基于三次样条函数的长线路GNSS高程拟合研究

Research on GNSS height fitting for long line area based on cubic spline function

论文介绍利用三次样条函数进行GNSS高程拟合的原理和方法。以某公路改扩建工程一级GNSS控制网和四等水准网为例进行高程拟合研究。设计线性、二次曲线、三次曲线及三次样条4种函数模型作为高程拟合方案。结果表明,线性函数模型精度最低;二次、三次曲线函数模型精度相当;三次样条函数拟合精度最高,拟合中误差小于5cm,且拟合误差曲线平滑震荡较小,具有很好的适应性。

This paper introduces the method and principle of GNSS elevation fitting by using cubic spline function.Four research approaches about linear function,quadratic curve function,three curve function and cubic spline function,as models of GNSS height fitting,are designed to study elevation fitting to the case about first class GNSS control network and fourth leveling for long highway project rebuilt.Results show that the precision for li-near model is the most,precisions for quadratic curve function and three curve function is equal and the precision for cubic spline function is the best.The method by cubic spline function has many advantages such as that error of mean squares to elevation is the less 5 cm and error curve is smooth.