加权整体最小二乘的验后估计在三维坐标转换中的应用

摘要

When solving EIV model for the three-dimensional small-angle coordinates transformation,the weight matrix of observation vector and coefficient matrix may be inaccurate because of the difference between their unit weight variances.So,the Helmert variance components estimation method is applied to resolve the problem with posterior estimation in the weighted total least squares (WTLS).Thus,the weight matrix of observation vector and coefficient matrix should be redistributed,so that the calculation model will be more reasonable.The calculated example proves that the new method can improve the precision of the coordinate transformation parameters and the parameter estimations are closer to true values.%在求解三雏小角度坐标转换EIV模型的过程中,顾及到两套坐标系下点坐标初始单位权方差可能不同导致定权不准确的问题,应用Helmert方差分量估计方法,对加权整体最小二乘的随机模型进行验后估计,从而重新分配观测向量和系数矩阵的权,使得解算模型更加合理.算例证明,利用该方法求解坐标转换参数的精确度有所提高,参数估值更接近真值.