一种相关观测的Partial EIV模型求解方法

王乐洋; 许光煜; 温贵森

doi:10.11947/j.AGCS.2017.20160430

测绘学报 >

2017 , Vol. 46 >Issue 8: 978 - 987

DOI: https://doi.org/10.11947/j.AGCS.2017.20160430

大地测量学与导航

一种相关观测的Partial EIV模型求解方法

王乐洋 ,
许光煜 ,
温贵森

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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. 江西省数字国土重点实验室, 江西南昌 330013;
4. 武汉大学测绘学院, 湖北武汉 430079

王乐洋(1983-),男,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。E-mail:wleyang@163.com

收稿日期: 2016-09-06

修回日期: 2017-06-02

网络出版日期: 2017-09-01

基金资助

国家自然科学基金（41664001；41204003）；江西省杰出青年人才资助计划项目（20162BCB23050）；国家重点研发计划（2016YFB0501405）；江西省教育厅科技项目（GJJ150595）

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A Method for Partial EIV Model with Correlated Observations

WANG Leyang ,
XU Guangyu ,
WEN Guisen

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1. Faculty of Geomatics, East China University of Technology, Nanchang 330013, China;
2. Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, Nanchang 330013, China;
3. Key Laboratory for Digital Land and Resources of Jiangxi Province, Nanchang 330013, China;
4. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China

Received date: 2016-09-06

Revised date: 2017-06-02

Online published: 2017-09-01

Supported by

The National Natural Science Foundation of China (Nos.41664001;41204003);Support Program for Outstanding Youth Talents in Jiangxi Province (No.20162BCB23050);National Key Research and Development Program (No.2016YFB0501405);Science and Technology Project of the Education Department of Jiangxi Province (No.GJJ150595)

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摘要

Partial errors-in-variables（Partial-EIV）模型作为EIV模型的扩展形式，其构造方式更有规律，解算方法更为简便，能有效应用于实际情况。针对已有Partial EIV模型方法未考虑观测向量和系数矩阵存在相关性这一情况，通过提取观测向量和系数矩阵组成的增广矩阵中非重复出现的随机元素，构建更具一般适用性的Partial EIV模型，在该模型的基础上，将特殊假定条件扩展到不限定观测数据相关性的一般情况，详细推导了观测向量和系数矩阵元素相关且不等精度情况下的加权总体最小二乘方法，通过算例试验，并与目前已有的解决EIV模型相关观测情况下的方法进行了比较分析，研究表明本文方法可以提高计算效率，更具一般性，特别是对于观测向量和系数矩阵中存在常数元素和重复元素的情况。

关键词： 总体最小二乘; 相关观测; 部分变量误差模型; 自回归模型

本文引用格式

王乐洋 , 许光煜 , 温贵森 . 一种相关观测的Partial EIV模型求解方法[J]. 测绘学报, 2017 , 46(8) : 978 -987 . DOI: 10.11947/j.AGCS.2017.20160430

Abstract

As an extended form of the errors-in-variables(EIV) model, partial errors-in-variables(Partial EIV) model has more advantages than the previous one, such as regular structure, simple solving method, which make it has a wide range of applications. Considering the situation that the correlation between the observations and elements in coefficient matrix is not taken into account in the existed algorithms derived from Partial EIV model, the non-repetitive random elements in the augmented matrix consisting of observation vector and coefficient matrix are extracted to build a more suitable partial EIV model. Based on this model, the special assumptions are extended to the general case where the observations are correlated, a new weighted total least squares(WTLS)algorithms is derived when the observations and elements in coefficient matrix are heteroscedastic and correlated. Through two examples, the algorithm proposed in this paper and the existed algorithms which consider the correlation of the observation in EIV model are compared and analyzed. Research shows that these algorithms can improve the calculation efficiency and more general, especially for the situation that coefficient matrix consists of constant elements and repeated elements.

Key words： total least squares; correlated observations; partial errors-in-variables; autoregression model

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