通用EIV平差模型的线性化估计算法  

Linearization Estimation Algorithm for Universal EIV Adjustment Model

作　　者：曾文宪[1] 刘泽邦 方兴[1] 李玉兵 ZENG Wenxian;LIU Zebang;FANG Xing;LI Yubing(School of Geodesy and Geomatics,Wuhan University,Wuhan 430079,China;College of Electronic Science and Technology,National University of Defense Technology,Changsha 410073,China;Jinan Real Estate Surveying and Mapping Research Institute,Jinan 250001,China)

机构地区：[1]武汉大学测绘学院,湖北武汉430079 [2]国防科技大学电子科学学院,湖南长沙410073 [3]济南房产测绘研究院,山东济南250001

出　　处：《武汉大学学报（信息科学版）》2021年第9期1284-1290,共7页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金(41674002,41774009);湖北省自然科学基金(2018CFB578)。

摘　　要：通用变量含误差(errors-in-variables, EIV)模型将EIV模型扩展至最一般化的形式,其加权整体最小二乘算法(weighted total least squares, WTLS)同时顾及观测向量、观测向量的系数矩阵和参数向量的系数矩阵中的随机误差。将通用EIV函数模型展开,将二阶项纳入模型的常数项,从而将非线性的通用EIV模型表示为线性的高斯-赫尔默特模型,推导出通用EIV模型的线性化整体最小二乘(linearized total least squares,LTLS)算法和近似精度估计公式。通过模拟数据和实例评估分析可知,LTLS算法与通用EIV模型的WTLS算法估计结果一致,验证了算法的正确性和可行性。当模型含大量估计量时,通用EIV模型的LTLS算法显著提升了计算效率,收敛速度更快。Objectives: The universal errors-in-variables(EIV) model extends the EIV model to the most general form, and the weighted total least squares(WTLS) algorithm is proposed to take into account the random errors in observation vector, observation vector coefficient matrix and parameter coefficient matrix.Methods: In this paper, the universal EIV function model is expanded and the secondorder term is included into the constant term of the model. Thus, the universal EIV model is represented as Gauss-Helmert model in linear form, and the linearized total least squares(LTLS) algorithm and approximate precision estimation formula of the universal EIV model are derived.Results: The estimation results of LTLS algorithm are consistent with that of WTLS algorithm of universal EIV model, which verifies the correctness and feasibility of the proposed algorithm.Conclusions: When the model contains a large number of estimators, the LTLS algorithm of the universal EIV model significantly improves the computational efficiency and converges faster.

关 键 词：通用EIV模型 整体最小二乘 高次项余项 非线性平差 

分 类 号：P207[天文地球—测绘科学与技术]