边角网赫尔默特方差分量估计的特征根法

Adjusting triangulateration nets using characteristic roots method in Helmert variance components estimation

叙述了赫尔默特方差分量估计的基本思想和基本公式;结合边角网方差分量估计的特点,总结边角网方差分量估计的定权规律;为避免赫尔默特方差分量估计的公式中存在矩阵求逆、多矩阵连乘再求迹的复杂运算,导出边角网方差分量估计的简化公式———特征根公式。

This paper narrates basic ideas and formula of Helmert Variance components estimation.Using characteristics of triangulateration nets variance components estimation,the paper sums up the law of calculating the weights of measured values in triangulateration nets variance components estimation,advances a simplified formula of estimating the variance components of measured values in triangulateration nets,namely characteristic roots formula.Using this formula,the complicated calculations between matrices in Helmert's formula will be turned away.