加权整体最小二乘EIV模型与算法——与“加权整体最小二乘EIO模型与算法”一文的讨论

doi:10.11947/j.AGCS.2019.20190155

测绘学报 ›› 2019, Vol. 48 ›› Issue (7): 931-937.doi: 10.11947/j.AGCS.2019.20190155

加权整体最小二乘EIV模型与算法——与“加权整体最小二乘EIO模型与算法”一文的讨论

王乐洋^1,2, 余航³, 邹传义², 鲁铁定²

1. 山东科技大学测绘科学与工程学院, 山东青岛 266590;
2. 东华理工大学测绘工程学院, 江西南昌 330013;
3. 中国矿业大学环境与测绘学院, 江苏徐州 221116

收稿日期:2019-04-28 修回日期:2019-05-09 出版日期:2019-07-20 发布日期:2019-07-26
作者简介:王乐洋(1983-),男,博士,教授,研究方向为大地测量反演及大地测量数据处理。
基金资助:
国家自然科学基金（41664001；41874001）；江西省杰出青年人才资助计划（20162BCB23050）；国家重点研发计划（2016YFB0501405）

EIV models and algorithms of weighted total least squares problem^*: discuss with “Weighted total least square adjustment EIO model and its algorithms”

WANG Leyang^1,2, YU Hang³, ZOU Chuanyi², LU Tieding²

1. Collage of Geomatics, Shandong University of Science and Technology, Qingdao 266590, China;
2. Faculty of Geomatics, East China University of Technology, Nanchang 330013, China;
3. School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China

Received:2019-04-28 Revised:2019-05-09 Online:2019-07-20 Published:2019-07-26
Supported by:
The National Natural Science Foundation of China (Nos. 41664001; 41874001); The Outstanding Youth Talents in Jiangxi Province (No. 20162BCB23050); The National Key Research and Development Program (No. 2016YFB0501405)

摘要/Abstract

摘要： 加权整体最小二乘方法是一种能同时顾及EIV（errors-in-variables）模型中系数矩阵和观测向量误差的参数估计方法。根据不同的应用场景，EIV模型则表现出不同的结构特征。"加权整体最小二乘EIO模型与算法"一文采用EIO模型处理EIV模型中的结构化问题^*。为了将其与现有方法进行对比，本文罗列出4种处理EIV模型结构特征的方法，并归纳了8种参数估计公式。同时从精度评定的角度讨论了整体最小二乘解的一阶及更高阶精度近似评定方法。需要强调的是，针对EIV模型及其参数估计理论可以从函数模型、随机模型和参数估计方法3个方面展开研究，但各方法殊途同归。

关键词: EIV模型, 加权整体最小二乘算法, 精度评定, 系数矩阵, 参数估计

Abstract: A weighted total least squares (WTLS) method is a kind of parameter estimation method which takes into account the observation errors in both the observation vector and the coefficient matrix of the EIV (errors-in-variables) model. The EIV model presents different structural characteristics in terms of different application scenarios. A EIO model is proposed by the paper "Weighted total least square adjustment EIO model and its algorithms" to deal with the structural problem of the EIV model^*. In order to compare the EIO model method with the existing EIV model parameter estimation method, four kinds of methods are listed to deal with the structural characteristics of the EIV model, and eight parameter estimation formulas are summed up. Furthermore, the first-order and higher-order approximate precision estimation methods of WTLS solutions are discussed. It is emphasized that the EIV model and its parameter estimation theory can be developed from three aspects:functional model, stochastic model and the WTLS parameter estimation method. Although different methods are proposed, the problem is solved in an equivalent way.

Key words: EIV model, weighted total least squares algorithm, precision estimation, coefficient matrix, parameter estimation

中图分类号:

P207

王乐洋, 余航, 邹传义, 鲁铁定. 加权整体最小二乘EIV模型与算法——与“加权整体最小二乘EIO模型与算法”一文的讨论[J]. 测绘学报, 2019, 48(7): 931-937.

WANG Leyang, YU Hang, ZOU Chuanyi, LU Tieding. EIV models and algorithms of weighted total least squares problem^*: discuss with “Weighted total least square adjustment EIO model and its algorithms”[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(7): 931-937.

参考文献

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加权整体最小二乘EIV模型与算法——与“加权整体最小二乘EIO模型与算法”一文的讨论

EIV models and algorithms of weighted total least squares problem^*: discuss with “Weighted total least square adjustment EIO model and its algorithms”

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加权整体最小二乘EIV模型与算法——与“加权整体最小二乘EIO模型与算法”一文的讨论

EIV models and algorithms of weighted total least squares problem*: discuss with “Weighted total least square adjustment EIO model and its algorithms”

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EIV models and algorithms of weighted total least squares problem^*: discuss with “Weighted total least square adjustment EIO model and its algorithms”