Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem

WANG Leyang; XU Guangyu

doi:10.13203/j.whugis20140275

Volume 41 Issue 2

Feb. 2016

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Geomatics and Information Science of Wuhan University > 2016 > 41(2): 255-261. > DOI: 10.13203/j.whugis20140275

WANG Leyang, XU Guangyu. Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem[J]. Geomatics and Information Science of Wuhan University, 2016, 41(2): 255-261. DOI: 10.13203/j.whugis20140275

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Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem

WANG Leyang^1,2,
XU Guangyu^1,3

1.
Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem1 Faculty of Geomatics, East China Institute of Technology, Nanchang 330013, China;
2.
Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, Nanchang 330013, China;
3.
School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China

Funds: The Project of Key Laboratory of Mapping from Space, NASG(K201502);The National Natural Science Foundation of China, Nos.41204003, 41161069, 41304020;National Department Public Benefit Research Foundation (Surveying,Mapping and Geoinformation), No. 201512026;Science and Technology Project of the Education Department of Jiangxi Province, Nos. KJLD12077, KJLD14049;The Project of Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, No.WE2015005;Scientific Research Foundation of ECIT, No. DHBK201113.

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Received Date: February 28, 2015
Published Date: February 04, 2016

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Abstract

Abstract

Considering the situation that the weight matrix of observation vector and coefficient matrix may be inaccurate, an available algorithm is introduced in this paper, which is derived on the basis of combining the Helmert variance component estimation with a kind of fast weighted total least squares algorithm in the errors-in-variables models. And the derivative process of the fast weighted total least squares is described in detail and the comparison with three other algorithms is implemented in this paper. Using the fast weighted total least squares algorithm combining Helmert variance component estimation derived in this paper, the stochastic model and the unknown parameters of the functional model can be solved simultaneously. Three empirical examples, two straight line fitting and one linear parameter estimation, are also used to investigate the application of posteriori estimation of stochastic model on weighted total least squares problem. Results show that the algorithm is very effective.
- weighted total least squares,
- variance components,
- line fitting,
- posteriori estimation

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[1]	Schaffrin B, Wieser A. On Weighted Total Least-squares Adjustment for Linear Regression[J]. Journal of Geodesy, 2008, 82(7):415-421
[2]	Mahboub V. On Weighted Total Least-squares for Geodetic Transformations[J].Journal of Geodesy, 2012, 86(5):359-367
[3]	Amiri-Simkooei A R, Jazaeri S. Weighted Total Least Squares Formulated by Standard Least Sq-uares Theory[J]. Journal of Geodetic Science, 2012, 2(2):113-124
[4]	Cui Xizhang, Yu Zongchou, Tao Benzao, et al. Generalized Surveying Adjustment (New Edition)[M].Wuhan:Wuhan University Press, 2005(崔希璋, 於宗俦, 陶本藻, 等. 广义测量平差(新版)[M]. 武汉:武汉大学出版社, 2005)
[5]	Liu Zhiping, Zhang Shubi. Variance-covariance Component Estimation Method Based on Generalization Adjustment Factor[J].Geomatics and Information Science of Wuhan University, 2013, 38(8):925-929(刘志平, 张书毕. 方差-协方差分量估计的概括平差因子法[J].武汉大学学报·信息科学版, 2013, 38(8):925-929)
[6]	Wang Leyang, Xu Caijun, Zhang Chaoyu. A Two-step Method to Determine Relative Weight Ratio Factors in Joint Inversion[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(1):19-24(王乐洋, 许才军, 张朝玉. 一种确定联合反演中相对权比的两步法[J].测绘学报,2012, 41(1):19-24)
[7]	Amiri-simkooei A R. Application of Least Squares Variance Component Estimation to Errors-in-Variables Models[J]. Journal of Geodesy, 2013, 87(10-12):935-944
[8]	Xu P, Liu J. Variance Components in Errors-in-Variables Models:Estimability, Stability and Bias Analysis[J]. Journal of Geodesy, 2014, 88(8):719-734
[9]	Neri F, Saitta G, Chiofalo S. An Accurate and Straightforward Approach to Line Regression Analysis of Error-affected Experimental Data[J]. Journal of Physics E:Scientific Instruments, 1989, 22(4):215-217
[10]	Wang Leyang. Research on Theory and Application of Total Least Squares in Geodetic Inversion[D]. Wuhan:Wuhan University, 2011(王乐洋. 基于总体最小二乘的大地测量反演理论及应用研究[D]. 武汉:武汉大学, 2011)
[11]	Wang Leyang. Trilateration Net's Coordinate Adjustment Based on Total Least Squares[J]. Journal of Geodesy and Geodynamics, 2012, 32(6):81-85(王乐洋. 测边网坐标的总体最小二乘平差方法[J].大地测量与地球动力学, 2012, 32(6):81-85)
[12]	Yao Yibin, Kong Jian. A New Combined LS Method Considering Random Errors of Design Matrix[J]. Geomatics and Information Science of Wuhan University, 2014, 39(9):1028-1032(姚宜斌,孔建. 顾及设计矩阵随机误差的最小二乘组合新解法[J]. 武汉大学学报·信息科学版, 2014, 39(9):1028-1032)
[13]	Shen Y, Li B, Chen Y. An Iterative Solution of Weighted Total Least-squares Adjustment[J]. Journal of Geodesy, 2011, 85(4):229-238

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