基于稳定分布理论的自适应Volterra滤波算法研究

项目名称： 基于稳定分布理论的自适应Volterra滤波算法研究

项目编号： No.60872092

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 赵知劲

作者单位： 杭州电子科技大学

项目金额： 35万元

中文摘要： α31283;定分布能够很好地描述各类脉冲型信号或噪声，Volterra滤波器(VF)能够有效建模非线性系统，项目研究基于α31283;定分布的自适应Volterra滤波方法。 1、利用实对称矩阵对角化分解，推导得到了VF各阶输出的向量内积表达式；基于此结果，提出了基于离散余弦变换的高阶VF结构，该结构大大减少了权系数个数，可降低算法复杂度，也为新算法的研究提供了一条新途径。基于此结构，研究了全解耦二阶VLMS算法、三阶VF的LMP算法，首次提出了变记忆长度二阶VLMP算法。 2、充分利用更多的输入信号和误差信号信息，首次提出了FIR滤波器和VF的三种数据块自适应算法。 3、提出了基于最小P范数准则的自适应格型算法、两种基于格型滤波的二阶VF自适应算法、一种FIR变抽头长度LMP算法、二阶VF变抽头长度LMP算法、分阶VF自适应算法，等。进一步提高了对应类的自适应算法性能。 发表核心期刊以上论文8篇，EI收录2篇，已录用核心期刊以上论文3篇，一本专著待出版；"多通道语音和心音信号的自适应处理与无线传输技术及其应用研究"项目获得2009年度浙江省科学技术二等奖，其中的自适应处理成果是本课题部分研究成果。

中文关键词： Volterra；α31283;定分布；自适应滤波器；高阶Volterra；变记忆长度

英文摘要： Signals and noises with type of impulses can be described by αtable distribution properly. On the other hand, nonlinear systems can be modeled by Volterra filters effectively. Therefore, adaptive Volterra filtering algorithms based on αtable distribution are studied in this project. Firstly, by using the diagonal decomposition of a real symmetric matrix, it is derived that the output of each order of Volterra filter can be represented as an inner product of vectors. Furthermore, from this representation, a structure of a higher order Volterra filter based on the discrete cosine transform (DCT) (DCT-Volterra) is proposed. This structure can greatly reduce the number of weighting coefficients, and therefore, computation complexity can also be reduced. More importantly, it also provides a way to study new algorithms. Specifically, based on this DCT-Volterra structure, a fully decoupled least mean square error algorithm (VLMS) of the second-order Volterra filter and a least mean p-norm filtering algorithm(LMP) of the third-order Volterra filter are analyzed, and an innovative, variable memory length LMP algorithm of the second-order Volterra filter is designed. Secondly, three data block algorithms for FIR filter and the second-order Volterra filter are proposed，respectively, by using the abundant information of input signals and error signals efficiently. Finally，an adaptive lattice filtering algorithm based on the least p-norm criterion, two adaptive algorithms based on the lattice filter for the second-order Volterra filter, variable tap-length LMP algorithms of FIR filter and the second-order Volterra filter, and a novel divided-order LMP algorithm of the second-order Volterra filter are designed and analyzed respectively. The performances corresponding to these types of algorithms are all improved further. Eight papers on kernal journals and two papers indexed by EI have been published. Three accepted papers on kernal journals have been finished too. Also a monograph will be published. The project, "the study on technologies of adaptive processing and wireless transmission of speech and heart signals from multi-channels" was awarded as the scientific and technological prize of Zhejiang province at the second level, where the achievements of the adaptive signal processing are ones of this project.

英文关键词： Volterra; αtable distribution; adaptive filter; higher-order Volterra; variable memory length