求解球面拟合的改进总体最小二乘算法

摘要

在球面拟合中,系数矩阵和观测向量的误差同源,均来源于球面点坐标.不同位置有相同元素存在,从理论上讲,这些相同元素应该有相同的改正数,并且非线性形式出现在观测向量中.为此,本文推导了一种改进的总体最小二乘算法,可以很好地克服上述问题.通过算例分析发现,本文方法得到的参数估值更为可靠,证明了本文方法的有效性.%In sphere surface fitting,the errors in the coefficient matrix and observation vector are from the same place,which is the coordinate of the spherical point.The same elements exist in different places.These same elements ought to have the same corrections.The linear form appears in the observation vector.Therefore,an improved total least squares algorithm is deduced which can overcome the above problems.Through analysis of examples,we discover that the parameters obtained from the method in the paper are more reliable.This demonstrates that the method is feasible and effective.