Comparison of Several Methods for Outlier Estimation

doi:10.11947/j.AGCS.2016.20130745

Abstract

Abstract: Computational problem of gross errors estimation is discussed based on the mean shift model, and the gross errors estimation formulas of the observed statistical correlation data snooping method are given. The relationships of gross errors estimation of the data snooping method, the method of simultaneous locating and evaluating multidimensional gross errors (LEGE), quasi-accurate detection of gross errors (QUAD) method and the partial least-squares (PLS) method are discussed. It is proved that ① in the case of correlated observations, calculation of gross errors estimation of the PLS method and the QUAD method are equivalent. However, these two methods are different with the data snooping method and the LEGE method; ② in the case of uncorrelated and unequal weight observations, calculation of gross errors estimation of the QUAD method, the PLS method and the data snooping method are equivalent, but these three methods are different with the LEGE method; ③ in the case of uncorrelated and equal weight observations, calculation of gross errors estimated value of these four methods are equivalent. Finally, the case studies verify the conclusions.

Key words: mean shift data snooping, outlier estimation, the method of simultaneous locating and evaluating multidimensional gross errors(LEGE), quasi-detection of gross errors(QUAD), partly least squares(PLS)

CLC Number:

P207

LU Tieding. Comparison of Several Methods for Outlier Estimation[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(6): 656-662.

References

[1] 周江文. 经典误差理论与抗差估计[J]. 测绘学报, 1989, 18(2):115-120. ZHOU Jiangwen. Classical Theory of Errors and Robust Estimation[J]. Acta Geodaetica et Cartographica Sinica, 1989, 18(2):115-120.
[2] BAARDA W. A Testing Procedure for Use in Geodetic Networks[M]. Delft:Netherlands Geodetic Commission, Publication on Geodesy, 1968.
[3] 杨元喜. 抗差估计理论及其应用[M]. 北京:八一出版社, 1993. YANG Yuanxi. Robust Estimation Theory and Its Applications[M]. Beijing:Bayi Publishing House, 1993.
[4] YANG Yuanxi, SONG Lijie, XU Tianhe. Robust Estimator for Correlated Observations Based on Bifactor Equivalent Weights[J]. Journal of Geodesy, 2002, 76(6-7):353-358.
[5] 孙海燕, 黄华兵, 王喜娜. 多维平差问题粗差的局部分析法[J]. 测绘学报, 2012, 41(1):54-58. SUN Haiyan, HUANG Huabing, WANG Xi'na. Local Analysis Method on Gross Error of Multidimensional Adjustment Problem[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(1):54-58.
[6] WOLF P R, GHILANI C D. Adjustment Computations:Statistics and Least Squares in Surveying and GIS[M]. 3rd ed. New York:Wiley, 1997.
[7] 於宗俦, 李明峰. 多维粗差的同时定位与定值[J]. 武汉测绘科技大学学报, 1996, 21(4):323-329. YU Zongchou, LI Mingfeng. Simultaneous Location and Evaluation of Multidimensional Gross Errors[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1996, 21(4):323-329.
[8] OU Jikun. A New Method of Identifying and Locating Gross Errors:Quasi-accurate Detection[J]. Chinese Science Bulletin, 1999, 44(23):2200-2204.
[9] 欧吉坤. 粗差的拟准检定法(QUAD法)[J]. 测绘学报, 1999, 28(1):15-20. OU Jikun. Quasi-accurate Detection of Gross Errors (QUAD)[J]. Acta Geodaetica et Cartographica Sinica, 1999, 28(1):15-20.
[10] GUO Jianfeng, OU Jikun, WANG Haitao. Quasi-accurate Detection of Outliers for Correlated Observations[J]. Journal of Surveying Engineering, 2007, 133(3):129-133.
[11] 王爱生, 欧吉坤. 部分最小二乘平差方法及在粗差定值与定位中的应用[J]. 测绘科学, 2005, 30(2):70-72. WANG Aisheng, OU Jikun. Method of Partly Least Squares and Application in Gross Error Location and Estimation[J]. Science of Surveying and Mapping, 2005, 30(2):70-72.
[12] 徐培亮. 可剔除多个粗差的F-T法[J]. 武汉测绘科技大学学报, 1987, 12(2):41-46. XU Peiliang. A F-T Method for Outliers[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1987, 12(2):41-46.
[13] 宋力杰, 杨元喜. 均值漂移模型粗差探测法与LEGE法的比较[J]. 测绘学报, 1999, 28(4):295-300. SONG Lijie, YANG Yuanxi. Comparison between Data Snooping and LEGE[J]. Acta Geodaetica et Cartographica Sinica, 1999, 28(4):295-300.
[14] 刘根友, 郝晓光, 柳林涛. 粗差检定的两种途径[J]. 大地测量与地球动力学, 2005, 25(3):29-33. LIU Genyou, HAO Xiaoguang, LIU Lintao. Two Approaches to Gross Error Detection[J]. Journal of Geodesy and Geodynamics, 2005, 25(3):29-33.
[15] 王海涛, 欧吉坤, 袁运斌, 等. 估计观测值粗差三种方法的等价性讨论[J]. 武汉大学学报(信息科学版), 2013, 38(2):162-166. WANG Haitao, OU Jikun, YUAN Yunbin, et al. On Equivalence of Three Estimators for Outliers in Linear Model[J]. Geomatics and Information Science of Wuhan University, 2013, 38(2):162-166.
[16] 李德仁, 袁修孝. 误差处理与可靠性理论[M]. 武汉:武汉大学出版社, 2002. LI Deren, YUAN Xiuxiao. Error Processing and Reliability Theory[M]. Wuhan:Wuhan University Press, 2002.
[17] 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. ZHOU Jiangwen, HUANG Youcai, YANG Yuanxi, et al. Robust Least Squares Method[M]. Wuhan:Huazhong University of Science and Technology Press, 1997.
[18] 王金岭, 陈永奇. 粗差数学期望平移模型的理论研究[J]. 武汉测绘科技大学学报, 1995, 20(2):146-150. WANG Jinling, CHEN Yongqi. A Research on the Mean Shift Outlier Models[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1995, 20(2):146-150.
[19] 宋力杰, 杨元喜. 论粗差修正与粗差剔除[J]. 测绘通报, 1999(6):5-6, 38. SONG Lijie, YANG Yuanxi. Discussion of Outlier Correction Model and Deleting Model[J]. Bulletin of Surveying and Mapping, 1999(6):5-6, 38.
[20] 郭建锋. 模型误差理论若干问题研究及其在GPS数据处理中的应用[D]. 武汉:中国科学院测量与地球物理研究所, 2007. GUO Jianfeng. Theory of Model Errors and Its Applications in GPS Data Processing[D]. Wuhan:Institute of Geodesy and Geophysics of Chinese Academy of Sciences, 2007.
[21] KNIGHT N L, WANG Jinling, RIZOS C. Generalised Measures of Reliability for Multiple Outliers[J]. Journal of Geodesy, 2010, 84(10):625-635.
[22] 王金岭, 陈永奇. 论观测值的可靠性度量[J]. 测绘学报, 1994, 23(4):252-258. WANG Jinling, CHEN Yongqi. On the Reliability Measure of Observations[J]. Acta Geodaetica et Cartographica Sinica, 1994, 23(4):252-258.