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测绘学报  2015 

抗差加权整体最小二乘模型的牛顿-高斯算法

DOI: 10.11947/j.AGCS.2015.20130704, PP. 602-608

Keywords: 整体最小二乘,抗差估计,牛顿-高斯法,标准化残差,中位数

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Abstract:

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。

References

[1]  FELUS Y A. Application of Total Least Squares for Spatial Point Process Analysis[J]. Journal of Surveying Engineering, 2004, 130(3): 126-133.
[2]  SCHAFFRIN B, LEE I, FELUS Y, et al. Total Least-squares (TLS) for Geodetic Straight-line and Plane Adjustment[J]. Bollettino di Geodesia e Scienze Affini, 2006, 65(3): 141-168.
[3]  MARKOVSKY I, VAN HUFFEL S. Overview of Total Least Squares Methods[J]. Signal Processing, 2007, 87(10): 2283-2302.
[4]  SCHAFFRIN B, FELUS Y A. On the Multivariate Total Least-squares Approach to Empirical Coordinate Transformations: Three Algorithms[J]. Journal of Geodesy, 2008, 82(6): 373-383.
[5]  CHEN Yi, LU Jue, ZHENG Bo. Application of Total Least Squares to Space Resection[J]. Geomatics and Information Science of Wuhan University, 2008, 33(12): 1271-1274. (陈义, 陆珏, 郑波. 总体最小二乘方法在空间后方交会中的应用[J]. 武汉大学学报: 信息科学版, 2008, 33(12): 1271-1274.)
[6]  SCHAFFRIN B, WIESER A. On Weighted Total Least-squares Adjustment for Linear Regression[J]. Journal of Geodesy, 2008, 82(7): 415-421.
[7]  NEITZEL F. Generalization of Total Least-squares on Example of Unweighted and Weighted 2D Similarity Transformation[J]. Journal of Geodesy, 2010, 84(12): 751-762.
[8]  SHEN Y Z, LI B F, CHEN Y. An Iterative Solution of Weighted Total Least Squares Adjustment[J]. Journal of Geodesy, 2011, 85(4): 229-238.
[9]  XU P L, LIU J N, SHI C. Total Least Squares Adjustment in Partial Errors-in-variables Models: Algorithm and Statistical Analysis[J]. Journal of Geodesy, 2012, 86(8): 661-675.
[10]  BAARDA W. A Testing Procedure for Use in Geodetic Networks[J]. Netherlands Geodetic Commission Publication on Geodesy: New Series, 1968, 2(5): 45-53.
[11]  OU Jikun. A New Method to Detect Gross Errors—Quasi-accurate Detection Method[J]. Chinese Science Bulletin, 1999, 44(16): 1777-1781. (欧吉坤. 一种检测粗差的新方法——拟准检定法[J]. 科学通报, 1999, 44(16): 1777-1781.)
[12]  ROUSSEEUW P J, LEROY A M. Robust Regression and Outlier Detection[M]. New York: John Wiley and Sons, 1987.
[13]  ZHOU Jiangwen, HUANG Youcai, YANG Yuanxi, et al. Robust Least Squares Method[M]. Wuhan: Huazhong University of Science and Technology Press, 1997. (周江文, 黄幼才, 杨元喜, 等. 抗差最小二乘法[M]. 武汉: 华中理工大学出版社, 1997.)
[14]  YANG Y. Robust Estimation of Geodetic Datum Transformation[J]. Journal of Geodesy, 1999, 73(5): 268-274.
[15]  YANG Yuanxi, SONG Lijie, XU Tianhe. Robust Parameter Estimation for Geodetic Correlated Observations[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(2): 95-99. (杨元喜, 宋力杰, 徐天河. 大地测量相关观测抗差估计理论[J]. 测绘学报, 2002, 31(2): 95-99.)
[16]  YANG Y X, SONG L J, XU T H. Robust Estimator for Correlated Observations Based on Bifactor Equivalent Weights[J]. Journal of Geodesy, 2002, 76(6-7): 353-358.
[17]  XU P L. Sign-constrained Robust Least Squares, Subjective Breakdown Point and the Effect of Weights of Observations on Robustness[J]. Journal of Geodesy, 2005, 79(1-3): 146-159.
[18]  CHEN Yi, LU Jue. Performing 3D Similarity Transformation by Robust Total Least Squares[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(5): 715-722. (陈义, 陆珏. 以三维坐标转换为例解算稳健总体最小二乘方法[J]. 测绘学报, 2012, 41(5): 715-722.)
[19]  LU J, CHEN Y, LI B F, et al. Robust Total Least Squares with Reweighting Iteration for Three-dimensional Similarity Transformation[J]. Survey Review, 46(334): 28-36.
[20]  GONG Xunqiang, LI Zhilin. A Robust Mixed LS-TLS Based on IGGII Scheme[J]. Geomatics and Information Science of Wuhan University, 2014, 39(4): 462-466. (龚循强, 李志林. 一种利用IGG Ⅱ方案的稳健混合总体最小二乘方法[J]. 武汉大学学报: 信息科学版, 2014, 39(4): 462-466.)
[21]  GONG Xunqiang, LI Zhilin. A Robust Weighted Total Least Squares Method[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(9): 888-894. (龚循强, 李志林. 稳健加权总体最小二乘法[J]. 测绘学报, 2014, 43(9): 888-894.)

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