基于等价方差-协方差的粗差探测敏感度分析及实现

Sensitivity Analysis and Implementation of Gross Error Detection Based on Equivalent Variance-covariance

选权迭代法在面对独立观测量中的粗差时能够表现出良好的探测效果,但由于其只是一种基于独立观测值的稳健估计法,没有考虑到观测值之间的相关性[1]。而现有的等价权函数虽然都满足稳健估计的要求,但由于所构造的等价权阵不对称,使得最后平差结果严重偏离实际情况。本文介绍在传统稳健估计的基础上,在定权时充分考虑相关观测值之间相关性的不变性,构造对称的方差—协方差阵不断扩大,并通过VB进行编程及实例分析,发现该方法对粗差的敏感度非常强,探测精度很高。

In the face of gross errors in independent observations,the weight selection iterative method can show good detection effect,but because it is only a robust estimation method based on independent observations,the correlation between observations is not considered.Although the existing equivalent weight functions meet the requirements of robust estimation,the final adjustment results are seriously deviated from the actual situation due to the asymmetry of the equivalent weight matrix.In this paper,based on the traditional robust estimation,the invariance of the correlation between the relevant observations is fully considered in the weight determination,and the symmetric variance covariance matrix is constructed,which is continuously expanded.Through the programming and example analysis of VB,it is found that the method is very sensitive to gross errors and has high detection accuracy.