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《ACTA GEODAETICA ET CARTOGRAPHIC SINICA》 1999-01
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Quasi Accurate Detection of gross errors (QUAD)

Ou Jikun (Institute of Geodesy and Geophysics, Laboratory of Dynamical Geodesy, Chinese Academy of Sciences, Wuhan,430077)  
The residuals in the Least Squares have been taken as the studied objects in the vary methods on dealing with gross errors in the past. A new idea and a distinctive method are proposed in this paper, which relate to real errors and their estimators. There exists a determinate and analytic representation relationship between real errors and observation values written as R Δ=- RL . However, the coefficiency matrix R is rank deficient. The unique solution on real errors in this equation can not be got directly. By using the idea of “Quasi Stable Adjustment” created by prof. Zhou Jiangwen for reference, the new concept on “Quasi Accurate Observation” is presented. Then the rank deficiency equation on real errors are resolved by adding the conditions in which the minimum of the norm of the real errors related to quasi accurate observations is restrained. The new method called as “Quasi Accurate Detection of gross errors (QUAD)” is derived in detail. The reliability and accuracy of the new method in detection of gross errors are much higher since the gross errors can be easily distinguished from the estimators of real errors according to their distributed characteristics. By using of this method, not only multiple gross errors can be exactly located and their estimators calculated accurately, but also the co variance matrices of the estimators can be evaluated strictly. The more the gross errors existed in the observations, the more evident the effectiveness of this method is. This method may be suitable to deal with the gross errors existed in different fields of science and engineering. Finally, the method of QUAD is illustrated by the two numerical examples.
【Fund】: 国家自然科学基金 中国科学院资源与生态环境研究重点项目
【CateGory Index】: P207
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Chinese Journal Full-text Database 10 Hits
1 Zhao Shuang;Wang Zhenjie;Wu Shaoyu;Wang Yi;Liu Huimin;Shan Rui;School of Geosciences,China University of Petroleum (East China);Laboratory for Marine Mineral Resources,National Laboratory for Marine Science and Technology;BGP Inc.,CNPC;Offshore Oil Engineering Corporation,CNOOC;Qingdao Institute of Marine Geology,China Geological Survey;;A ship-board acoustic difference positioning method based on selection weight iteration[J];石油地球物理勘探;2017-06
2 TAO Wuyong;LU Tieding;XU Guangyu;YANG Shi'an;Department of Surveying and Mapping,Jiangxi Information Institute of Profession Technology;Faculty of Geomatic,East China Institute of Technology;School of Geodesy and Geomatics,Wuhan University;;Helmert Variance Component Estimation for Robust Total Least Squares[J];大地测量与地球动力学;2017-11
3 Wang Yuli;Bao Weiming;College of Hydrology & Water Resources,Hohai Univ.;;Study of Three-stepwise Robust Correct Effect of Rainfall[J];三峡大学学报(自然科学版);2017-05
4 PAN Yi;YUE Jianping;ZHANG Peng;College of Earth Science and Engineering,Hohai University;;An Algorithm Fusing Robust and Collinear Rank-defect Adjustment[J];海洋测绘;2017-05
5 LIU Ning;DAI Wujiao;LIU Bin;Department of Surveying and Remote Sensing Science,Central South University;Key Lab.of Precise Engineering Surveying & Deformation Disaster Monitoring of Hunan Province;;A interpolation method of deformation monitoring data series[J];测绘科学;2017-09
6 JIANG Chen;ZHANG Shubi;ZHANG Qiuzhao;School of Environment Science and Spatial Information,China University of Mining and Technology;Collaborative Innovation Center for Resource Utilization and Ecological Restoration of Old Industrial Base,China University of Mining & Technology;;Equivalent weight function and robust estimation method with adaptive criterion[J];中国矿业大学学报;2017-04
7 Pan Guanping;Shanghai Marine Geological Exploration and Design CO.,LTD;;Change method of the selecting weight factor based on anti-error weight factor IGGⅢ programs[J];矿山测量;2017-03
8 LI Zhongmei;BIAN Shaofeng;QU Yong;Department of Navigation,Naval University of Engineering;College of Science,Naval University of Engineering;;Robust Total Least Squares Estimation of Space Intersection Appropriate for Multi-images[J];测绘学报;2017-05
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【Co-references】
Chinese Journal Full-text Database 10 Hits
1 ZHAO Feiyan;;Four Parameters Coordinate Transformation Method and Its Application[J];地理空间信息;2016-07
2 PAN Xiong;LV Yuting;WANG Yao;LUO Jing;XU Jingtian;Faculty of Information Engineering,China University of Geosciences;Patent Examination Cooperation Center of the Patent Office,State Intellectual Property Office of the P.R.C;;Research of the Location and Valuation of Gross Error Based on Semi-parametric Adjustment Model[J];武汉大学学报(信息科学版);2016-11
3 DENG Xiaodong;ZHANG Xianyun;ZHANG Jun;WANG Bo;PAN Shaolin;Mining College,Guizhou University;Guizhou Key Laboratory of Comprehensive Utilization of Non-Metallic Mineral Resources,Guizhou University;;Resolution of Polluted Semi-Parametric Model with Wavelet Assisted Quasi-Accurate Detection and Penalized Least Square Estimation[J];大地测量与地球动力学;2016-05
4 NI Fei;FANG Shilong;ZHAO Suzheng;School of Traffic Engineering,Nantong Shipping College;;Application of QUAD Method in Coordinate Transformation[J];测绘地理信息;2015-06
5 ZHANG Jun;DU ZHi-xing;DU Ning;ZHANG Xian-yun;Geomatics College,Shandong University of Science and Technology;Mining College of Guizhou University;;Resolution of polluted semi-parameter model with quasi-accurate detection and penalized least square[J];测绘科学;2014-10
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1 Jiang Bo;;Research on Gross Error Detection Method of Semi-parametric Model[J];铁道勘察;2017-03
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Chinese Journal Full-text Database 1 Hits
1 Zhou Jiangwen(Institute of Geodssy and Ceophysics, Chinese Academy of Science);CLASSICAL THEORY OF ERRORS AND ROBUSTESTIMATION[J];测绘学报;1989-02
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