总体最小二乘方法在空间后方交会中的应用
Application of Total Least Squares to Space Resection
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摘要: 在空间后方交会的解算过程中,利用共线条件方程式列出误差方程后,针对地面控制点以及像点坐标均存在误差这一特点,引入总体最小二乘(total least squares,TLS)的方法,对系数矩阵A以及观测向量b同时进行改正,计算像片的6个外方位元素,建立更加合理的计算模型,可获得精度更高、更稳定的解。Abstract: In space resection computing,the error equations are based on the collinearity equations.Because the coordinates of the ground point and the image point all exist errors.So total least squares(TLS) method is used.The method of TLS is one of several linear parameter estimation techniques that have been devised to compensate for data errors.Furthermore,TLS is the method of fitting that is appropriate when there are errors in both the observation vector b and the variable matrix A.So it can establish a more practical and suitable model so-called error-in-variables model.On the basis of this model,the errors in the observation vector b(e) and the variable matrix A(EA) can be corrected at the same time.