基于稳健估计局部多项式插值定权模型分析

Analysis of local polynomial interpolation weighting model based on robust estimation

在对DEM数据进行插值时,插值算法中对其插值精度影响最为显著的是权指数,但插值时对于含粗差的观测数据,传统的定权方法在计算时会将粗差引入,导致差值结果不准确。针对常用的局部多项式插值法,基于动态球半径选点法选取采样点,分别采用传统的反距离加权法和稳健估计选权迭代法中的Huber权函数法、Andrews权函数法、IGG方案对局部多项式插值的采样点进行定权,通过对比分析采用不同定权方法得到的插值曲面、预测高程相似度以及拟合优度,探讨在数据含有粗差时通过采用不同定权方法对粗差数据进行降权,以得到插值高程值与真实值最为接近的定权方法,对局部多项式插值的定权模型改进。结果表明:在对含粗差的测量数据进行多项式插值时,传统的反距离权重法的插值拟合优度为1.4333,稳健估计选权迭代法中Huber权函数法的拟合优度为0.7428;Andrews权函数法的拟合优度为0.6832;IGG方案的拟合优度最高为0.5318,并且IGG方案对采样点定权所得到的高程值与真实值最为接近,插值曲面的拟合精度更高,插值效果更好。

In the interpolation of DEM data,the weight index has the most significant influence on the interpolation accuracy.The traditional weight method,however,will introduce gross error in the calculation,for the observation data with gross error,which leads to inaccurate difference results.In this paper,from the commonly-used local polynomial interpolation method,the sampling points are selected based on the dynamic spherical radius method.The traditional inverse distance weighting method and Huber weight function method,Andrews weight function method and IGG scheme in the robust estimation weight iteration method are used to determine the weights of the sampling points of local polynomial interpolation.The interpolation surface,and the similarity as well as goodness of fit of the predicted elevation obtained by different weight methods are compared and analyzed to examine the weight reduction of gross error data by using different weighting methods when the data contains gross error,so as to obtain the weighting method that the interpolation elevation value is closest to the real values,which would improve the local polynomial interpolation weighting model.The results show that the goodness of fit of traditional inverse distance weight method is 1.4333,that of Huber weight function method is 0.7428,that of Andrews weight function method is 0.6832,and that of IGG scheme is 0.5318.And the height value obtained by the IGG scheme is the closest to the real value and the fitting accuracy of the interpolation surface is higher,with the interpolation effect better.