摘要
以往整体最小二乘的研究是在二维基础上探讨模型的适用性,但从二维延伸到多维的过程中,会引入过多的自变量与因变量误差,而在模型解算过程中,又不能完全考虑每一个误差变量,造成了误差的偏执,形成整体最小二乘最优结果的虚假现象。本文对二维延伸到多维的整体最小二乘、所产生的误差偏执、模型变异问题进行分析,引入了多维正交整体最小二乘,避开了误差变量的影响,使得二维、多维的整体最小二乘解算结果都可以达到最优。
The past total least squares discussed the applicability of the model in the two-dimensional. It will introduce too many errors of the independent variables and the dependent variable in the process of extending the multi-dimensional from two-dimensional. The error of each variable cannot be considered in the process of solving the model. As a result, the paranoia of the error is caused. So, the false phenomenon of the Total least squares opti-mal results form. This paper analyzes the paranoia of error and model variation in the process of extending to the multi-dimensional from two-dimensional, and then introduces the multi-dimensional orthogonal total least squares. The model avoids the impact of error variables, and makes the two-dimensional, multi-dimensional total least squares achieve optimal results.
出处
《科技广场》
2014年第10期29-33,共5页
Science Mosaic
基金
精密工程与工业测量国家测绘局重点实验室开放基金项目资助(编号:PF2013-9)
关键词
正交整体
最小二乘
曲面拟合
多维正交
Total Least Squares
Orthogonal Total Least Squares
Least Squares
Surface Fitting
Multi-Di-mensional Orthogonal