球坐标多面函数空间数据插值方法研究  

Research on the method of space data interpolation using multi-quadric equations with spherical coordinates

作　　者：吴啸龙 杨志强[2] 龚云[1] WU Xiaolong;YANG Zhiqicing;GONG Yun(Xi'an University of Science and Technology,Xi'an 710054, China;Chang'an University, Xi'an 710054 ,China)

机构地区：[1]西安科技大学,西安710054 [2]长安大学,西安710054

出　　处：《测绘科学》2019年第3期47-50,85,共5页Science of Surveying and Mapping

基　　金：西安科技大学博士(后)启动金项目(2016QDJ049)

摘　　要：针对目前球坐标多面函数主要局限于球面任意区域对应的最优内部球层参数难以精确计算的问题,该文提出了利用Delaunay三角剖分技术的任意单连通区域球面面积的数值计算方法,解决了球坐标多面函数对球面局部空间数据插值的参数计算问题。为了评估球坐标多面函数对局部区域离散数据的插值精度,利用分布在120°～135°E,18°～28°N的843个大地水准面高程数据建立了两种坐标系的多面函数模型。均方根误差统计结果显示,球坐标多面函数模型的插值精度及稳定性均优于笛卡尔坐标模型。将球坐标多面函数模型分别与几种常用插值方法进行的插值结果精度对比,结果显示该模型仍然具有较好的精确度与稳定性。The spherical coordinate multi-quadric equations mainly confined to accurately calculate the optimal internal sphere parameters corresponding with the sphere of arbitrary simply connected region. this paper present a new numericeil calculation method to calculate the spherical area of any single connected region using Delaunay triangulation technique, and solved the problem of the parameter calculation of spherical coordinates multi-quadric equations for the local spatial data interpolation. In order to evaluate the interpolation accuracy of spherical coordinate multi-quadric equations for the regional discrete data, we established two kinds of coordinate systems multi-quadric equations models based on 843 geoid elevations distributed in 120°~ 135°E, 18°~28°N. The error statistics results of root mean square shows that, interpolation accuracy and stability of spherical coordinate multiquadric equations model are better than the Cartesian coordinate model. Comparing the accuracy of the interpolation results of spherical coordinate multi-quadric equations model with several frequently-used interpolation methods, the results show that this model has better accuracy and stability.

关 键 词：球坐标系 多面函数 空间数据插值 DELAUNAY三角形 均方根误差 

分 类 号：P226[天文地球—大地测量学与测量工程]