测绘学报 ›› 2015, Vol. 44 ›› Issue (6): 602-608.doi: 10.11947/j.AGCS.2015.20130704

• 大地测量学与导航 • 上一篇    下一篇

抗差加权整体最小二乘模型的牛顿-高斯算法

王彬1, 李建成1, 高井祥2, 刘超3   

  1. 1. 武汉大学测绘学院, 湖北 武汉 430079;
    2. 中国矿业大学环境与测绘学院 江苏 徐州 221116;
    3. 安徽理工大学测绘学院, 安徽 淮南 232001
  • 收稿日期:2013-12-12 修回日期:2014-11-19 出版日期:2015-06-20 发布日期:2015-07-28
  • 作者简介:王彬(1988—),男,博士生,研究方向为测量数据处理与GPS坐标时间序列分析。E-mail: rainkingwang881107@163.com
  • 基金资助:
    国家973计划(2013CB733300);国家自然科学基金青年基金(41404004);中国博士后科学基金(2014M551790)

Newton-Gauss Algorithm of Robust Weighted Total Least Squares Model

WANG Bin1, LI Jiancheng1, GAO Jingxiang2, LIU Chao3   

  1. 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:2013-12-12 Revised:2014-11-19 Online:2015-06-20 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)

摘要: 基于加权整体最小二乘的牛顿-高斯迭代算法,提出了一种抗差加权整体最小二乘模型。利用标准化残差构造权因子函数,并采用中位数法获得具有抗差性的单位权中误差估值,能同时实现观测空间和结构空间抗差。为获得标准化残差,利用线性近似的协因数传播律推导了加权整体最小二乘残差协因数阵的表达式,并给出模型的迭代计算方法。试验结果表明:对于加权整体最小二乘的粗差处理问题,本文提出的方法具有良好的抗差性能,参数估值与不含粗差时加权整体最小二乘的结果没有显著的差异,性能优于直接由残差构造的稳健加权整体最小二乘模型。

关键词: 整体最小二乘, 抗差估计, 牛顿-高斯法, 标准化残差, 中位数

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

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