基于验后方差原理的选择权迭代法定位粗差

Gross ErrorLocation Based on the Weight Iteration of Posterior Variance Principle

当观测数据中存在粗差时,使用经典的最小二乘算法往往不能得到高精度的参数解,此时需要使用具有抗差估计的算法。基于验后方差的选权迭代法,克服了单位权方差未知或者权函数靠经验选取的情况,利用验后方差检验求出方差异常大(即含粗差)的观测值,然后通过不断的迭代,使含粗差的权逐渐趋于一个较小的数,最终实现粗差的探测和改正。结合工程实例,分别比较了不含粗差和含粗差的情况下,利用经典最小二乘法与本文所提的基于验后方差原理的选权迭代法进行平差,结果表明,二者的平差结果相差在1mm以内,解算精度相当。

If there are gross errors in observation data,it is always impossible to get highly accurate parameter solutions with traditional least squares algorithm,and then an algorithm including robust estimation is needed.Weighted iteration method based on posterior variance principle avoids the occurrence of unknown variances of unit weight and selection of weight functions by experience.It first uses posterior variance principle to get observation data withextremely big variances(including gross errors),then makes them smaller and smaller by continuous iterations,and finally accomplishes the detection and correction of gross errors.Combined with actual engineering examples,the article makes a comparison between conditions with and without gross errors,and respectively gets adjustment with traditional least squares algorithm and weighted iteration method based on posterior variance principle.The result shows that the adjustment results of these two methods is only less than 1mm different,and they are equal in calculation accuracy.