结构加权整体最小二乘模型平差准则的优化选取
Optimal Selection of the Adjustment Principles for Structured Weighted Total Least Squares Model
谢建 1周璀 2林东方 3龙四春 1赖咸根4
作者信息
- 1. 湖南科技大学地球科学与空间信息工程学院,湖南 湘潭,411201
- 2. 中南林业科技大学前沿交叉学科学院,湖南 长沙,410018
- 3. 湖南科技大学地理空间信息技术国家地方联合工程实验室,湖南 湘潭,411201
- 4. 中建五局土木工程有限公司,湖南 长沙,410011
- 折叠
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.
Abstract
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.
关键词
结构变量含误差模型/加权整体最小二乘/Gauss-Helmert模型/平差准则/精度评定Key words
structured errors-in-variables model/weighted total least squares/Gauss-Helmert model/adjustment principles/accuracy evaluation引用本文复制引用
出版年
2024
NETL
NSTL
万方数据