一种涉及大地坐标的大角度三维坐标转换方法

A big rotation angle 3D coordinate transformation method involving geodetic coordinate

在转换问题中存在大地坐标时,通常是将大地坐标换算为同坐标系下的直角坐标,然后通过Helmert转换模型进行转换参数的求解。上述换算过程属于非线性传播,因此点位精度的传播产生了精度损失。提出一种直接采用大地坐标进行坐标转换的方法,首先利用Taylor级数对坐标转换模型进行线性化,将其转换为经典最小二乘的Gauss-Markov模型,求解转换参数。通过仿真实验表明:此文提出的方法相比较于常用方法,平移、尺度和旋转参数的RMS分别提高23%,28%,19%,15%,27%,10%以及8%,非公共点的转换精度得到明显改善,验证了此文提出的直接采用大地坐标可以有效避免大地坐标变换为直角坐标时产生的精度损失,提高转换参数以及非公共站转换的精度。

In the conversion problem with the geodetic coordinates,the genenal method is that the geodetic coordinates are converted to Cartesian coordinates in the same coordinate system,and then the transformation parameters are solved through the Helmert conversion model.The above-mentioned conversion process belongs to nonlinear propagation,so the propagation of point accuracy causes a loss of accuracy.This paper proposes a method of directly using geodetic coordinates for coordinate transformation.First,the Taylor series is used to linearize the coordinate transformation model,which is converted into a classic least squares Gauss-Markov model,and the least square solution of the transformation parameters are solved.Simulation experiments show that the proposed method improves the RMS of translation,scale,and rotation parameters by 23%,28%,19%,15%,27%,10%,and 8%,respectively.The transformation accuracy of non-common stations have been significantly improved.It is verified that the directly using geodetic coordinates proposed in this paper can effectively avoid the loss of accuracy when the geodetic coordinates are converted into Cartesian coordinates,and improve the accuracy including the transformation parameters solutions and the transformation coordinates of non-common station.