稳健加权总体最小二乘法

A Robust Weighted Total Least Squares Method

加权总体最小二乘估计没有考虑观测数据中可能存在的粗差。本文基于IGG权函数,采用选权迭代法求解加权总体最小二乘问题。结合模拟数据和真实数据,系统地比较了加权总体最小二乘方法、基于Huber权函数的稳健加权总体最小二乘方法和基于IGG权函数的稳健加权总体最小二乘方法的参数估计结果。通过对比分析表明,两种稳健加权总体最小二乘方法的参数估计结果比加权总体最小二乘方法更加可靠,且以基于IGG权函数的稳健加权总体最小二乘方法为最优。

In weighted total least squares,gross errors of observation data are not taken into consideration.In order to resolve this problem,a robust method of weighted total least squares with reweighting iteration is proposed,which is based on IGG weight function.Thorough experimental evaluation with a large number of simulation datasets and a set of real-life data has been carried out.The results of parameter estimations are systematically compared with weighted total least squares,and robust weighted total least squares based on Huber weight function.It is shown that:1more reliable parameter estimations can be obtained by two robust weighted total least squares;2more importantly,the proposed method performs better than the two others.