GPS高程拟合的加权总体最小二乘抗差估计

Robust Weighted Total Least Squares Estimation for GPS Leveling Fitting

结合标准化方差,构造了基于Huber、IGG和IGGⅢ三种权函数的加权总体最小二乘抗差模型,并运用选权迭代法予以求解。GPS高程拟合数据处理实例表明,基于Huber、IGG和IGGⅢ三种权函数的稳健加权总体最小二乘抗差方法对误差和粗差具有较好的削弱和消除效果,其中基于IGGⅢ权函数的稳健加权总体最小二乘方法抗差效果最优。

This paper provides a robust weighted total least squares estimation method （RWTLS）, in which the functions of Huber, IGG and IGG Ⅲ are taken respectively with the application of the standard variance. Furthermore, it adopts a reweighting iteration to solve RWTLS. Then, GPS level- ing fitting schemes are performed. The results demonstrate that robust estimation methods based on the function of Huber, IGG and IGGⅢ increase reliability in dealing with total least squares; further- more, the method based on IGGⅢ weight function presents optimal solutions.