基于非线性高斯-赫尔默特模型的混合整体最小二乘估计

doi:10.11947/j.AGCS.2016.20150157

测绘学报 ›› 2016, Vol. 45 ›› Issue (3): 291-296.doi: 10.11947/j.AGCS.2016.20150157

基于非线性高斯-赫尔默特模型的混合整体最小二乘估计

方兴¹, 曾文宪¹, 刘经南^1,2, 姚宜斌¹, 王勇³

1. 武汉大学测绘学院, 湖北武汉 430079;
2. 武汉大学卫星导航定位技术研究中心, 湖北武汉 430079;
3. 郑州测绘学校, 河南郑州 450015

收稿日期:2015-03-26 修回日期:2015-11-01 出版日期:2016-03-20 发布日期:2016-03-25
通讯作者: 曾文宪,E-mail:wxzeng@sgg.whu.edu.cn E-mail:wxzeng@sgg.whu.edu.cn
作者简介:方兴(1981-),男,博士,主要从事测量数据处理理论与应用的研究。
基金资助:
国家自然科学基金(41404005;41474006;41231174;41274022);中央高校基本科研基金(2042014kf053)

Mixed LS-TLS Estimation Based on Nonlinear Gauss-Helmert Model

FANG Xing¹, ZENG Wenxian¹, LIU Jingnan^1,2, YAO Yibin¹, WANG Yong³

1. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China;
2. Research Center of GNSS, Wuhan University, Wuhan 430079, China;
3. Surveying and Mapping School of Zhengzhou, Zhengzhou 450015, China

Received:2015-03-26 Revised:2015-11-01 Online:2016-03-20 Published:2016-03-25
Supported by:
The National Natural Science Foundation of China(Nos.41404005;41474006;41231174;41274022);The Fundamental Research Founds for the Central Universities(No.2042014kf053)

摘要/Abstract

摘要： 针对EIV模型的系数矩阵同时包含固定量和随机量的情况,通过将系数矩阵中的随机量提取出来纳入平差的随机模型,从而将EIV模型表示为非线性高斯-赫尔默特(Gauss-Herlmert,GH)模型形式,推导了混合LS-TLS(least squares-total least squares, LS-TLS)算法及其精度估计公式。算法适用于系数矩阵包含固定列、固定元素和随机元素的一般情况。模拟实例结果表明,混合LS-TLS算法与已有能够解决系数矩阵同时含固定量和随机量的结构性或加权TLS算法的估计结果一致;混合LS-TLS的估计结果统计上要优于LS或TLS估计结果。

关键词: 混合整体最小二乘估计, 精度估计, EIV模型, 非线性高斯-赫尔默特模型

Abstract: For the case of design matrix in EIV(errors-in-variables) model containing both fixed elements and random elements, this paper proposes a mixed LS-TLS(least squares-total least squares) algorithm and deduces the precision estimator by reformulating an EIV model as a nonlinear Gauss-Helmert model, in which random elements are extracted to the random model of adjustment. This algorithm can be applied to the general design matrix including simultaneously fixed columns, fixed elements and random elements. The example illustrates that the solution of mixed LS-TLS equal the solution of structured or weighted TLS algorithms which can solve mixed LS-TLS problem. Additionally, the solution of mixed LS-TLS statistically superior to solution of LS or TLS.

Key words: mixed LS-TLS estimation, precision estimator, errors-in-variables model, nonlinear Gauss-Herlmert model

中图分类号:

P207

方兴, 曾文宪, 刘经南, 姚宜斌, 王勇. 基于非线性高斯-赫尔默特模型的混合整体最小二乘估计[J]. 测绘学报, 2016, 45(3): 291-296.

FANG Xing, ZENG Wenxian, LIU Jingnan, YAO Yibin, WANG Yong. Mixed LS-TLS Estimation Based on Nonlinear Gauss-Helmert Model[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(3): 291-296.

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基于非线性高斯-赫尔默特模型的混合整体最小二乘估计

Mixed LS-TLS Estimation Based on Nonlinear Gauss-Helmert Model

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