| 非等间距GM(1,1)模型的总体最小二乘算法及其病态问题 |
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| 引用本文： | 陶武勇,花向红,鲁铁定,陈西江,张伟.非等间距GM(1,1)模型的总体最小二乘算法及其病态问题[J].大地测量与地球动力学,2019,39(1):45-50. |
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| 作者姓名： | 陶武勇 花向红 鲁铁定 陈西江 张伟 |
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| 作者单位： | 武汉大学测绘学院,武汉市珞喻路129号,430079;东华理工大学测绘工程学院,南昌市广兰大道418号,330013;武汉理工大学资源与环境工程学院,武汉市珞狮路122号,430070 |
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| 基金项目： | 国家自然科学基金;国家自然科学基金;国家自然科学基金;国家自然科学基金;武汉市测绘研究院博士后创新实践基地科研项目;江西省教育厅科技项目;江西省教育厅科技项目;江西省自然科学基金;国家重点研发计划;国家重点研发计划;江西省数字国土重点实验室开放基金;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 |
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| 摘 要： | 在非等间距GM(1,1)模型中，系数矩阵中有无误差的常数项和有误差的随机项，并且系数矩阵与观测向量误差同源，即系数矩阵与观测向量中有相同的元素存在，这些相同元素应该有相同的改正数，为此本文推导了一种适合非等间距GM(1,1)模型求解的总体最小二乘算法。同时，考虑到非等间距GM(1,1)模型中存在病态问题时影响总体最小二乘计算结果的稳定性，提出对系数矩阵常数列乘以某一常数的方法，以改善病态问题。
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| 关 键 词： | 总体最小二乘 病态问题 非等间距GM(1 1)模型 条件数 稳定性 |
A Total Least Squares Algorithm for Non-Equidistant GM(1,1) Model and Its Ill-Posed Problem |
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| TAO Wuyong,HUA Xianghong,LU Tieding,CHEN Xijiang,ZHANG Wei.A Total Least Squares Algorithm for Non-Equidistant GM(1,1) Model and Its Ill-Posed Problem[J].Journal of Geodesy and Geodynamics,2019,39(1):45-50. |
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| Authors: | TAO Wuyong HUA Xianghong LU Tieding CHEN Xijiang ZHANG Wei |
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| Abstract: | 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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| Keywords: | total least squares ill-posed problem non-equidistant GM(1 1) model condition number stability |
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