带有反馈机制的核自适应滤波算法研究

发布时间：2018-04-19 17:21

本文选题：核方法 + 再生核希尔伯特空间　；参考：《西南大学》2016年硕士论文

【摘要】：在信号处理领域,滤波技术有着举足轻重的作用,因为待处理信号或多或少含有外界的干扰,故过滤或减轻这些噪声是很有必要的。经典的滤波技术有:低通滤波、高通滤波、带通滤波以及带阻滤波,然而,这四种滤波技术在噪声频段与信号频段重合时,滤波效果往往不尽人意。自适应滤波器作为现代统计滤波技术,相对于固定滤波器来说,其滤波的频率是自动地适应输入信号的变化。在没有任何有关信号和噪声的先验知识的条件下,自适应滤波器可以利用过去时间已获得的滤波器参数来自动地调整当前时刻的滤波器参数,因此,自适应滤波技术从出现到发展一直倍受人们的关注。然而,随着待处理问题的非线性程度的增加,对非线性自适应滤波方法的要求便越来越高。因此,出现了各种复杂但又性能欠佳的非线性滤波技术,故有效地设计非线性滤波系统逐渐成为研究热点。值得庆幸的是,核函数方法(Kernel Method)有着突出的非线性处理能力,它可以将低维的非线性问题转化到高维的线性问题。而在高维空间(或再生核希尔伯特空间,RKHS)中的内积运算又能有效的利用核技巧进行处理,所以核函数方法一直受到人们的普遍关注。近年来,研究者们创新性地将核函数方法与自适应滤波理论相结合,从而产生了核自适应滤波算法(Kernel Adaptive Filtering Algorithm,KAF),由于其有效的非线性处理能力以及实时处理能力使其成为信号处理和控制领域的重要分支。目前存在的大多数核自适应滤波算法都属于前馈型方法,而本文主要讨论与研究的是带有反馈机制的核自适应滤波算法,本文的主要工作为:(1)通过将前一时刻的输出反馈到当前系统,以探索过去信息对于算法的影响程度;再考虑最简单的瞬时误差函数的优化问题,采用梯度下降法来训练网络的连接权重;最终得到了带有单反馈的核最小均方算法(Kernel Least Mean Square with Single Feedback,SF-KLMS)。由于SF-KLMS过多的调节参数以及抖动性较大的学习率,故在维持其结构的情况下,重新设计了调节参数少且具有平滑学习率的滤波算法,即,带有单反馈变学习率的核自适应滤波器(variable learning rates kernel adaptive filter with single feedback,SF-VLRKAF)。并在加性高斯白噪声的前提下,利用能量守恒定律对SF-VLRKAF进行稳定性的分析,得到了有效的均方收敛条件以及额外均方误差的界限。值得说明的是,SF-KLMS与SF-VLRKAF在结构上考虑前一时刻输出的原因在于:该结构可以让权重更新形式中带有动量项,从而加速算法收敛以及避免局部最小点。最后,将单反馈思想拓展至任意时滞反馈,得到了带任意时滞反馈的核自适应滤波器(kernel adaptive filter with random feedbacks,RFs-KAF)。通过相关的实验仿真,发现了这三种算法有着各自的优势与不足。(2)本文在SF-KLMS、SF-VLRKAF以及RFs-KAF算法中,设计了不同的自适应学习率,目的在于加强算法的滤波或学习性能。其中,SF-VLRKAF所对应的学习率具有调节参数少,变化平滑的特性,从而成为作者进行SF-VLRKAF收敛性分析的重要原因。
[Abstract]:In the field of signal processing, filtering technology plays an important role, because the signal to be treated is more or less containing external interference, so it is necessary to filter or reduce the noise. The classic filtering techniques include low pass filtering, high pass filtering, bandpass filtering and band stop filtering, however, these four filtering techniques are in noise frequency bands and letters. When the number band is reclose, the filtering effect is often unsatisfactory. As a modern statistical filtering technique, the adaptive filter is automatically adapted to the change of the input signal compared with the fixed filter. In the absence of any prior knowledge about the signal and noise, the adaptive filter can use the past time. The obtained filter parameters automatically adjust the filter parameters of the current time, so the adaptive filtering technology has been attracting more and more attention from the emergence to the development. However, with the increase of the nonlinear degree of the problem to be treated, the demand for the nonlinear adaptive filtering method is getting higher and higher. Therefore, various complex but sexual characteristics have appeared. Therefore, it is good to be thankful that the kernel function method (Kernel Method) has a prominent nonlinear processing capability, which can transform the low dimensional nonlinear problem to the high dimensional linear problem, and in the high dimensional space (or the regenerated nuclear Hilbert space). The inner product operation in RKHS can be effectively processed by the kernel technique, so the kernel function method has been widely concerned. In recent years, the researchers combine the kernel function method with the adaptive filtering theory to produce the kernel adaptive filtering algorithm (Kernel Adaptive Filtering Algorithm, KAF). Its effective nonlinear processing ability and real-time processing ability make it an important branch in the field of signal processing and control. Most of the existing kernel adaptive filtering algorithms belong to the feedforward method. This paper mainly discusses and studies the kernel adaptive filtering algorithm with feedback mechanism. The main work of this paper is: (1) The output of the previous moment is fed back to the current system to explore the impact of the past information on the algorithm, and then the optimization problem of the simplest instantaneous error function is considered, and the gradient descent method is used to train the network connection weight; finally, the Kernel Least Mean Square with Single Fe with single feedback is obtained. Edback, SF-KLMS). Due to the excessive adjustment parameters of SF-KLMS and the higher learning rate of jitter, a filtering algorithm with less adjustment parameters and a smooth learning rate is redesigned, that is, a kernel adaptive filter with a single feed back learning rate (variable learning rates kernel adaptive filter with sin) in the case of maintaining its structure. Gle feedback, SF-VLRKAF). And on the premise of additive Gauss white noise, the stability of SF-VLRKAF is analyzed by the law of conservation of energy. The effective mean square convergence condition and the boundary of the extra mean square error are obtained. It is worth explaining that the reason that SF-KLMS and SF-VLRKAF are structurally considering the output at the first time is that the structure is available In order to make the weight renewal form with the momentum term, the algorithm converges and avoids the local minimum point. Finally, the single feedback idea is extended to any time delay feedback, and the kernel adaptive filter (kernel adaptive filter with random feedbacks, RFs-KAF) with any time delay feedback is obtained. The three algorithms have their own advantages and disadvantages. (2) in this paper, in SF-KLMS, SF-VLRKAF and RFs-KAF algorithms, different adaptive learning rates are designed to strengthen the filtering or learning performance of the algorithm. Among them, the corresponding learning rate of SF-VLRKAF has the characteristics of less adjustment parameters and smooth change, thus the author carries out SF-VLRKAF collection. An important reason for the analysis of convergence.

【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TN713

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