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《Journal of Geodesy and Geodynamics》 2019-01
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A Total Least Squares Algorithm for Non-Equidistant GM(1,1)Model and Its Ill-Posed Problem

TAO Wuyong;HUA Xianghong;LU Tieding;CHEN Xijiang;ZHANG Wei;School of Geodesy and Geomatics,Wuhan University;Faculty of Geomatics,East China University of Technology;School of Resources and Environment Engineering,Wuhan University of Technology;  
In non-equidistant GM(1,1)model there are constant terms without error and random terms with errors in the coefficient matrix.The errors of the coefficient matrix and observation vector are from the same source;the same elements are in the coefficient matrix and observation vector.These same elements ought to have the same corrected value.Therefore,a total least squares algorithm that is suitable to solve non-equidistant GM(1,1)model is deduced in this paper.The ill-posed problem in the non-equidistant GM(1,1)model is taken into consideration,which has an influence on the stability of the calculated results of total least squares.The method,which is to multiply the constant column in coefficient matrix by a constant,is proposed to alleviate the ill-posed problem.
【Fund】: 国家自然科学基金(41674005 41374007 41464001 41501502);; 武汉市测绘研究院博士后创新实践基地科研项目(WGF2016002);; 江西省教育厅科技项目(KJLD12077 GJJ13457);; 江西省自然科学基金(2017BAB203032);; 国家重点研发计划(2016YFB0501405 2016YFB0502601-04);; 江西省数字国土重点实验室开放基金(DLLJ201702);; 精密工程与工业测量国家测绘地理信息局重点实验室开放基金(PF2017-9)~~
【CateGory Index】: P207
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1 XU Ting-xue;CONG Lin-hu;DONG Qi;Naval Aeronautical and Astronautical University;;State Prediction Method for Missile Guidance and Control Systems Based on UGM-ULSSVM[J];上海交通大学学报;2015-12
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