广义岭估计在矩阵病态问题中的应用  

Application of Generalized Ridge Estimation in Matrix Ill-conditioned Problems

作　　者：王其腾 吴风华 WANG Qi-teng;WU Feng-hua(College of Mining Engineering,North China University of Science and Technology,Tangshan Hebei 063210,China)

机构地区：[1]华北理工大学矿业工程学院,河北唐山063210

出　　处：《华北理工大学学报（自然科学版）》2022年第2期29-34,共6页Journal of North China University of Science and Technology：Natural Science Edition

基　　金：河北省自然科学基金(D2019209598)。

摘　　要：针对工程测量中经常出现的设计矩阵病态问题,采用广义岭估计的估计方法对设计矩阵病态进行处理。同时应用最小二乘估计、岭估计与主成分估计分别对具体测量数据进行处理,最后利用均方误差及2-范数2种运算对估计结果进行分析。结果表明:相对于其他2种估计方法,广义岭估计在处理设计矩阵病态问题时具有更好的效果。Aiming at the problem of bad condition of design matrix,which is common in engineering research,Generalized ridge estimation method was used to process bad condition design matrix.The specific measurement data were processed by using least squares estimation,ridge estimation and principal component estimation separately,and finally the estimation results were analyzed by using two operations such as mean square error and 2 norms.The results show that generalized ridge estimation is better than the other two estimation methods when dealing with the problem of adverse design ill-conditioned matrix.

关 键 词：岭估计 主成分估计 广义岭估计 矩阵病态 

分 类 号：P207.2[天文地球—测绘科学与技术]