均值漂移模式几种粗差探测法的MDB比较
|
摘要
针对均值漂移模式的几种粗差定位与定值方法,在显著水平和检验功效下,推出最小可探测偏差(minimal detectable bias,MDB)的计算公式。通过数值分析比较,得出观测值独立等精度时,几种方法的MDB的计算结果相同;独立不等精度时,数据探测法、拟准检定法和部分最小二乘法的MDB结果相同,而多维粗差同时定位与定值法略大于其他方法;相关观测情形下,拟准检定法和部分最小二乘法的MDB结果相同,数据探测法的MDB结果最小,多维粗差的同时定位和定值法的MDB结果最大。
Quality control is described by internal and external reliability according to the Delft philosophy. Internal reliability describes the ability to find biases in observational data and is represented accordingly by the minimal detectable bias(MDB). The MDBs formulas of four popular outliers detection methods include data snooping, quasi-accurate detection of gross errors(QUAD), partly least squares(PLS) and the method of simultaneous locating and evaluating multiple gross errors(LEGE) are derived with the given significance level α_0 and given power of test β_0. The numerical example reveals that MDBs are same value when the observations have the same weight. If the clean data are not equally weighted, the MDBs of data snooping are equal to that of QUAD and PLS,but all are slightly smaller than the MDBs of LEGE. If the clean data are correlated observations, the MDBs of QUAD are equal to that of PLS, but both are larger than that of data snooping and smaller than that of LEGE.
Quality control is described by internal and external reliability according to the Delft philosophy. Internal reliability describes the ability to find biases in observational data and is represented accordingly by the minimal detectable bias(MDB). The MDBs formulas of four popular outliers detection methods include data snooping, quasi-accurate detection of gross errors(QUAD), partly least squares(PLS) and the method of simultaneous locating and evaluating multiple gross errors(LEGE) are derived with the given significance level α_0 and given power of test β_0. The numerical example reveals that MDBs are same value when the observations have the same weight. If the clean data are not equally weighted, the MDBs of data snooping are equal to that of QUAD and PLS,but all are slightly smaller than the MDBs of LEGE. If the clean data are correlated observations, the MDBs of QUAD are equal to that of PLS, but both are larger than that of data snooping and smaller than that of LEGE.
引文
[1] Baarda W. A Testing Procedure for Use in Geodetic Networks[J]. Netherlands Geodetic Commission,Publication on Geodesy,1968,2(5):45-53
[2] Yang Yuanxi. Robust Estimation Theory and Its Applications[M]. Beijing: Bayi Publishing House,1993(杨元喜. 抗差估计及其应用[M]. 北京:八一出版社,1993)
[3] Yang Yuanxi. Robust Estimation for Correlated Observations[C]// Proceedings on Robust Estimation. Beijing: Surveying and Mapping Press,1992:14-22(杨元喜.相关观测抗差估计[C]//抗差估计论文集.北京: 测绘出版社,1992)
[4] Yu Zongchou,Li Mingfeng. Simultaneous Location and Evaluation of Multi-dimensional Gross Errors[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1996,21(4):323-329(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)
[5] Ou J K. A New Method of Identifying and Locating Gross Errors: Quasi-accurate Detection[J]. Chin Sci Bull, 1999, 44(23): 2 200-2 204
[6] Ou Jikun. Quasi-Accurate Detection of Gross Errors(QUAD)[J]. Acta Geodaetica et Cartograghica Sinica,1999,28(1):15-20(欧吉坤. 粗差的拟准检定法(QUAD法)[J]. 测绘学报,1999,28(1):15-20)
[7] Wang Aisheng, Ou Jikun. Method of Partly Least Squares and Application in Gross Error Location and Estimation[J]. Journal of Geodesy and geodynamics,2005,30(2):70-72(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]. 大地测量与地球动力学,2005,30(2):70-72)
[8] Xu Peiliang. A F-T Method for Outliers[J]. Journal of Wuhan Technical University of Surveying and Mapping,1987,12(2):41-46(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)
[9] Song Lijie, Yang Yuanxi. Comparison Between Data Snooping and LEGE[J]. Acta Geodaetica et Cartograghica Sinica, 1999,28(1):15-20(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(1):15-20)
[10] Liu Genyou, Hao Xiaoguang, Liu Lintao. Two Approaches to Gross Error Detection[J]. Journal of Geodesy and Geodynamics,2005,25(3):29-33(刘根友,郝晓光,柳林涛. 粗差鉴定的两种途径[J]. 大地测量与地球动力学,2005,25(3):29-33)
[11] Wang Haitao,Ou Jikun, Yuan Yunbin, et al. On Equivalence of Three Estimators for Outliers in Li-near Model[J]. Geomatics and Information Science of Wuhan University, 2013,38(2):162-166(王海涛,欧吉坤,袁运斌,等. 估计观测值粗差的三种方法的等价性讨论[J]. 武汉大学学报·信息学科版,2013,38(2):162-166)
[12] Teunissen P J G. On the Minimal Detectable Biases of GPS Phase Ambiguity Slips[C]. First International Symposium on Real Time Differential Applications of the GPS, Stuttgart,Geomany, 1991
[13] F?rstner W. Reliability Analysis of Parameter Estimation in Linear Models with Applications to Mensuration Problems in Computer Vision[J]. Computer vision,Graphics and Image Procession,1987, 40(3):273-310
[14] Schaffrin B. Reliability Measures for Correlated Observations[J]. Journal of Surveying Engineering,1997,123:126-137
[15] Li Deren, Yuan Xiuxiao. Error Processing and Reliability Theory[M]. Wuhan: Wuhan University Press,2002(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)
[16] Wang Jinling, Chen Yongqi. On the Reliability Measurement of Observations[J]. Acta Geodaetica et Cartograghica Sinica,1994,23(4):252-258(王金岭,陈永奇.论观测的可靠性度量[J].测绘学报,1994,23(4):252-258)
[17] Knight N L, Wang J L, Rizos C. Generalised Measures of Reliability for Multiple Outliers[J]. Journal of Geodesy, 2010,84:625-635
[18] Ou Jikun. On the Reliability for the Situation of Correlated Observations[J]. Acta Geodaetica et Cartograghica Sinica,1999,28(3):189-194(欧吉坤. 相关观测情况的可靠性研究[J]. 测绘学报,1999,28(3):189-194)
[19] Tao Benzao. Statistic Theory and Method of Surveying Data Processing[M].Beijing:Surveying and Mapping Press,2007(陶本藻. 测量数据处理的统计理论和方法[M]. 北京:测绘出版社,2007)
[20] Hewitson S,Lee H K,Wang J. Localizability Analysis for GPS/Galileo Receiver Autonomous Integrity Monitoring[J]. J Nav, 2004, 57(2):245-259
[21] 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)
[22] 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(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)
[23] Song Lijie, Yang Yuanxi. Discussion of Outlier Correction Model and Deleting Model[J]. Bulletin of Surveying and Mapping,1999(6):5-6(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)
[2] Yang Yuanxi. Robust Estimation Theory and Its Applications[M]. Beijing: Bayi Publishing House,1993(杨元喜. 抗差估计及其应用[M]. 北京:八一出版社,1993)
[3] Yang Yuanxi. Robust Estimation for Correlated Observations[C]// Proceedings on Robust Estimation. Beijing: Surveying and Mapping Press,1992:14-22(杨元喜.相关观测抗差估计[C]//抗差估计论文集.北京: 测绘出版社,1992)
[4] Yu Zongchou,Li Mingfeng. Simultaneous Location and Evaluation of Multi-dimensional Gross Errors[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1996,21(4):323-329(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)
[5] Ou J K. A New Method of Identifying and Locating Gross Errors: Quasi-accurate Detection[J]. Chin Sci Bull, 1999, 44(23): 2 200-2 204
[6] Ou Jikun. Quasi-Accurate Detection of Gross Errors(QUAD)[J]. Acta Geodaetica et Cartograghica Sinica,1999,28(1):15-20(欧吉坤. 粗差的拟准检定法(QUAD法)[J]. 测绘学报,1999,28(1):15-20)
[7] Wang Aisheng, Ou Jikun. Method of Partly Least Squares and Application in Gross Error Location and Estimation[J]. Journal of Geodesy and geodynamics,2005,30(2):70-72(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]. 大地测量与地球动力学,2005,30(2):70-72)
[8] Xu Peiliang. A F-T Method for Outliers[J]. Journal of Wuhan Technical University of Surveying and Mapping,1987,12(2):41-46(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)
[9] Song Lijie, Yang Yuanxi. Comparison Between Data Snooping and LEGE[J]. Acta Geodaetica et Cartograghica Sinica, 1999,28(1):15-20(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(1):15-20)
[10] Liu Genyou, Hao Xiaoguang, Liu Lintao. Two Approaches to Gross Error Detection[J]. Journal of Geodesy and Geodynamics,2005,25(3):29-33(刘根友,郝晓光,柳林涛. 粗差鉴定的两种途径[J]. 大地测量与地球动力学,2005,25(3):29-33)
[11] Wang Haitao,Ou Jikun, Yuan Yunbin, et al. On Equivalence of Three Estimators for Outliers in Li-near Model[J]. Geomatics and Information Science of Wuhan University, 2013,38(2):162-166(王海涛,欧吉坤,袁运斌,等. 估计观测值粗差的三种方法的等价性讨论[J]. 武汉大学学报·信息学科版,2013,38(2):162-166)
[12] Teunissen P J G. On the Minimal Detectable Biases of GPS Phase Ambiguity Slips[C]. First International Symposium on Real Time Differential Applications of the GPS, Stuttgart,Geomany, 1991
[13] F?rstner W. Reliability Analysis of Parameter Estimation in Linear Models with Applications to Mensuration Problems in Computer Vision[J]. Computer vision,Graphics and Image Procession,1987, 40(3):273-310
[14] Schaffrin B. Reliability Measures for Correlated Observations[J]. Journal of Surveying Engineering,1997,123:126-137
[15] Li Deren, Yuan Xiuxiao. Error Processing and Reliability Theory[M]. Wuhan: Wuhan University Press,2002(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)
[16] Wang Jinling, Chen Yongqi. On the Reliability Measurement of Observations[J]. Acta Geodaetica et Cartograghica Sinica,1994,23(4):252-258(王金岭,陈永奇.论观测的可靠性度量[J].测绘学报,1994,23(4):252-258)
[17] Knight N L, Wang J L, Rizos C. Generalised Measures of Reliability for Multiple Outliers[J]. Journal of Geodesy, 2010,84:625-635
[18] Ou Jikun. On the Reliability for the Situation of Correlated Observations[J]. Acta Geodaetica et Cartograghica Sinica,1999,28(3):189-194(欧吉坤. 相关观测情况的可靠性研究[J]. 测绘学报,1999,28(3):189-194)
[19] Tao Benzao. Statistic Theory and Method of Surveying Data Processing[M].Beijing:Surveying and Mapping Press,2007(陶本藻. 测量数据处理的统计理论和方法[M]. 北京:测绘出版社,2007)
[20] Hewitson S,Lee H K,Wang J. Localizability Analysis for GPS/Galileo Receiver Autonomous Integrity Monitoring[J]. J Nav, 2004, 57(2):245-259
[21] 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)
[22] 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(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)
[23] Song Lijie, Yang Yuanxi. Discussion of Outlier Correction Model and Deleting Model[J]. Bulletin of Surveying and Mapping,1999(6):5-6(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)