顾及设计矩阵随机误差的最小二乘组合新解法

姚宜斌; 孔建

doi:10.13203/j.whugis20130030

顾及设计矩阵随机误差的最小二乘组合新解法

姚宜斌¹,
孔建^1,2

¹ 武汉大学测绘学院,湖北武汉,430079;² 俄亥俄州立大学地球科学学院,美国哥伦布,43210

基金项目: 国家自然科学基金资助项目(41174012,41274022)；国家863计划资助项目(2013AA122502)；国家教育部新世纪优秀人才支持计划资助项目(NCET-12-0428)

详细信息

作者简介:
姚宜斌,教授,博士生导师,现从事测量数据处理基础理论与方法研究。

中图分类号: P207.2
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出版历程
- 收稿日期: 2013-04-10
- 修回日期: 2014-09-04
- 发布日期: 2014-09-04

A New Combined LS Method Considering Random Errors of Design Matrix

YAO Yibin¹,
KONG Jian^1,2

¹School of Geodesy and Geomatics,Wuhan University,129Luoyu Road,Wuhan 430079,China;²School of Earth Science,Ohio State University,Columbus,OH 43210,USA

Funds: The National Natural Science Foundation of China,Nos.41174012,41274022;the National 863Program of China,No.2013AA122502;the Ministry of Education Program for New Century Excellent Talents Project,NECT.-12-0428.

More Information

Author Bio:
YAO Yibin,PhD,professor,specializes in surveying data processing.

摘要

摘要: 目的提出了一种顾及设计矩阵随机误差的最小二乘组合解法(combined least square,CLS),该算法适用于整体最小二乘(TLS)的参数估计。给出了整体最小二乘平差新算法下的精度评定公式,解决了传统TLS解算方法难以进行严密的精度评定的难题,并通过算例验证了新算法的可行性和正确性。
- 整体最小二乘 /
- 奇异值分解法 /
- 迭代法 /
- 虚拟观测值 /
- 精度评定
Abstract: Objective A new combined LS(CLS)method is proposed which considers the random error in a designmatrix after a brief introduction of TLS and its iteration algorithm and the SVD algorithm.The newalgorithm can be applied for TLS parameter estimation,so that TLS can be integrated with classicalLS in theory.By proposing rigorous accuracy assessment formulas for TLS under the new algorithm,this paper solves the bottleneck problem which restricts the application of TLS,and then shows thefeasibility and correctness of the new method through examples.The research results are meaningfulnot only for TLS theory,but also for the whole data processing theory.
- TLS /
- SVD method /
- iteration method /
- virtual observations /
- accuracy assessment

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参考文献(1)

[1]

van Loan G C.An Analysis of the Total Least-Squares Problem[J].SIAM J Numer Anal,1980,17:883-893[2] Yu Jincheng.On the Solvability of the Total LeastSquares Problem[J].Journal of Nanjng NormalUniversity(Nature Science),1996,19(1):13-16(俞锦成.关于整体最小二乘问题的可解性[J].南京师大学报(自然科学版),1996,19(1):13-16)[3] Kong Jian,Yao Yibin,Wu Han.Iterative Methodfor Total Least-Squares[J].Geomatics and Infor-mation Science of Wuhan University,2010,35(6):711-714(孔建,姚宜斌,吴寒.整体最小二乘的迭代解法[J].武汉大学学报 · 信息科学版,2010,35(6):711-714)[4] van Huffel S,Zha Hongyuan.The Total LeastSquares Problem[J]. Handbook of Statistics,1993,9:377-407[5] Hu Shengwu,Tao Benzao.Nonlinear Error Propa-gation and Its Application in GIS[J].Journal ofWuhan Technical University of Surveying and1031武汉大学学报 · 信息科学版2014年9月Mapping,1997,22(2):129-131(胡圣武,陶本藻.非线性模型的误差传播及其在GIS中的应用[J].武汉测绘科技大学学报,1997,22(2):129-131)[6] Qiu Weining,Tao Benzao,Yao Yibin.The Theoryand Method of Surveying Data Processing[M].Wu-han:Wuhan University Press,2008(邱卫宁,陶本藻,姚宜斌,等.测量数据处理理论与方法[M].武汉:武汉大学出版社,2008)[7] Burkhard S.Total Least-Sqares(TLS)for GeodeticStraight-Line and Plane Adjustment[J].Anno lxvBollettino Di Geodesiae Scienze Affinin,2006,65(3):141-166[8] Krystek M,Anton M.A Weighted Total Least-Squares Algorithm for Fitting a Straight Line[J].Meas Sci Technol,2007,18:3438-3442[9] Ding Keliang,Ou Jikun,Zhao Chunmei.Mthod ofLeast-Squares Prthogonal Curve Fitting[J].Scienceof Surveying and Mapping,2007,32(3):17-19(丁克良,欧吉坤,赵春梅.正交最小二乘曲线拟合法[J].测绘科学,2007,32(3):17-19)[10]Akyilmaz O.Total Least Squares Solution of Coor-dinate Transformation[J].Survey Review,2007(1):68-80[11]Neri F,Saitta G,Chiofalo S.An Accurate andStraightforward Approach to Line Regression Anal-ysis of Error-Affected Experimental Data[J].JPhys E:Sci Instrum,1989,22:215-217[12]Mahboub V.On Weighted Total Least-Squares forGeodetic Transformations[J].J Geod,2011,DOI: 10.1007/s00190-011-0524-5

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顾及设计矩阵随机误差的最小二乘组合新解法

作者简介: 姚宜斌,教授,博士生导师,现从事测量数据处理基础理论与方法研究。

计量

出版历程

A New Combined LS Method Considering Random Errors of Design Matrix

Author Bio: YAO Yibin,PhD,professor,specializes in surveying data processing.

计量

出版历程

目录

作者简介:
姚宜斌,教授,博士生导师,现从事测量数据处理基础理论与方法研究。

Author Bio:
YAO Yibin,PhD,professor,specializes in surveying data processing.