基于输入信号方向和滤波结构自正交化的自适应方法研究

项目名称： 基于输入信号方向和滤波结构自正交化的自适应方法研究

项目编号： No.61201321

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 电子学与信息系统

项目作者： 智永锋

作者单位： 西北工业大学

项目金额： 23万元

中文摘要： 工程问题中自适应滤波算法的复杂度、鲁棒性、收敛性和失调量经常不相容，各性能之间需要权衡，自正交化的自适应方法提供了一种"权衡"的方法。本项目将基于自正交化的自适应方法，从输入信号方向、滤波结构、综合考虑输入信号和滤波结构三方面进行研究，以提高自适应滤波性能并实现有效的权衡。为了解决仿射投影算法迭代方向与引起估计输出误差的方向不一致问题，分析估计权值在迭代方向引起的误差，提出并建立新算法及其收敛性和跟踪性的随机统计模型；通过研究参数化离散时间系统的平衡实现，建立新的自适应滤波结构，使得系统可控与可观Grammian矩阵最大与最小特征值的比值和迭代参数的敏感度最小化，并有效降低计算复杂度；通过分析"布朗运动"激励的输入信号方向同平衡实现结构之间的联系，建立优化的自适应滤波算法。本项目的研究成果将进一步拓展输入信号方向的概念和系统结构的设计方法，对系统辨识、信道均衡等理论的发展具有重要意义。

中文关键词： 自适应滤波；最小均方误差；仿射投影；平衡实现；算法

英文摘要： Ideally, one would like to have a computationally-simple and numerically-robust adaptive filter with high rate of convergence and small misadjustment that can be implemented easily on a computer. As in any engineering problem, these desirable characteristics, in most cases, are incompatible with each other and some kind of trade-off is needed. Algorithms such as self-orthogonalizing adaptation algorithms attempt to reduce the complexity, by trading-off on convergence rate. We aim at improving the performance (achieving better trade-off) by developing new adaptation algorithms based input vectors and by using "unconventional" structures for adaptive filters. The first part of this project attempts to improve the adaptive filter performance by refining the adaptation algorithm. The normalized least mean square is a very popular algorithm. Unfortunately, for highly colored input signals - with a covariance matrix that exhibits a large dynamic range of eigenvalues - this algorithm suffers from slow convergence. The affine projection algorithms have been proposed to ameliorate this problem. However, for the affine projection algorithms, the iteration direction is the direction vector, and the iteration error of the adaptive filter is caused by the input vector. These two directions are not the same, which leads more

英文关键词： Adaptive Filtering；Least Mean Square Error；Affine Projection；Balanced Realization；Algorithm