α稳定分布噪声环境下DLMP算法的收敛特性分析  

Robustness Analysis of DLMP Algorithm Under α-Stable Noise Environments

作　　者：张金凤[1] 邱天爽[1] 唐洪[1] 

机构地区：[1]大连理工大学电子与信息工程学院

出　　处：《电子学报》2007年第3期515-519,共5页Acta Electronica Sinica

基　　金：国家自然科学基金(No.301702593057047560372081);教育部博士点基金(No.20051401025)

摘　　要：本文给出了分数低阶统计量的一个定理,对DLMP算法的收敛性进行了数学分析和理论证明.包括:DLMP算法代价函数的收敛性证明以及DLMP算法步长因子μ值的选取分析.当p=2时,DLMP算法的代价函数,算法估计结果的无偏性以及算法的步长因子μ值的选取范围均与基于二阶统计量的DLMS算法保持了统一.证明了DLMP算法为DLMS算法在α(1<α≤2)稳定分布噪声环境下的推广.The direct least mean p-norm （DLMP） algorithm is a robust algorithm for time delay estimation under both Guassian and fractional lower order α-stable noise conditions. Based on an important theorem of fractional lower order statistics, this paper gives an integrated mathematical analysis of the convergence property of the DLMP algorithm, including the convergence property of the cost function and the appropriate selection of the convergence parameter μ .In the case of p = 2,it is presented that DLMP algorithm keeps consistent with DLMS algorithm, which is based on second order statistics, involving the cost function, the unbiashess of the estimate and the selection of the convergence parameter. Therefore,this paper proves in theory that DLMP algorithm is a generalization of DLMS algorithm in α-stable distribution noisy environments.

关 键 词：DLMP算法 Α稳定分布 分数低阶统计量 

分 类 号：TN911.7[电子电信—通信与信息系统]