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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.
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