一种Partial EIV半参数模型的系统误差处理方法

doi:10.11947/j.AGCS.2018.20160613

测绘学报 ›› 2018, Vol. 47 ›› Issue (1): 25-34.doi: 10.11947/j.AGCS.2018.20160613

一种Partial EIV半参数模型的系统误差处理方法

王乐洋^1,2,3, 熊露雲^1,2

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

收稿日期:2016-12-05 修回日期:2017-11-16 出版日期:2018-01-20 发布日期:2018-02-05
作者简介: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
基金资助:
国家自然科学基金（41664001）；江西省杰出青年人才资助计划（20162BCB23050）；国家重点研发计划（2016YFB0501405）

A Method for Dealing with the Systematic Errors of Partial EIV Semi-parametric Model

WANG Leyang^1,2,3, XIONG Luyun^1,2

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:2016-12-05 Revised:2017-11-16 Online:2018-01-20 Published:2018-02-05
Supported by:
The National Natural Science Foundation of China (No. 41664001);Support Program for Outstanding Youth Talents in Jiangxi Province (No. 20162BCB23050);National Key Research and Development Program(No. 2016YFB0501405)

摘要/Abstract

摘要： 在使用总体最小二乘求解参数时，若观测值中包含系统误差，此时得到的参数估值则会受到系统误差的影响，从而得到不可靠的解，因此必须削弱系统误差对参数估计的影响，以获得相对可靠的解。本文提出在partial errors-in-variables （Partial EIV）模型的基础上给观测值增加非参数部分（系统误差），从而构建Partial EIV半参数模型；基于补偿最小二乘准则进行公式推导，并分别通过选取适当的正则化矩阵及通过L曲线法确定平滑因子。通过算例结果分析表明，与传统方法相比，本文的方法在一定程度上能够削弱系统误差的影响，得到更为可靠的参数解，从而验证了该方法的有效性和可行性。

关键词: Partial EIV半参数模型, 系统误差, 正则化矩阵, L曲线, 平滑因子

Abstract: The estimated values are affected so that they are not reliable if the observations contain systematic errors under the solution of total least squares.Thus the bad effect on the estimated values should be weakened so the relatively reliable solution can be obtained.This paper adds non parametric part (systematic errors) in the partial errors-in-variables (Partial EIV) model,building Partial EIV semi-parametric model.The penalized least square criterion is introduced to derive formula,and choose the proper regularization matrix in the experiments.The smoothing factor is acquired by the method of L-curve.The results of experiments show that the algorithm of Partial EIV semi-parametric model can mitigate systematic errors to a certain extent and obtain the more reliable solution than the traditional method.So the validity of the algorithm is verified.

Key words: Partial EIV semi-parametric model, systematic errors, regularization matrix, L-curve, smoothing factor

中图分类号:

P207

王乐洋, 熊露雲. 一种Partial EIV半参数模型的系统误差处理方法[J]. 测绘学报, 2018, 47(1): 25-34.

WANG Leyang, XIONG Luyun. A Method for Dealing with the Systematic Errors of Partial EIV Semi-parametric Model[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(1): 25-34.

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一种Partial EIV半参数模型的系统误差处理方法

A Method for Dealing with the Systematic Errors of Partial EIV Semi-parametric Model

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