等式约束病态最小二乘的主成分Liu估计解法  

Principal Component Liu Estimation Method of the Equation Constrained Ⅲ-Conditioned Least Squares

作　　者：翁烨 邵德盛 甘淑[1,3] WENG Ye;SHAO Desheng;GAN Shu(Faculty of Land Resource Engineering,Kunming University of Science and Technology,Kunming Yunnan 650093,China;Yunnan Earthquake Agency,Kunming Yunnan 650041,China;Plateau Mountain Spatial Information Survey Technique Application Engineering Research Center at Yunnan Province’s University,Kunming Yunnan 650093,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 [3]云南省高校高原山地空间信息测绘技术应用工程研究中心,云南昆明650093

出　　处：《广西师范大学学报（自然科学版）》2022年第4期115-125,共11页Journal of Guangxi Normal University:Natural Science Edition

基　　金：李建成院士工作站(2015IC015);国家重点研发计划(2018YFC1503604)。

摘　　要：针对病态平差问题的参数估计,参数之间合理的等式先验信息有助于提高模型解的精度。本文在样本信息和等式先验信息下进行联合计算,基于病态最小二乘平差准则,通过主成分估计和Liu估计,构建一种新的有偏估计算法——主成分Liu估计;推导出等式约束最小二乘的主成分Liu估计参数解式,并利用均方误差最小化原理,导出修正因子的计算式;通过算例验证本文方法的有效性和可靠性,可适用于等式约束病态最小二乘参数求解问题。For the parameter estimation of theⅢ-conditioned adjustment problem,reasonable equality prior information among parameters helps to improve the accuracy of the model solution.The joint calculation is carried out under the sample information and the prior information of the equation.Based on the morbid least squares adjustment criterion,a new biased estimation algorithm,principal component Liu estimation,is constructed through the principal component estimation and Liu estimation.The parameter solution of the principal component Liu estimation with equality constrained least squares is derived,and the formula of correction factor is derived by using the principle of mean square error minimization.The effectiveness and reliability of the proposed method are verified by an example,which can be applied to the problem of solvingⅢ-conditioned least squares parameters with equality constraints.

关 键 词：等式先验信息 主成分估计 Liu估计 主成分Liu估计 修正因子 

分 类 号：O212[理学—概率论与数理统计] P207[理学—数学]