摘要
利用最小二乘法讨论三维空间的坐标转换问题,先对已知数据进行中心化处理使得坐标转换化为向量形式的最小二乘线性拟合问题,进而化为矩阵形式的最小二乘问题,最后得到法方程以及最小二乘解.如果已知数据量大且维数高,可通过奇异值分解确定相应的转换参数.和现有方法比较,方法的拟合过程不需迭代,简单易行.算例结果表明,拟合结果和原文数据吻合较好.
Coordinate transformation in three-dimensional space is discussed in this paper by using the least square method.Firstly,the transformation problem between vectors is formulated as a least square problem based on the centralized data,and then the problem is reduced to a linear least square problem in matrix form,and finally the least square solution is obtained from the normal equation,or from the singular value decomposition of an associated matrix if the date is large scale or high-dimensional.The process is simple and feasible without iteration,and the results are consistent with the original data as demonstrated in the examples.
作者
李静
LI Jing(Department of Elementary Education,Army Engineering University of PLA,Nanjing 211106,China)
出处
《数学的实践与认识》
2022年第9期115-120,共6页
Mathematics in Practice and Theory
基金
陆军工程大学基础学科培育基金KYJBJQZL1915。
关键词
坐标转换
最小二乘法
广义逆
奇异值分解
coordinate transformation
least square method
generalized inverse
singular value decomposition
