基于累积量的递归最小二乘算法研究

从基于累积量的均方误差（ＣＭＳＥ）准则，本文推导了一种基于累积量的递归最小二乘（ＣＲＬＳ）算法．并从信号检验和估计的角度对三阶ＣＲＩＳ算法中出现的加权求和系数给出的一种物理解释，以说明其抗高斯噪声的机理．本文提出应根据三种不同条件下信号的最优估计来确定最佳窗口函数的原则，并进一步证明了在极大似（ＭＬ）和线性均方（ＬＭＳ）估计意义下的最佳窗口都是矩形窗而非Ｄｅｌｏｐｏｕｌｏｓ和Ｇｉａｎｎａｋｉｓ建议的Ｈａｍｍｉｎｇ窗~［３］。仿真实验证实：ＣＲＬＳ算法采用矩形窗确定比采用Ｈａｍｍｉｎｇ窗具有更上的结果偏差。

A Study on Cumulant-Based RLS Algorithm

On the basis of Cumulant-based Mean Square Error (CMSE) criteria, a new kind of cumulant-based Recursive Lease Square (CRLS) algoritm is proposed. To better understand the Gaussian noise re jection property of this algoritm a physical explanation on a the weighted summing coefficient which plays an importnat role in th4e CRLS algorithm, is given. After that three rots used for choosing optimal window func tion are obtained bud on signal detection and estimation theory. It is concluded that the optimal window func tions based on ML and LMS estimations are both rectangles, not Hamming window as suggested by Delopoulos and Giannakis in 3]. Our simulations prove that the results of CRLS algorithm of rectangular window show less bias compared with that of Hamming window.