带有稀疏化机制的核自适应滤波算法研究

发布时间：2018-01-10 19:06

本文关键词：带有稀疏化机制的核自适应滤波算法研究　出处：《西南大学》2017年硕士论文　论文类型：学位论文

【摘要】：核自适应滤波器(kernel adaptive filter,KAF)作为一类新型的自适应滤波器(AF,adaptive filter),它借助于核方法的手段使得滤波器的学习能力和泛化能力得以进一步增强。然而,KAF在应用过程中会有较大的计算量,同时对设备的存储要求较高。为了应对这一难题,研究者们提出了不同类型的稀疏化办法。作为目前最受欢迎的稀疏化办法,在线矢量量化(VQ,vector quantization)的策略已被广泛应用于KAF以抑制其线性增长的网络结构问题,因此产生了一类量化的核自适应滤波器(QKAF,quantized kernel adaptive filter)。本论文以量化的核最小均方(QKLMS,quantized kernel least mean square)算法为代表,研究了QKAF中存在的不足,从而提出改进的办法并进一步探索新的QKAF。这将对非线性自适应滤波器的理论发展提供坚实的应用支撑,也将进一步促进KAF的实时应用。本文的工作集中在以下几个方面。(1)结构上的改进。为了同时提高QKLMS的收敛速度和滤波精度,提出了一种凸组合的结构,因而产生了凸组合的量化核最小均方(CC-QKLMS,convex combination of quantized kernel least mean square)算法。由于结合了在线VQ办法,CC-QKLMS自然避免了线性增长的网络结构问题。此外,这里组合参数为核宽度,因而只要滤波过程采用了高斯核,这种建议的凸组合结构就能够很容易扩展到新的滤波器中。(2)更新过程的改进。考虑到QKLMS在系数更新的过程中,仅仅使用了当前的预测误差,而忽略了当前输入与“字典”中与其最近的中心的差异性。梯度下降办法被用来执行更新“字典”中与当前元素最近的中心对应的系数,产生了改进的量化核最小均方(M-QKLMS,modified quantized kernel least mean square)算法。不难发现,在M-QKLMS更新过程中引入了一个基于核的加权操作,它反映了当前输入与“字典”中与其最近的中心的差异性,从而利用了更多的信息,能够提高滤波精确性。(3)代价函数的改进。基于均方误差(MSE,mean square error)准则的QKAF在面对非高斯噪声环境时往往会出现一定程度的性能退化。为了提高QKAF应对复杂噪声的能力,这里以最大相关熵准则(MCC,maximum correntropy criterion)作为代价函数,推导出了量化的核最大相关熵(QKMC,quantized kernel maximum correntropy)算法。作为类似QKLMS的简单版本,QKMC表现出了良好的应对脉冲噪声等复杂噪声的能力,理论分析证明了其能够实现比QKLMS更高的滤波精度。(4)综合更新过程与代价函数两方面,基于双边梯度的QKMC(QKMCBG,quantized kernel maximum correntropy based on bilateral gradient)被提出来。QKMC-BG在更新“字典”中与当前输入最近的中心所对应的系数的同时,会同步更新当前的期望信号。这样一来,QKMC-BG考虑了对于输入空间中两个很近的元素,它们对应的期望输出可能离的很远,从而作出必要的调整。作为固定预算版本的QKMC-BG,QKMC-BG-FB(QKMC-BG with fixed budget)能够实现最终的网络大小可控的目的,又不会造成大的精度丢失。
[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.

【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN713

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