通用EIV平差模型及其加权整体最小二乘估计

doi:10.11947/j.AGCS.2016.20150156

测绘学报 ›› 2016, Vol. 45 ›› Issue (8): 890-894.doi: 10.11947/j.AGCS.2016.20150156

通用EIV平差模型及其加权整体最小二乘估计

曾文宪¹, 方兴¹, 刘经南^1,2, 姚宜斌¹

1. 武汉大学测绘学院, 湖北武汉 430079;
2. 武汉大学卫星导航定位技术研究中心, 湖北武汉 430079

收稿日期:2015-03-25 修回日期:2016-06-10 出版日期:2016-08-20 发布日期:2016-08-31
通讯作者: 方兴,E-mail:xfang@sgg.whu.edu.cn E-mail:xfang@sgg.whu.edu.cn
作者简介:曾文宪(1975-),女,博士,主要从事测量数据处理理论与应用研究。E-mail:wxzeng@sgg.whu.edu.cn
基金资助:
国家自然科学基金（41404005；41474006；41231174；41274022）；中央高校基本科研基金（2042016kf0175）

Weighted Total Least Squares of Universal EIV Adjustment Model

ZENG Wenxian¹, FANG Xing¹, LIU Jingnan^1,2, YAO Yibin¹

1. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China;
2. Research Center of GNSS, Wuhan University, Wuhan 430079, China

Received:2015-03-25 Revised:2016-06-10 Online:2016-08-20 Published:2016-08-31
Supported by:
The National Natural Science Foundation of China (Nos. 41404005;41474006;41231174;41274022);The Fundamental Research Founds for the Central Universities(No. 2042016kf0175)

摘要/Abstract

摘要： 以平差基本理论为基础，提出了EIV（errors-in-variables）平差模型的通用形式，涵盖了间接平差、条件平差、附有参数的条件平差及附有限制条件的间接平差等基本EIV模型形式。基于整体最小二乘估计准则，研究了通用EIV模型的加权整体最小二乘算法，并推导了估计结果的近似精度公式。通用EIV模型及其整体最小二乘算法是对EIV模型估计理论的进一步完善，统一的整体最小二乘算法有利于软件的编程实现，有助于推动EIV模型估计理论的应用。

关键词: 通用EIV平差模型, 加权整体最小二乘算法, 估计精度, 非线性最优化算法

Abstract: This paper proposes the universal errors-in-variables (EIV) adjustment model based on the fundamental adjustment theory, which covers the parametric adjustment model, conditional adjustment model,conditional adjustment model with parameters and parametric adjustment model with constrains. Applying total least squares (TLS) principle, we deduce the weighted TLS (WTLS) algorithm and the approximated precision of the EIV model. The universal EIV adjustment model and its estimator of WTLS contribute to the integrity of theory of EIV model estimation. The proposed uniform WTLS algorithm is appropriate for programming in software, which can contribute to the geodetic application of the theory of the EIV model estimation.

Key words: universal EIV adjustment model, weighted total least squares, precision, nonlinear optimization

中图分类号:

P207

曾文宪, 方兴, 刘经南, 姚宜斌. 通用EIV平差模型及其加权整体最小二乘估计[J]. 测绘学报, 2016, 45(8): 890-894.

ZENG Wenxian, FANG Xing, LIU Jingnan, YAO Yibin. Weighted Total Least Squares of Universal EIV Adjustment Model[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(8): 890-894.

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通用EIV平差模型及其加权整体最小二乘估计

Weighted Total Least Squares of Universal EIV Adjustment Model

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