权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

STUDY OF GLOBAL CONVERGENCE OF ADAPTIVE IIR FILTER BASED ON PSEUDO LINEAR REGRESSION METHOD

基于伪线性回归方法的自适应IIR滤波器全局收敛性研究

基本信息

批准号：
09650489
负责人：
MATSUMOTO Naoki
金额：
$ 1.6万
依托单位：
MEIJI UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

项目摘要

The convergence analysis of the pseudo linear regression method (which is equal to output error RLS method with forgetting factor) has been done and its performance has been compared with other adaptive IIR filtering algorithms such as normalized LMS method, equation error RLS method with forgetting factor, unit norm equation error LMS method.(1) The fastest convergence velocity in the initial phase under high SNR environment is marked by equation error RLS method with forgetting factor. We have explained this result by using a simple statistical model theoretically.(2) The abrupt change of the characteristics of unknown system causes the slow convergence of equation error RLS method. In case of the output error RLS method with forgetting factor, the convergence velocity is always almost equal even in the initial phase or in the period just after the abrupt change of the characteristics of unknown system.(3) The slow convergence of the equation error RLS method after the abrupt change … More of the characteristics of the unknown system can be improved by reinitializing the covariance matrix of the signal vector. This technique is also valid to output RLS method.(4) In case of output error RLS method with forgetting factor, the degradation of ERLE can be prevented by using small step size in the update formula for parameter vector. But, in case of equation error method, the degradation of ERLE can not be prevented by step size control.(5) The parameter vector of the output error RLS method converges to a local optimal solution if unknown system does not satisfy the strictly positive real condition. The theoretical resolution to this hard problem has resulted in fail. However, if we increase the order of the adaptive IIR filter up to three times of that of unknown system, the identification of impulse response is possible within sufficient accuracy under high SNR environment. Hence if we apply the system reduction technique to this result, we can carry out the approximate identification of the unknown systems which do not satisfy strictly positive real condition.(6) Detection of the abrupt change of SNR and characteristic of unknown system is possible by using NLMS adaptive filter and the author's formula. The development of the adaptive IIR filter which enables those detection is left as the future task. Less

对伪线性回归方法（相当于带遗忘因子的输出误差RLS方法）的收敛性进行了分析，并与归一化LMS方法、带遗忘因子的方程误差RLS方法、单位范数方程误差LMS方法等自适应IIR滤波算法的性能进行了比较。(1)在高信噪比环境下，方程误差RLS方法在初始阶段收敛速度最快。我们用一个简单的统计模型从理论上解释了这一结果。(2)未知系统特性的突变导致方程误差RLS法收敛缓慢。对于带遗忘因子的输出误差RLS方法，即使在初始阶段或未知系统特性突变后的一段时间内，收敛速度也几乎相等。(3)方程误差RLS法在突变后的慢收敛性 ...更多信息通过重新初始化信号向量的协方差矩阵，可以改善未知系统的特性。该方法也适用于输出RLS方法。(4)对于带遗忘因子的输出误差RLS方法，通过在参数向量的更新公式中采用小步长，可以防止ERLE的退化。但是，在方程误差法的情况下，ERLE的退化不能通过步长控制来防止。(5)当未知系统不满足严格正真实的条件时，输出误差RLS方法的参数向量收敛于局部最优解。对这一难题的理论解决已经失败。然而，如果我们增加自适应IIR滤波器的阶数到未知系统的阶数的三倍，则可以在高信噪比环境下在足够的精度内识别冲激响应。因此，如果我们将系统降阶技术应用于这一结果，我们可以对不满足严格正真实的条件的未知系统进行近似辨识。(6)利用NLMS自适应滤波器和作者的公式，可以检测信噪比的突变和未知系统的特性。使这些检测的自适应IIR滤波器的发展是留给未来的任务。少