摘要
在空间直角坐标转换等结构变量含误差(errors-in-variables,EIV)模型中,系数矩阵中有部分随机观测值(或其负值)会在系数矩阵的不同位置重复出现。对于随机变量重复出现的结构EIV模型,重复的次数是否应纳入整体最小二乘准则以及重复次数如何纳入,已有研究尚未形成定论。提出了一种通用结构EIV模型,通过引入综合权矩阵来表达不同的平差准则并推导了通用模型的算法;然后采用线性化方法将通用EIV模型转换为Gauss-Helmert模型求解并推导了参数的近似精度公式。从模型分析和数值模拟两方面分别验证了独立随机误差的重复次数不应计入结构整体最小二乘准则。最终确立了结构EIV模型的最优平差准则,并证明了近似精度评定公式是可行有效的。
Objectives:In the structured errors-in-variables(EIV)model encountered in spatial coordinate transformation,part of the random observations(or their negative values)in the coefficient matrix appear repeatedly in different positions.Whether the repetitions of the random errors should be taken into account and how to deal with the repetitions in the adjustment principle,no consensus has been reached up to now.Methods:A generalized structured EIV model is proposed and a synthetic weight is introduced to describe different adjustment principles.The generalized EIV model is transformed to the Gauss-Helmert model through linear approximation.The solution and its approximate variance are derived.Results:It is verified that the repetitions should not be taken into consideration in the adjustment principle from the aspects of model analysis and numerical simulation.Conclusions:The optimal adjustment principle is confirmed and the approximate formula to calculate the accuracy is proved to be feasible and effective.
作者
谢建
周璀
林东方
龙四春
赖咸根
XIE Jian;ZHOU Cui;LIN Dongfang;LONG Sichun;LAI Xiangen(School of Earth Science and Spatial Information Engineering,Hunan University of Science and Technology,Xiangtan 411201,China;College of Advanced Interdisciplinary Studies,Central South University of Forestry and Technology,Changsha 410018,China;National-Local Joint Engineering Laboratory of Geo-spatial Information Technology,Hunan University of Science and Technology,Xiangtan 411201,China;China Construction Fifth Engineering Bureau Civil Engineering Co.Ltd,Changsha 410011,China)
出处
《武汉大学学报（信息科学版）》
EI
CAS
CSCD
北大核心
2024年第12期2223-2231,共9页
Geomatics and Information Science of Wuhan University
基金
国家自然科学基金(42474052,42377453,42074016,42104025,41704007)
湖南省杰出青年科学基金(2024JJ2100)
湖南省自然科学基金(2021JJ30244)
湖南省教育厅资助科研项目(22B0496)。
