GNSS高程转换的B样条函数模型精度与分析  

Accuracy and Analysis of B-Spline Function Model Using inGNSS Height Transformation

作　　者：周广华[1] 田泽海[1] 梁建青 ZHOU Guanghua;TIAN Zehai;LIANG Jianqing(Guangzhou Urban Planning&Design Survey Research Institute,Guangzhou 510000,China)

机构地区：[1]广州市城市规划勘测设计研究院,广东广州510000

出　　处：《测绘与空间地理信息》2023年第4期127-129,134,共4页Geomatics & Spatial Information Technology

摘　　要：详细研究了B样条函数用于GNSS高程转换的函数模型与转换精度,并与三次样条函数、三次赫米特插值的高程转换精度进行比较,分析得出以下结论:1)当控制点间距约为5 km时,三次非均匀B样条函数、三次样条函数和三次赫米特插值的高程转换精度优于1.0 cm,且95%以上的转换高差都满足四等几何水准的限差要求,整体上三次非均匀B样条函数的高程转换精度与三次样条函数、三次赫米特插值的高程转换精度基本相当。2)算例一表明三次均匀B样条函数的高程转换精度差于三次非均匀B样条函数、三次样条函数以及三次赫米特插值,原因是控制点间距不均匀。当控制点的间距小于30 km时,三次非均匀B样条函数、三次样条函数以及三次赫米特插值均有87%以上的转换高差满足四等几何水准的限差要求。在高程异常变化较为平坦的线性工程中,采用三次非均匀B样条函数模型进行高程转换的控制点间距建议不大于30 km,且在高程异常剧烈变化区域相应增加控制点有利于提高高程转换精度。The function model and conversion accuracy of B-spline function used for GNSS elevation conversion are studied in detail,and compared with the elevation conversion accuracy of cubic spline function and cubic Hermite interpolation.The study results are as follows:(1)When the distance between control points is about 5 km,the accuracy of height transformation of cubic non-uniform B-spline function,cubic spline function and cubic Hermite interpolation is better than1.0 cm,and more than 95%of heights meet four-class level tolerance requirements.The accuracy of height transformation of cubic non-uniform B-spline function is basically equivalent to that of cubic spline function and cubic Hermite interpolation.(2)First example shows that accuracy of height transformation of cubic uniform B-spline function is worse than that of cubic non-uniform B-spline function,cubic spline function and cubic Hermite interpolation because of non-uniform distances of the control points.If the distance between control points is less than 30 km,cubic non-uniform B-spline function,cubic spline function and cubic Hermite interpolation have better effect,because more than 87%of their fitted heights meet four-class level tolerance requirements.In the linear engineering with relatively slow variation of height anomaly,the distance between control points should not be greater than 30 km if cubic non-uniform B-spline functon is used in height transformation,and accuracy of height transformation can be improved by increasing control points in the area with drastic variation of height anomaly.

关 键 词：B样条函数 GNSS高程转换 高程转换精度 

分 类 号：P228[天文地球—大地测量学与测量工程]