三维线性坐标转换的适用性研究

Application Study of 3D Linear Coordinate Transformation

三维空间坐标转换的严密数学模型是一个非线性模型,计算公式较为复杂,在假设两坐标系旋转角很小的情况下,可以得到简化或线性化的转换模型。通过模拟计算,研究该线性模型的适用性,计算结果表明:在不考虑点坐标误差的情况下,对于120 km2左右的测区,当旋转角不大于9'时,用该模型所得到的转换参数发生了较大变化,尤其是3个平移参数的精度较差,但是公共点所包含区域内的点的坐标转换结果仍然可用,可达到毫米级精度。

Rigorous 3D coordinate transformation is a nonlinear mathematical model, the formula is complicated, the simplified or linear transformation model can be achieved on the assumption that a small rotation angle between two coordinate systems. In this paper, simulation study for the applicability of the linear model have been done, results show that if the error of point coordinates is not considered, for 120 km2 around the test area, when the rotation angle is not more than 9＇, although the use of the model transformation parameters obtained undergone biggish changes, especially the precision of 3 D translated parameters is poor, but the coordinate of the point conversion result within the common point is still available, up to ram-level precision.