同时考虑公共点新老坐标误差的三维坐标转换模型

摘要

Traditional three-dimensional coordinate transformation method,estimates seven transformation parameters,namely the translate,rotation and scale parameter,using conventional least square estimator.It considers only the coordinate error of the common sites in the transformed coordinate system.In fact,station coordinates in both coordinate systems may have errors,and the mis-modelling of such error may lead to bigger uncertainty of the estimated parameters.This paper considers the station coordinates error of the com-mon sites in both systems,and applies the conditional adjustment model for parameter esti-mation.A local GPS network is used to test the new model.The magnitude distribution his-togram of the coordinate transformation residuals shows that the residuals from the new model is more concentrated around zero,and its distribution area is significantly smaller than that of the traditional model.Also,the mean square error of unit weight of the new model is about 1/3 to 2/3 in the order of the traditional model.%传统意义上求解三维坐标转换的7个参数是基于间接平差模型，仅考虑新坐标系下公共点的误差。本文在此基础上，同时考虑老坐标系的公共点误差，采用附有参数的条件平差模型进行解算，通过实例计算，两种平差模型所求转换参数一致。精度分析时，绘制坐标转换残差的频率分布直方图，新模型的转换残差分布的更集中，其分布区域明显小于间接平差模型；当公共点个数在3个以上时，新模型的验后单位权中误差σ0始终小于间接平差模型，其σ0值约为间接平差模型的1/3到2/3.