总体最小二乘法在坐标转换中的应用

Application of Total Least Square in Coordinate Transformation

在测量数据处理中,最为经典的处理方法是最小二乘法,认为误差只是包含在观测向量当中,系数矩阵中不包含误差。实际上由于模型等因素,系数矩阵中经常存在着误差。为了平差的严密性和精确性,采用一种可以同时顾及观测向量误差和系数矩阵误差的总体最小二乘方法,应用于测量数据处理和坐标转换中,得到更符合实际的平差处理,获得更准确的坐标转换参数。

In measurement data processing, the most classic data processing method is the least square （LS） method. The error is contained in the observation vector, and the coefficient matrix does not contain error. Actually, the coefficient matrix also contains errors, which result from the model error. For rigor and accurate adjustment, this paper explores a way to take the observation vector error and the error of the coefficient matrix into account and this method is called the total least square method. Applied to the measurement data processing and coordinate transformation, this method obtains a more accurate model, more real differential treatment and more accurate coordinate transformation parameters.