多元总体最小二乘在大旋转角三维坐标转换中的应用

摘要

Due to the negligence to the random errors in the application of coordinate transformation, some defects can be found in the traditional method based on the Seven Parameters of Bursa Model. And the method of multiva-riate total least squares based on the Errors-In-Variabals Model overcomes such deficiencies to some extent, which not only considers the coefficient matrix and the observed value but also dramatically simplifies calculation proce-dures by solving the matrix of coordinate transformation with Singular Value Decomposition ( SVD) , not needing it-erative computation.A conversion algorithm based on the formula derivation of multivariate total least squares is de-sign in this paper, and some virtual data are also applied to testify its effectiveness in three-dimensional datum transformation with big rotation angle. The verification demonstrates that the multivariate total least squares has a more efficient performance in precision computation than the least squares based on Gauss-Markov ( GM) model.%传统的Bursa七参数模型坐标转换方法在大旋转角应用中存在不足，且未考虑到随机误差。基于EIV模型的多元总体最小二乘方法，不仅考虑了系数矩阵和观测值的随机误差，而且直接通过奇异值分解求解坐标旋转矩阵，大大简化了计算步骤，无须迭代计算。推导了多元总体最小二乘的坐标转换公式，设计了转换算法，并利用模拟数据对大角度三维坐标转换进行了验证。结果表明：多元总体最小二乘方法比基于Gauss-Markov ( GM)模型的最小二乘方法的精度更高，且无须迭代计算，计算过程更加高效。