加权总体最小二乘平差随机模型的验后估计

王乐洋; 许光煜

doi:10.13203/j.whugis20140275

加权总体最小二乘平差随机模型的验后估计

王乐洋^1,2,
许光煜^1,3

1.
东华理工大学测绘工程学院, 江西南昌, 330013;
2.
流域生态与地理环境监测国家测绘地理信息局重点实验室, 江西南昌, 330013;
3.
武汉大学测绘学院, 湖北武汉, 430079

基金项目: 对地观测技术国家测绘地理信息局重点实验室项目(K201502);国家自然科学基金(41204003, 41161069, 41304020);测绘地理信息公益性行业科研专项(201512026);江西省教育厅科技项目(KJLD12077; KJLD14049);流域生态与地理环境监测国家测绘地理信息局重点实验室项目(WE2015005);东华理工大学博士科研启动金项目(DHBK201113)。

详细信息

作者简介:
王乐洋,博士,副教授,主要研究方向为大地测量反演及大地测量数据处理。wleyang@163.com

中图分类号: P207
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出版历程
- 收稿日期: 2015-02-28
- 发布日期: 2016-02-04

Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem

WANG Leyang^1,2,
XU Guangyu^1,3

1.
Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem1 Faculty of Geomatics, East China Institute of Technology, Nanchang 330013, China;
2.
Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, Nanchang 330013, China;
3.
School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China

Funds: The Project of Key Laboratory of Mapping from Space, NASG(K201502);The National Natural Science Foundation of China, Nos.41204003, 41161069, 41304020;National Department Public Benefit Research Foundation (Surveying,Mapping and Geoinformation), No. 201512026;Science and Technology Project of the Education Department of Jiangxi Province, Nos. KJLD12077, KJLD14049;The Project of Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, No.WE2015005;Scientific Research Foundation of ECIT, No. DHBK201113.

摘要

摘要: 针对随机模型中观测向量和系数矩阵存在定权不准确的问题,提出了一种加权总体最小二乘随机模型验后估计方法。将赫尔默特方差分量估计方法应用于EIV(errors-in-variables)模型中,结合本文推导的加权总体最小二乘方法,对平差问题的函数模型和随机模型同时进行求解。通过采用真实和模拟数据的三个算例对该方法的有效性进行了验证,结果表明随机模型的验后估计方法在解决加权总体最小二乘问题时更合理、有效。
- 加权总体最小二乘 /
- 方差分量 /
- 直线拟合 /
- 验后估计
Abstract: Considering the situation that the weight matrix of observation vector and coefficient matrix may be inaccurate, an available algorithm is introduced in this paper, which is derived on the basis of combining the Helmert variance component estimation with a kind of fast weighted total least squares algorithm in the errors-in-variables models. And the derivative process of the fast weighted total least squares is described in detail and the comparison with three other algorithms is implemented in this paper. Using the fast weighted total least squares algorithm combining Helmert variance component estimation derived in this paper, the stochastic model and the unknown parameters of the functional model can be solved simultaneously. Three empirical examples, two straight line fitting and one linear parameter estimation, are also used to investigate the application of posteriori estimation of stochastic model on weighted total least squares problem. Results show that the algorithm is very effective.
- weighted total least squares /
- variance components /
- line fitting /
- posteriori estimation

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参考文献(13)

[1]	Schaffrin B, Wieser A. On Weighted Total Least-squares Adjustment for Linear Regression[J]. Journal of Geodesy, 2008, 82(7):415-421
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[6]	Wang Leyang, Xu Caijun, Zhang Chaoyu. A Two-step Method to Determine Relative Weight Ratio Factors in Joint Inversion[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(1):19-24(王乐洋, 许才军, 张朝玉. 一种确定联合反演中相对权比的两步法[J].测绘学报,2012, 41(1):19-24)
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[10]	Wang Leyang. Research on Theory and Application of Total Least Squares in Geodetic Inversion[D]. Wuhan:Wuhan University, 2011(王乐洋. 基于总体最小二乘的大地测量反演理论及应用研究[D]. 武汉:武汉大学, 2011)
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施引文献(11)

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2.	王乐洋，孙坚强. 总体最小二乘回归预测模型的方差分量估计. 武汉大学学报(信息科学版). 2021(02): 280-288 . 百度学术
3.	王祝安，陈义，毛鹏宇. 加权整体最小二乘的验后估计在三维坐标转换中的应用. 大地测量与地球动力学. 2018(02): 216-220 . 百度学术
4.	王乐洋，李海燕，陈晓勇. 拟牛顿修正法解算不等式约束加权总体最小二乘问题. 武汉大学学报(信息科学版). 2018(01): 127-132 . 百度学术
5.	陶武勇，鲁铁定，许光煜，杨世安. 稳健总体最小二乘Helmert方差分量估计. 大地测量与地球动力学. 2017(11): 1193-1197 . 百度学术

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文章访问数: 1597
HTML全文浏览量: 71
PDF下载量: 489
被引次数: 11

加权总体最小二乘平差随机模型的验后估计

作者简介: 王乐洋,博士,副教授,主要研究方向为大地测量反演及大地测量数据处理。wleyang@163.com

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出版历程

Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem

期刊类型引用(5)

其他类型引用(6)

计量

出版历程

目录

作者简介:
王乐洋,博士,副教授,主要研究方向为大地测量反演及大地测量数据处理。wleyang@163.com