广义整体最小二乘粗差探测的三维坐标转换方法

3D coordinate transformation method of the outlier detection for generalized total least squares

针对观测坐标受到粗差污染时导致参数估值受到影响的问题,本文将三维坐标转换问题描述为一个非线性变量误差(EIV)模型,并提出相应的数据探测算法。首先利用Euler-Lagrange方法推导出了非线性EIV模型的广义整体最小二乘(GTLS)解,将其转化为经典最小二乘问题;然后在已知方差分量和未知方差分量的条件下,基于经典最小二乘理论,构造了两类数据探测的检验统计量。试验结果表明,本文提出的数据探测算法可有效减少粗差的影响,获得可靠的转换参数。

The parameter estimation will be adversely affected when the observation coordinates are polluted by gross errors.In this study,the 3D coordinate transformation problem is described as a generalized errors-in-variables(EIV)model,and the data snooping algorithm for this model is proposed.Firstly,the generalized total least squares(GTLS)solution of the nonlinear EIV model is derived by using the Euler Lagrange method,and then it is transformed into the classical least squares problem.Two types of test statistics for data snooping are constructed based on the classical least squares theory under the conditions with known and unknown variance component,respectively.The experimental results show that the proposed data detection algorithm can effectively reduce the influence of gross errors and obtain reliable conversion parameters.