加权整体最小二乘EIO模型与算法

doi:10.11947/j.AGCS.2019.20170021

测绘学报 ›› 2019, Vol. 48 ›› Issue (7): 926-930.doi: 10.11947/j.AGCS.2019.20170021

加权整体最小二乘EIO模型与算法

邓兴升¹, 彭思淳¹, 游扬声²

1. 长沙理工大学交通运输工程学院, 湖南长沙 410114;
2. 重庆大学土木工程学院, 重庆 400044

收稿日期:2017-01-12 修回日期:2017-05-10 出版日期:2019-07-20 发布日期:2019-07-26
作者简介:邓兴升(1971-),男,博士,副教授,研究方向为大地测量数据处理。
基金资助:
国家自然科学基金（41671498）；公路地质灾变预警空间信息技术湖南省工程实验室基金（KFJ150602）

Weighted total least square adjustment EIO model and its algorithms

DENG Xingsheng¹, PENG Sichun¹, YOU Yangsheng²

1. School of Traffic and Transportation Engineering, Changsha University of Science & Technology, Changsha 410114, China;
2. School of Civil Engineering, Chongqing University, Chongqing 400044, China

Received:2017-01-12 Revised:2017-05-10 Online:2019-07-20 Published:2019-07-26
Supported by:
The National Natural Science Foundation of China (No. 41671498); The Open Fund of Engineering laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province (No. KFJ150602)

摘要/Abstract

摘要： 构造了加权整体最小二乘EIO（errors-in-observations）模型，只改正独立观测值，观测值协因数阵最简洁，可克服EIV模型缺陷。基于EIO模型推导了参数估计和协因数阵精确迭代算法，实例结果正确，计算效率高。

关键词: 加权整体最小二乘, EIO模型, 参数估计, 协因数阵, 迭代算法

Abstract: EIO (errors-in-observations) model is proposed for the weighted total least squares adjustment problem. The EIO model only corrects the independent observations. The observation cofactor matrix has the simplest structure. The flaw of EIV model is overcome. Based on the EIO model, the precise parameter estimation and cofactor matrix formulations are derived and proved by several examples, which show that the results are correct and the algorithm is efficient.

Key words: weight total least square (WTLS), errors-in-observations (EIO) model, parameter estimation, cofactor matrix, iterative algorithm

中图分类号:

P207

邓兴升, 彭思淳, 游扬声. 加权整体最小二乘EIO模型与算法[J]. 测绘学报, 2019, 48(7): 926-930.

DENG Xingsheng, PENG Sichun, YOU Yangsheng. Weighted total least square adjustment EIO model and its algorithms[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(7): 926-930.

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加权整体最小二乘EIO模型与算法

Weighted total least square adjustment EIO model and its algorithms

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