非线性曲线TLS法拟合

如今,整体最小二乘法越来越受到学者们的重视。虽然传统的高斯最小二乘法运用最为广泛,但是由于其只考虑了因变量观测值的误差而认为自变量是精确的,所以与实际观测情况不太符合。而整体最小二乘兼顾了自变量与因变量存在的观测误差,所以在理论上更为严谨且更为符合实际。本文介绍了一种适用性相对广泛的非线性函数整体最小二乘拟合方法。并采用一组模拟数据对该方法进行验证,且与通过最小二乘解算出来的结果进行了比较。对比得出,整体最小二乘法解算出来的结果更接近理论值。

Non-Linear Curve Fitting with TLS Method

Nowadays, the total least square is increasingly paid attention to by the researchers.The traditional least square method is widely used in practice , but it doesn’ t match the practical situation very well because only the error of dependent variable is taken into consideration and the argument is regarded as accurate.However, the total least square is more rigorous in theory and closer to prac-tice with the advantage of taking both dependent variable error and argument error into consideration.This paper introduce a relatively more general TLS method in non-linear curve fitting and use a experiment to check this method compared with LS method.The con-clusion is, TLS method is closer to the theoretical result.