球坐标多面函数空间数据插值方法研究
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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 numerical 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.
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 numerical 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.
引文
[1]HARDY R L.Multiquadric equations of topographyand other irregular surfaces[J].Journal of GeophysicalResearch,1971,76(8):1905-1915.
[2]陈传法,刘凤英,闫长青.DEM建模的多面函数Huber抗差算法[J].武汉大学学报(信息科学版),2016,41(6):803-809.(CHEN Chuanfa,LIU Fengying,YANChangqing.A Huber-derived robust multi-quadricinterpolation method for DEM construction[J].Geomatics and Information Science of Wuhan Unversity,2016,41(6):803-809.)
[3]刘经南,施闯.多面函数拟合法及其在建立中国地壳平面运动速度场模型中的应用研究[J].武汉大学学报(信息科学版),2001,26(6):500-503.(LIU Jingnan,SHI Chuang.Hardy function interpolation and itsapplication to the establishment of crustal movementspeed field[J].Geomatics and Information Science ofWuhan University,2001,26(6):500-503.)
[4]陶本藻,姚宜斌.论多面函数推估与协方差推估[J].测绘通报,2002(9):4-6.(TAO Benzao,YAO Yibin.Onprediction of multi-quadric function and covariance[J].Bulletin of Surveying and Mapping,2002(9):4-6.)
[5]吕言.数字地面模型中多面函数内插法的研究[J].武汉测绘学院学报,1981,6(2):14-28.(LYU Yan.Onthe multisurface function method in DTM interpolation[J].Journal of Wuhan Institute of Surveying andMapping,1981,6(2):14-28.)
[6]张怀亮,李晓莉,朱赛虎.改进多面函数拟合跨带区域高程异常的研究[J].测绘科学,2016,41(3):132-137.(ZHANG Huailiang,LI Xiaoli,ZHU Saihu.Applica-tion of improved polyhedral function in fitting heightanomaly in cross-band region[J].Science of Surveyingand Mapping,2016,41(3):132-137.)
[7]HARDY R L.The application of multiquadric equationsand point mass anomaly models to crustal movementstudies[M].[S.l.]:Department of Commerce,NationalOceanic and Atmospheric Administration,National OceanSurvey,National Geodetic Survey,1978.
[8]KROHN D H.Gravity terrain corrections usingmultiquadric equations[J].Geophysics,1976,41(2):266-275.
[9]GOLBERG M A,CHEN C S,KARUR S R.Improvedmultiquadric approximation for partial differentialequations[J].Engineering Analysis with BoundaryElements,1996,18(1):9-17.
[10]吴啸龙,杨志强,武继峰,等.基于多面函数法的青藏高原应变特征分析[J].大地测量与地球动力学,2013,33(4):17-21.(WU Xiaolong,YANG Zhiqiang,WUJifeng,et al.Analysis of Qinghai-Tibet Plateau strainfield and method of calculating strain parameters onreference ellipsoid by using multi-surface function[J].Journal of Geodesy and Geodynamics,2013,33(4):17-21.)
[11]曾安敏,秦显平,刘光明,等.中国大陆水平运动速度场的多面函数模型[J].武汉大学学报(信息科学版),2013,38(4):394-398.(ZENG Anmin,QIN Xianpig,LIU Guangming,et al.Hardy multi-quadric fittingmodel of chinese mainland horizontal crustal movement[J].Geomatics and Information Science of WuhanUniversity,2013,38(4):394-398.)
[2]陈传法,刘凤英,闫长青.DEM建模的多面函数Huber抗差算法[J].武汉大学学报(信息科学版),2016,41(6):803-809.(CHEN Chuanfa,LIU Fengying,YANChangqing.A Huber-derived robust multi-quadricinterpolation method for DEM construction[J].Geomatics and Information Science of Wuhan Unversity,2016,41(6):803-809.)
[3]刘经南,施闯.多面函数拟合法及其在建立中国地壳平面运动速度场模型中的应用研究[J].武汉大学学报(信息科学版),2001,26(6):500-503.(LIU Jingnan,SHI Chuang.Hardy function interpolation and itsapplication to the establishment of crustal movementspeed field[J].Geomatics and Information Science ofWuhan University,2001,26(6):500-503.)
[4]陶本藻,姚宜斌.论多面函数推估与协方差推估[J].测绘通报,2002(9):4-6.(TAO Benzao,YAO Yibin.Onprediction of multi-quadric function and covariance[J].Bulletin of Surveying and Mapping,2002(9):4-6.)
[5]吕言.数字地面模型中多面函数内插法的研究[J].武汉测绘学院学报,1981,6(2):14-28.(LYU Yan.Onthe multisurface function method in DTM interpolation[J].Journal of Wuhan Institute of Surveying andMapping,1981,6(2):14-28.)
[6]张怀亮,李晓莉,朱赛虎.改进多面函数拟合跨带区域高程异常的研究[J].测绘科学,2016,41(3):132-137.(ZHANG Huailiang,LI Xiaoli,ZHU Saihu.Applica-tion of improved polyhedral function in fitting heightanomaly in cross-band region[J].Science of Surveyingand Mapping,2016,41(3):132-137.)
[7]HARDY R L.The application of multiquadric equationsand point mass anomaly models to crustal movementstudies[M].[S.l.]:Department of Commerce,NationalOceanic and Atmospheric Administration,National OceanSurvey,National Geodetic Survey,1978.
[8]KROHN D H.Gravity terrain corrections usingmultiquadric equations[J].Geophysics,1976,41(2):266-275.
[9]GOLBERG M A,CHEN C S,KARUR S R.Improvedmultiquadric approximation for partial differentialequations[J].Engineering Analysis with BoundaryElements,1996,18(1):9-17.
[10]吴啸龙,杨志强,武继峰,等.基于多面函数法的青藏高原应变特征分析[J].大地测量与地球动力学,2013,33(4):17-21.(WU Xiaolong,YANG Zhiqiang,WUJifeng,et al.Analysis of Qinghai-Tibet Plateau strainfield and method of calculating strain parameters onreference ellipsoid by using multi-surface function[J].Journal of Geodesy and Geodynamics,2013,33(4):17-21.)
[11]曾安敏,秦显平,刘光明,等.中国大陆水平运动速度场的多面函数模型[J].武汉大学学报(信息科学版),2013,38(4):394-398.(ZENG Anmin,QIN Xianpig,LIU Guangming,et al.Hardy multi-quadric fittingmodel of chinese mainland horizontal crustal movement[J].Geomatics and Information Science of WuhanUniversity,2013,38(4):394-398.)