Bursa模型用于局部区域坐标变换的病态问题及其解法

Ill-posed Problem in Determination of Coordinate Transformation Parameters with Small Area's Data Based on Bursa Model

GPS应用经常涉及坐标变换。用局部区域的GPS网数据求解的3维坐标变换模型的转换参数时,求得的转换参数特别是平移参数的精度较差。这是由于GPS网的范围太小,引起平移参数与旋转参数间存在强相关性,导致解算模型病态。正则化解法是求解病态方程的有效工具,本文探讨用正则化方法解算小范围GPS网3维坐标变换的转换参数,以提高转换参数的解算精度,扩大参数的使用范围;给出只对平移参数进行正则化的计算模型。500次模拟计算结果表明:正则化解参数转换外围点坐标的精度在统计上明显优于最小二乘解;且随外推距离增大,精度几乎成线性降低。

The application of GPS is often needed to transform coordinates. If the transformation parameters are solved with the GPS data in a small area, the precision of transformation parameters may be very poor, especially the translation parameters. The reason is that the translation parameters and rotation parameters are high correlated in this case, which causes the solution model to be ill-posed, and regularization solution is an efficient method in dealing with ill-posed model. This paper discusses the regularization solution in solving 3-dimensional coordinate transformation parameters with small area＇s data, in order to improve the precision and extend the application range of the solved transformation parameters; a solution model only to regularize translation parameters is also derived in this paper. The model and algorithm are verified with 500 numerical simulated examples; and the results show that the precision of the transformed coordinates in peripheral area can be significantly improved by regularization; and will linearly decrease as the extension of extrapolating distance.