Partial EIV模型的非负最小二乘方差分量估计

王乐洋; 温贵森

doi:10.11947/j.AGCS.2017.20160501

测绘学报 >

2017 , Vol. 46 >Issue 7: 857 - 865

DOI: https://doi.org/10.11947/j.AGCS.2017.20160501

大地测量学与导航

Partial EIV模型的非负最小二乘方差分量估计

王乐洋 ,
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

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。

收稿日期: 2016-10-11

修回日期: 2017-05-27

网络出版日期: 2017-07-25

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）；江西省数字国土重点实验室开放研究基金资助项目（DLLJ201705）；东华理工大学研究生创新专项资金资助项目（DHYC-2016005）

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Non-negative Least Squares Variance Component Estimation of Partial EIV Model

WANG Leyang ,
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

Received date: 2016-10-11

Revised date: 2017-05-27

Online published: 2017-07-25

Supported by

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);the Project of Key Laboratory for Digital Land and Resources of Jiangxi Province(No.DLLJ201705);Innovation Fund Designated for Graduate Students of ECUT(No.DHYC-2016005)

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摘要

Partial Errors-in-Variables（Partial EIV）模型是EIV模型的扩展形式，权阵构造简单，当系数矩阵中存在非随机元素和随机元素时，Partial EIV模型的适用性更强。针对Partial EIV模型中随机模型不准确的情况，将系数矩阵和观测向量分别作为一类数据，本文在该模型的基础上，使用最小二乘方差分量估计方法，推导相关计算公式及迭代算法，分别估计出相应的方差分量估值。并对出现的负方差使用非负最小二乘理论，增加约束条件，对随机模型进行修正，得到更加合理的参数估值。试实验结果表明，本文的方法与其他方差分量估计方法等价。

关键词： Partial EIV模型; EIV模型; 最小二乘方差分量估计; 非负最小二乘

本文引用格式

王乐洋 , 温贵森 . Partial EIV模型的非负最小二乘方差分量估计[J]. 测绘学报, 2017 , 46(7) : 857 -865 . DOI: 10.11947/j.AGCS.2017.20160501

Abstract

As an extended form of the errors-in-variables (EIV) model, and the weight matrix is easy to structure, the applicability is stronger when both non-random elements and random elements exist in the coefficient matrix. According to the inaccurate stochastic model in the Partial EIV model, the coefficient matrix and observation vector are used as a kind of data respectively. The least squares variance component estimation method based on Partial EIV model is used and the relevant calculated formulas and iterative algorithm are derived. Then the corresponded variance components are estimated. The non-negative least squares is used when the negative variance appears, then add constraint condition to correct the rand model, so the estimated parameters are more reasonable. The experiments show that the results obtained by the method of this paper and other methods are equivalent.

Key words： Partial EIV model; EIV model; least squares variance component estimation; non-negative least squares

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