一种三步抗差方案的设计

DESIGN OF A NEW SCHEME OF ROBUST ESTIMATION BY THREE STEPS

抗差估计的关键是选择恰当的极值函数ρ（·）或（·）函数。本文针对抗差估计涉及的几个重要问题，提出一种新的抗差方案的构想。新的抗差方案试图实现如下三阶段目标：１）选取抗差性能很强的初值，包括定位参数和单位权中误差的初值。２）综合抗差，即要求能实现系数阵空间和观测空间同时抗差，能解决相关观测抗差估计问题，实现定位参数与单位权中误差的联合抗差。３）剔除粗差，给出有关估值的准确统计特性。实施这种三步抗差估计，将以加权最小二乘迭代作为基本算法。迭代权以ＩＧＧ方案为基础，在不同阶段取不同的调制因子ｋ０和ｋ１，可以采用同一主程序结构。因而也可称为变动调制因子法。本文用算例对比了几种常见抗差方案的效果，验证了三步抗差方案的有效性。

A better scheme of robust estimation should possess not only strong robustness,but also high efficiency.The new scheme put forward in the present paper can realize this object by the following stages:1)to select the suitable beginning values for iterative solution ;2)to synthesize several important principles for robust estimation,which take into account reducing the influence of the space of coefficient matrix and also of the space of dependent observations.This stage will give the combined robust estimators of the parameters and the RMS of the unit weight.3)to detect and delete the gross errors automatically.This stage can give precise statiatical properties of the estimators,There are the same structures of the main program, but the different tuning factots k0 and k1in the three stages,and therefore this three-steps scheme can be called a method of changing tuning factors. Finally,the computed results on a small net with the several schemes of robust estimation are compared.The three-steps scheme is certified more efficient than the others.