几种粗差估值方法的比较

doi:10.11947/j.AGCS.2016.20130745

测绘学报 ›› 2016, Vol. 45 ›› Issue (6): 656-662.doi: 10.11947/j.AGCS.2016.20130745

几种粗差估值方法的比较

鲁铁定^1,2,3

1. 东华理工大学测绘工程学院, 江西南昌 330013;
2. 长安大学地质工程与测量学院, 陕西西安 710054;
3. 流域生态与地理环境监测国家测绘地理信息局重点实验室, 江西南昌 330013

收稿日期:2013-12-09 修回日期:2016-03-08 出版日期:2016-06-20 发布日期:2016-06-29
作者简介:鲁铁定(1974-),男,博士,教授,研究方向为误差理论与测量平差。E-mail:tdlu@whu.edu.cn
基金资助:
国家自然科学基金(41464001;41374007);测绘地理信息公益性行业科技专项(201512026);江西省教育厅科技项目(KJLD12077;GJJ13457);中国博士后基金(2012M511962);江西省远航工程计划(2013);江西省中青年教师发展计划访问学者专项(2012132)

Comparison of Several Methods for Outlier Estimation

LU Tieding^1,2,3

1. School of Geomatics, East China University of Technology, Nanchang 330013, China;
2. School of Geological and Surveying Engineering, Chang'an University, Xi'an 710054, China;
3. Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, Nanchang 330013, China

Received:2013-12-09 Revised:2016-03-08 Online:2016-06-20 Published:2016-06-29
Supported by:
The National Natural Science Foundation of China(Nos.41464001;41374007);National Department Public Benefit Research Foundation of Surveying, Mapping and Geoinformation (No.201512026);Science and Technology Project of the Education Department of Jiangxi Province (Nos. KJLD12077;GJJ13457);China Postdoctoral Science Foundation (No.2012M511962);Voyage Project of Jiangxi Province (No.2013);Visiting Scholar Project of Faculty Development of Jiangxi Province (No.2012132)

摘要/Abstract

摘要： 基于均值漂移模型,重点讨论粗差估值的计算问题,给出了观测值统计相关时数据探测法(data snooping)的粗差估值公式。探讨数据探测法粗差估值与粗差的同时定位与定值法(LEGE)、拟准检定法(QUAD)、部分最小二乘法(PLS)的粗差估值之间的关系,证明当观测值统计相关时,部分最小二乘法和QUAD法在粗差估值的计算上具有等价性,与数据探测法和LEGE法都不一致。当观测值统计独立且不等权时,QUAD法、PLS法和数据探测法具有等价性,与LEGE法在粗差估值上不同;当观测值统计独立且等权时,4种方法在粗差估值计算上具有等价性。最后通过算例验证了结论。

关键词: 数据探测法, 粗差估值, 粗差的同时定位与定值法(LEGE), 拟准检定法(QUAD), 部分最小二乘法(PLS)

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)

中图分类号:

P207

鲁铁定. 几种粗差估值方法的比较[J]. 测绘学报, 2016, 45(6): 656-662.

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

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几种粗差估值方法的比较

Comparison of Several Methods for Outlier Estimation

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