线性化通用EIV平差模型的正则化解法  

Regularization Method for Linearized General EIV Adjustment Model

作　　者：翁烨 陈丽 王岩[2] Weng Ye;Chen Li;Wang Yan(Geomatics Engineering Department,Sichuan College of Architectural Technology;Information Center,Yunnan Earthquake Agency)

机构地区：[1]四川建筑职业技术学院测绘工程系,四川德阳618000 [2]云南省地震局信息中心,昆明市650200

出　　处：《勘察科学技术》2023年第5期1-5,共5页Site Investigation Science and Technology

基　　金：国家重点研发计划课题(2018YFC1503604)。

摘　　要：通用EIV平差模型具有顾及多种随机误差的优势,在其加权线性化基础上,引入正则化准则,添加拉格朗日目标函数,通过对目标函数的最小化,导出线性化加权通用EIV平差模型对应的正则化解式;给出确定正则化参数的U曲线法和正则化矩阵的构造方法。该文通过两个算例计算加权总体最小二乘估计、线性化估计、岭估计以及正则化估计,验证了正则化方法对通用EIV模型的加权线性化估计具有促进性,病态情形下同样适用,提升了参数估值的可靠性。The general EIV adjustment model has the advantage of taking into account a variety of random errors.Based on its weighted linearization,a regularization criterion is introduced,and a lagrangian objective function is added.By minimizing the objective function,the regularization solution formula corresponding to the linearized weighted general EIV adjustment model is derived.The U curve method for determining regularization parameter and the construction method of regularization matrix are given.In this paper,the weighted totals least squares estimation,linearization estimation,ridge estimation and regularization estimation are calculated through two examples.It is verified that the regularization method can promote the weighted linearization estimation of the general EIV model and is also applicable in illconditioned cases,which improves the reliability of parameter estimation.

关 键 词：通用EIV平差模型 线性化 加权总体最小二乘算法 正则化 U曲线法 

分 类 号：P207.2[天文地球—测绘科学与技术]