中文摘要：

通过对离散GPS／水准点观测数据进行拟合从而获得区域内任意一点的高程异常是工程实践中经常遇到的问题．本文将径向基函数（RBF）神经网络方法应用于GPS／水准高程异常拟合，提出了一种新型网络学习方法．该方法首先通过对GPS／水准数据点进行Delaunay三角剖分，以其对偶Voronoi图的节点来构造选择基函数中心，再通过广义交叉验证（GCV）来最优确定基函数的宽度参数，最后利用最小二乘来确定RBF的输出权值，从而优化网络学习效果．实验结果表明，该学习方法取得良好的网络性能，和其它常用拟合方法的比较结果也反映出RBF神经网络适合应用于GPS／水准高程异常拟合．

英文摘要：

To determine an orthometric height using GPS, it is necessary to know the geoid/ quasi-geoid undulation. Fitting of GPS/leveling scatting data is one of main methods to get the quasi-geoid unknown. This paper proposed a new method for the fitting of GPS/leveling data based on radial basis functions （RBF） neural networks. The new learning algorithm selected the centers among the vertices of the Vornoni diagram of the sample data points. The bandwidth parameters of RBF, which was supposed experientially to be linear related to the distance from the center to the nearest scattering data point, were chosen optimizedly using generalized cross validation （GCV）. The numerical results tested in one zone indicate that the new method is efficient for the geoid/quasi-geoid undulation fitting.