Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study

Abstract

This study evaluated different methods for geoid undulation prediction and included two types of artificial neural networks (ANNs)-the radial basis function neural network (RBFNN) and the generalized regression neural network (GRNN)-as well as conventional methods including multiple linear regression (MLR) and ten different interpolation techniques. In this work, k-fold cross-validation was used to evaluate the model and its behavior on the independent dataset. With this validation method, each of a k number of groups has the chance to be divided into training and testing data. The performances of the methods were evaluated in terms of the root mean square error (RMSE), mean absolute error (MAE), Nash–Sutcliffe efficiency coefficient (NSE), correlation coefficient (R2), and using graphical in-dicators. The evaluation of the performance of the datasets obtained using cross-validation was performed in two ways. When the method having the minimum error result was accepted as the most appropriate method, the natural neighbor (NN) gave better results than the other methods (RMSE = 0.142 m, MAE = 0.097 m, NSE = 0.98986, and R2 = 0.99011). On the other hand, it was observed that on average, the GRNN exhibited the best performance (RMSE = 0.185 m, MAE = 0.137 m, NSE = 0.98229, and R2 = 0.98249).