本文關鍵詞：帶有稀疏化機制的核自適應濾波算法研究　出處：《西南大學》2017年碩士論文　論文類型：學位論文

  更多相關文章： 核自適應濾波器 網絡結構 在線矢量量化 量化的核最小均方 濾波精度

【摘要】：核自適應濾波器(kernel adaptive filter,KAF)作為一類新型的自適應濾波器(AF,adaptive filter),它借助于核方法的手段使得濾波器的學習能力和泛化能力得以進一步增強。然而,KAF在應用過程中會有較大的計算量,同時對設備的存儲要求較高。為了應對這一難題,研究者們提出了不同類型的稀疏化辦法。作為目前最受歡迎的稀疏化辦法,在線矢量量化(VQ,vector quantization)的策略已被廣泛應用于KAF以抑制其線性增長的網絡結構問題,因此產生了一類量化的核自適應濾波器(QKAF,quantized kernel adaptive filter)。本論文以量化的核最小均方(QKLMS,quantized kernel least mean square)算法為代表,研究了QKAF中存在的不足,從而提出改進的辦法并進一步探索新的QKAF。這將對非線性自適應濾波器的理論發(fā)展提供堅實的應用支撐,也將進一步促進KAF的實時應用。本文的工作集中在以下幾個方面。(1)結構上的改進。為了同時提高QKLMS的收斂速度和濾波精度,提出了一種凸組合的結構,因而產生了凸組合的量化核最小均方(CC-QKLMS,convex combination of quantized kernel least mean square)算法。由于結合了在線VQ辦法,CC-QKLMS自然避免了線性增長的網絡結構問題。此外,這里組合參數為核寬度,因而只要濾波過程采用了高斯核,這種建議的凸組合結構就能夠很容易擴展到新的濾波器中。(2)更新過程的改進。考慮到QKLMS在系數更新的過程中,僅僅使用了當前的預測誤差,而忽略了當前輸入與“字典”中與其最近的中心的差異性。梯度下降辦法被用來執(zhí)行更新“字典”中與當前元素最近的中心對應的系數,產生了改進的量化核最小均方(M-QKLMS,modified quantized kernel least mean square)算法。不難發(fā)現,在M-QKLMS更新過程中引入了一個基于核的加權操作,它反映了當前輸入與“字典”中與其最近的中心的差異性,從而利用了更多的信息,能夠提高濾波精確性。(3)代價函數的改進。基于均方誤差(MSE,mean square error)準則的QKAF在面對非高斯噪聲環(huán)境時往往會出現一定程度的性能退化。為了提高QKAF應對復雜噪聲的能力,這里以最大相關熵準則(MCC,maximum correntropy criterion)作為代價函數,推導出了量化的核最大相關熵(QKMC,quantized kernel maximum correntropy)算法。作為類似QKLMS的簡單版本,QKMC表現出了良好的應對脈沖噪聲等復雜噪聲的能力,理論分析證明了其能夠實現比QKLMS更高的濾波精度。(4)綜合更新過程與代價函數兩方面,基于雙邊梯度的QKMC(QKMCBG,quantized kernel maximum correntropy based on bilateral gradient)被提出來。QKMC-BG在更新“字典”中與當前輸入最近的中心所對應的系數的同時,會同步更新當前的期望信號。這樣一來,QKMC-BG考慮了對于輸入空間中兩個很近的元素,它們對應的期望輸出可能離的很遠,從而作出必要的調整。作為固定預算版本的QKMC-BG,QKMC-BG-FB(QKMC-BG with fixed budget)能夠實現最終的網絡大小可控的目的,又不會造成大的精度丟失。
[Abstract]:Adaptive filter (kernel adaptive nuclear filter, KAF) as a new type of adaptive filter (AF, adaptive, filter), with the help of nuclear methods enable the filter to further enhance the learning ability and generalization ability. However, KAF will have a large amount of calculation in the application process, and the equipment high storage requirements in order to deal with this problem, researchers proposed a sparse way different types. As a sparse way by far the most popular, online vector quantization (VQ, vector quantization) network structure strategy has been widely used in KAF to inhibit its linear growth, resulting in a kind of adaptive filter core (QKAF, quantized kernel quantitative adaptive filter). In this paper, the quantitative nuclear LMS (QKLMS, quantized kernel least mean square) algorithm for the generation of tables in the QKAF Insufficient, thus put forward the improvement measures and the application will provide solid support of the development of the theory of nonlinear adaptive filter to further explore the new QKAF., real-time applications will also further promote the KAF. This paper focuses on the following aspects. (1) the improvement of structure. In order to improve the convergence speed and the precision of the filter QKLMS and we propose a structure of convex combination, resulting in a convex combination of quantitative kernel least mean square (CC-QKLMS, convex combination of quantized kernel least mean square) algorithm. Due to the combination of online VQ, CC-QKLMS natural network structure to avoid the linear growth. In addition, this combination of parameters for the kernel width, so long as the filtering process using the Gauss kernel, convex combination structure of the proposed can be easily extended to the new filter. (2) improve the update process. Considering the QKLMS coefficient in the In the process of updating, only using current prediction error, while ignoring the difference between the current input and the "dictionary" in the nearest center. Can be used to perform gradient descent update "dictionary" in the center of the current element coefficient and recent correspondence, the improved quantization kernel least mean square (M-QKLMS. Modified quantized kernel least mean square) algorithm. It is not difficult to find, in the M-QKLMS update process is introduced based on a weighted kernel operation, it reflects the difference between the current input and the "dictionary" in the nearest center, the use of more information, can improve the filtering accuracy (3) improved. Cost function. Based on the mean square error (MSE, mean square error) criterion QKAF will often appear a certain degree of performance degradation in the face of the non Gauss noise environment. In order to improve the QKAF ability to deal with the complicated noise here. The maximum relative entropy criterion (MCC maximum, correntropy criterion) as the cost function, deduced the maximum relative entropy quantization (QKMC quantized nuclear kernel maximum correntropy) algorithm. As a simple version of similar QKLMS, QKMC showed a good ability to deal with impulse noise and complex noise. Theoretical analysis shows that it can be more to achieve high filtering accuracy than QKLMS. (4) the two comprehensive renewal process and the cost function based on bilateral gradient QKMC (QKMCBG, quantized kernel maximum correntropy based on bilateral gradient) is proposed to.QKMC-BG the input coefficient corresponding to the nearest center at the same time with the current update in the "dictionary", will update expectations the current signal. As a result, QKMC-BG is considered for the two elements close to the input space, their corresponding expected output may be far away, so as to make Necessary adjustment. As a fixed budget version of QKMC-BG, QKMC-BG-FB (QKMC-BG with fixed budget) can achieve the ultimate goal of network size controllable, without causing great accuracy loss.

【學位授予單位】：西南大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN713

【參考文獻】

相關期刊論文 前4條

1 洪丹楓;苗俊;蘇健;吳鑫;潘振寬;;一種變步長凸組合LMS自適應濾波算法改進及分析[J];電子學報;2014年11期

2 郭瑩;侯明云;;基于指數梯度和凸組合的稀疏自適應濾波算法[J];儀器儀表學報;2014年04期

3 芮國勝;苗俊;張洋;王林;;變寬度凸組合變階數LMS自適應濾波算法[J];系統(tǒng)工程與電子技術;2012年03期

4 張新建;龍漢;;W_2~m[a，b]空間中再生核的計算(Ⅰ)[J];計算數學;2008年03期

相關碩士學位論文 前1條

1 苗秋園;核自適應濾波算法的研究[D];浙江大學;2012年

，

本文編號：1406434