基于复共线性诊断的抗差正则化方法  

Robust Regularization Method Based on Diagnosis of Multicolinearity

作　　者：马朝忠[1] 归庆明[1] 顾勇为[1] 张宁[1] 

机构地区：[1]信息工程大学理学院,郑州450001

出　　处：《河南科学》2013年第6期728-732,共5页Henan Science

基　　金：国家自然科学基金项目(41174005;40974009);河南省基础与前沿研究计划项目(082300410240);郑州市科技计划攻关项目(0910SGYG21198)

摘　　要：针对测量数据中,法矩阵病态性和观测值粗差同时存在的问题,以复共线性诊断和度量为基础,融合抗差M估计的思想,提出了基于复共线性诊断和度量的抗差正则化方法,并给出了正则化矩阵的选取方法和正则化参数的确定公式及相应的抗差解.通过模拟算例表明,该方法不仅可以抵御病态性带来的不良影响也能消除粗差对估计产生的严重危害.In order to solve the problems of the normal equation being ill-conditioned and observations containing outliers in the large number of measured data processing,a kind of new robust regularization methods based on analyzing and diagnosing of multicolinearity is presented.The choice method of regularization matrix and the calculation formula of regularization parameters are established.Numerical simulation results demonstrate that the new estimator has the characteristics of resisting outliers,high precision and good stability.

关 键 词：不适定问题 正则化方法 复共线性 正则化矩阵 正则化参数 

分 类 号：P207[天文地球—测绘科学与技术] O241.1[理学—计算数学]