摘要
采用GHM方法将EIV模型在最优解处线性化,得到解的近似方差。然后,将EIV模型表达成与Gauss-Markov模型相似的形式,利用标准最小二乘理论推导EIV模型的解及近似方差矩阵,得到与已有算法等价的结论。最后,推导观测值估值和残差的统计性质,建立起一整套EIV模型参数估计和精度评定的体系。
First,the EIV model is linearized at the optimal solution through the GHM method and the approximate variance matrix is derived.Then,the EIV model is reformulated in the form of the Gauss-Markov model.The solution to EIV model and its approximate dispersion matrix are derived using the standard least squares theory,which is equivalent to the existing results.Finally,the statistical properties of the estimation of observations and residuals are derived and the system of parameter estimation and accuracy assessment of EIV model are established.
作者
谢建
龙四春
XIE Jian;LONG Sichun(Hunan Province Key Laboratory of Coal Resources Clean-Utilization and Mine Environment Protection,Hunan University of Science and Technology,Taoyuan Road,Xiangtan 411201,China)
出处
《大地测量与地球动力学》
CSCD
北大核心
2019年第5期544-546,550,共4页
Journal of Geodesy and Geodynamics
基金
国家自然科学基金(41704007
41877283)
湖南省教育厅科研项目(16C0632)
湖南科技大学博士科研启动基金(E51673)
煤炭资源清洁利用与矿山环境保护湖南省重点实验室开放基金(E21610)~~
关键词
经典最小二乘
变量含误差模型
加权整体最小二乘
直线拟合
classic least squares
error-in-variables(EIV)model
weighted total least squares(WTLS)
line fitting
