(wěn)態(tài)誤差低，但收斂速度慢。因此，標準APA算法不能滿足工程實踐對自適應算法應具有高收斂速度與低穩(wěn)態(tài)誤差性能的需求。2.當系統(tǒng)遭受沖激噪聲干擾時，標準APA算法的跟蹤性能衰減嚴重，即魯棒性能差。本文從提高APA類型算法的跟蹤性能與魯棒性能兩個方面進行研究，具有重要的理論與實踐意義。 首先，本文簡要闡述標準仿射投影算法及其典型的改進算法。 其次，針對APA算法跟蹤性能差的問題，，本文提出一種變正則因子仿射投影算法(Variable Regularization APA, VR-APA)。區(qū)別于傳統(tǒng)文獻中以盡可能使后驗錯誤為零作為標準來推導變正則因子表達式的方法，本文提出通過最小化無噪后驗錯誤矢量信號能量來推導自適應變正則因子表達式的方法。在實踐逼近中，該方法利用測量噪聲的統(tǒng)計方差特性，并提出一種更加光滑且更加容易控制的指數(shù)縮放因子評估方法。除此之外，文中還討論了該算法的穩(wěn)定性能。系統(tǒng)辨識的仿真結果表明新算法比現(xiàn)有方法收斂速度更快且穩(wěn)態(tài)誤差更低。 最后，針對APA算法在沖激噪聲干擾下魯棒性能差的問題，本文提出通過凸組合技術來提高算法跟蹤性能與魯棒性能的方法。仿真實驗結果表明提出算法不僅收斂速度快，穩(wěn)態(tài)誤差低，而且在沖激噪聲干擾下魯棒性能好。
[Abstract]:Adaptive filters are widely used in engineering practice, such as system identification, channel equalization, interference cancellation, linear and nonlinear prediction and so on. The common adaptive filtering algorithms are least Mean squared (LMS) and least square algorithm (RLS).LMS), which have low computational complexity, but slow convergence rate. RLS is the opposite, that is, the convergence speed is fast, but the computational complexity is high. In order to improve the convergence rate of LMS, affine Projection algorithm (LMS) is commonly used instead of LMS to improve the convergence speed of the algorithm. But the standard APA algorithm has two main drawbacks: 1. The large step size or small regular factor APA algorithm converges fast, but the steady-state error is high, while the small step size or large regular factor APA algorithm has a low steady state error but a slow convergence rate. Therefore, the standard APA algorithm can not meet the need of engineering practice that adaptive algorithm should have high convergence rate and low steady-state error performance. When the system is disturbed by impulse noise, the tracking performance of the standard APA algorithm attenuates seriously, that is, the robust performance is poor. This paper focuses on improving the tracking performance and robust performance of APA type algorithms, which has important theoretical and practical significance. First, this paper briefly describes the standard affine projection algorithm and its typical improved algorithm. Secondly, aiming at the poor tracking performance of APA algorithm, a variable variable Regularization APA (VR-APA) algorithm is proposed in this paper. Different from the traditional method of deducing variable canonical factor expressions by minimizing the energy of noise free posteriori error vector signals, this paper presents a method to derive adaptive variable regular factor expressions by minimizing the energy of noise free posteriori error vector signals. In practical approximation, this method utilizes the statistical variance characteristics of measurement noise, and proposes a more smooth and easily controlled exponential scaling factor evaluation method. In addition, the stability of the algorithm is discussed. The simulation results of system identification show that the new algorithm converges faster and the steady-state error is lower than the existing methods. Finally, aiming at the problem of poor robustness of APA algorithm under impulse noise interference, this paper proposes a method to improve the tracking performance and robust performance of the algorithm by convex combination technique. The simulation results show that the proposed algorithm not only has the advantages of fast convergence, low steady-state error, but also good robustness under impulse noise interference.
【學位授予單位】：重慶郵電大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TN713

【參考文獻】

相關期刊論文 前1條

1 師黎明;林云;;基于無噪后驗錯誤矢量信號能量的變正則因子仿射投影算法[J];電子學報;2015年01期

本文編號：1846873