常用平面坐标转换模型的空间适用范围研究

测绘和煤矿行业中经常需进行北京54坐标和西安80坐标的相互转换。以陕西某矿务局2个煤矿所测地面和井下控制导线的北京54坐标和西安80坐标成果为基础,通过数学仿真,研究了赫尔默特相似变换、仿射变换、双线性变换3种常用转换模型伴随空间范围的增大,坐标转换精度的变换规律。探索了不同模型的空间适用范围,在综合考虑转换精度和空间适用范围的基础上,确定了适合该矿务局的最优转换模型,及建模控制点个数。就面积在100 km2以上的常见煤矿地区,在建立2种坐标系间的平面坐标转换模型时,仿射变换模型转换精度最高,所需控制点数量较少,宜在10个以上,且分布尽可能均匀,所得转换参数的适用范围最广,能够起到减轻野外工作量和人工计算量的作用。该研究在实际工作中具有一定的理论和指导意义。

Research on space suitable scope of commonly used plane coordinate transformation models

In the daily production of surveying and coal mine, the mutual conversion of Beijing 54 and Xi＇ an 80 coordinate system is often needed. In this paper, based on the results of Beijing 54 and Xi＇ an 80 coordinate of the points of control traverse on the ground and under the shaft at two coal mines of certain mining bureau in Shaanxi province, by means of mathematical simulation, the changing laws of coor- dinate transformation precision of common used transformation models such as Helmed＇ s similarity transformation, affine transformation and bilinear transformation following the adding of space scope is studied systematically. The space suitable scope of different models is explored. On the basis of compre- hensively thinking about transformation precision and space suitable scope, the optimal transformation model for the mining bureau is determined. In the common coal region of larger than 100 km2 ,when the plane coordinate transformation model is established between the two coordinate systems, the highest conversion accuracy of affine transformation model, the uniformity distribution as far as possible of more than 10 control points needed, and the extremely wide scope of application of the resulting transformation parameters make the field work and artificial calculation less than before.