三维非线性基准转换的加权和加约束总体最小二乘解算模型

PERFORMING NONLINEAR 3D DATUM TRANSFORMATION USING WTLS AND CTLS METHOD

介绍三维空间坐标非线性转换的加权总体最小二乘(WTLS)和加约束总体最小二乘(CTLS)解算模型。以方向余弦为未知参数,旋转矩阵的正交性为约束条件,由于转换模型的系数矩阵和观测向量都是可能存在误差的随机量,因此采用WTLS和CTLS方法进行计算。通过模拟和实测数据的计算分析,验证了该方法的有效性,解算的转换参数精度得到提高。

This paper describes a simplified model of three-dimensional datum transformation, which uses the direction cosines instead of rotation angles as parameters to be estimated. The Weighted Total Least Squares （WTLS） solution and Constrained Total Least Squares（TLS） solution are preferable to estimate the parameters when errors exist both in the observation vector and the coefficient matrix. Finally, the simulation and real experi- ments are investigated to verify that the coordinate transformation method described in this paper is effective. Com- pared with Least Squares solution, the result of Total Least Squares solution is more accurate.