Acta Geodaetica et Cartographica Sinica >

2015 , Vol. 44 >Issue 6: 602 - 608

DOI: https://doi.org/10.11947/j.AGCS.2015.20130704

Newton-Gauss Algorithm of Robust Weighted Total Least Squares Model

  • WANG Bin ,
  • LI Jiancheng ,
  • GAO Jingxiang ,
  • LIU Chao
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  • 1. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China;
    2. School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China;
    3. School of Geodesy and Geomatics, Anhui University of Science and Technology, Huainan 232001, China

Received date: 2013-12-12

  Revised date: 2014-11-19

  Online published: 2015-07-28

Supported by

The National Basic Research Program of China(973 Program)(No. 2013CB733300);The National Natural Science Foundation of China(No. 41404004);The China Postdoctoral Science Foundation(No. 2014M551790)

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Abstract

Based on the Newton-Gauss iterative algorithm of weighted total least squares (WTLS), a robust WTLS (RWTLS) model is presented. The model utilizes the standardized residuals to construct the weight factor function and the square root of the variance component estimator with robustness is obtained by introducing the median method. Therefore, the robustness in both the observation and structure spaces can be simultaneously achieved. To obtain standardized residuals, the linearly approximate cofactor propagation law is employed to derive the expression of the cofactor matrix of WTLS residuals. The iterative calculation steps for RWTLS are also described. The experiment indicates that the model proposed in this paper exhibits satisfactory robustness for gross errors handling problem of WTLS, the obtained parameters have no significant difference with the results of WTLS without gross errors. Therefore, it is superior to the robust weighted total least squares model directly constructed with residuals.

Key words： total least squares; robust estimation; Newton-Gauss method; standardized residuals; median

Cite this article

WANG Bin , LI Jiancheng , GAO Jingxiang , LIU Chao . Newton-Gauss Algorithm of Robust Weighted Total Least Squares Model[J]. Acta Geodaetica et Cartographica Sinica, 2015 , 44(6) : 602 -608 . DOI: 10.11947/j.AGCS.2015.20130704

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