摘要
针对三维坐标转换模型中系数矩阵部分元素存在误差的问题,将观测向量和系数矩阵中的误差项组成新的改正数向量,重新构造拉格朗日方程。提出总体最小二乘(Total Least Square,TLS)迭代法求解三维坐标转换参数的新方法,只对系数矩阵中含误差的元素进行改正,同时保证系数矩阵中不同位置的相同元素具有相同改正数,理论模型更加严谨。最后,通过算例数据验证,结果表明新方法可行且解算结果更优。
Aiming at the problem of some elements in coefficient matrix in three-dimensional coordinate transformation model, the error vectors in the observation vector and the coefficient matrix form a new correction vector, and the Lagrange equations are reconstructed. A new method of total least square（TLS） iterative method for solving the three-dimensional coordinate transformation parameters is proposed. Only the elements with errors in the coefficient matrix are corrected, and the same correction numbers are guaranteed for the same elements at different positions in the coefficient matrix. The theoretical model is more rigorous. Finally, the numerical results show that the new method is feasible and the solution is better.
作者
曾昭福
ZENG Zhao-fu(Dongguan City,Guangdong Province Tangxia mapping team,Dongguan 523710,China)
出处
《廊坊师范学院学报（自然科学版）》
2018年第2期20-24,共5页
Journal of Langfang Normal University(Natural Science Edition)
关键词
三维坐标转换
七参数
TLS
混合总体最小二乘
three-dimensional coordinate transformation
seven parameters
TLS
mixed total least squares
