等式约束病态加权EIV平差模型的主成分解法  

Principal Component Solution of Ill-conditioned Weighted EIV Adjustment Model with Equality Constraint

作　　者：翁烨 邵德盛 WENG Ye;SHAO Desheng(Faculty of Land Resource Engineering,Kunming University of Science and Technology,Kunming 650093,China;Yunnan Earthquake Agency,Kunming 650041,China)

机构地区：[1]昆明理工大学国土资源工程学院,云南昆明650093 [2]云南省地震局,云南昆明650041

出　　处：《测绘与空间地理信息》2023年第2期34-38,共5页Geomatics & Spatial Information Technology

基　　金：李建成院士工作站(2015IC015);国家重点研发计划课题——中国大陆主要活动构造断裂带的分段运动特征研究(2018YFC1503604)资助。

摘　　要：合理的等式约束条件有利于提高参数解的精度。针对病态总体最小二乘问题,考虑等式约束条件,对EIV平差模型进行线性化,通过对奇异值分析设置截取门限,在等式约束下利用主成分方法得到一种迭代解法,对参数估值进行精度评定。本文设计了两个算例,验证了加权最小二乘估计、加权总体最小二乘估计、等式约束加权总体最小二乘估计以及本文方法估计。本文方法对等式约束病态EIV模型估计具有促进性,提升了病态EIV平差模型参数估计的可靠性。Reasonable equality constraint condition can improve the precision of parameter solution.For the ill-conditioned total least squares problem,considering equality constraints,the EIV adjustment model is linearized.By setting the intercept threshold for singular value analysis,an iterative solution is obtained by using principal component method under equality constraints,and the accuracy of parameter estimation is evaluated.In this paper,two examples are designed to verify the weighted least squares estimation,the weighted total least squares estimation,the weighted total least squares estimation with equality constraints,and the method estimation in this paper.The method in this paper has a promoting effect on the estimation of the EIV model with equality constraints,which improves the reliability of the parameter estimation of the EIV adjustment model.

关 键 词：等式约束 病态总体最小二乘 线性化 奇异值 主成分估计 

分 类 号：P209[天文地球—测绘科学与技术]