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

Abstract

The present work aimed to develop a prediction model to estimate geoid undulation and to compare its efficiency with other methods including radial basis function neural network (RBFNN), generalized regression neural network (GRNN), multiple linear regression (MLR) and, ten different interpolation methods. In this study, the k-fold cross-validation method 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), and correlation coefficient (R2) and using graphical indicators. The evaluation of the performance of the datasets obtained using cross-validation was done in two ways. If we accept the method having the minimum error result as the most appropriate method, the natural neighbor (NN) method in the DS#5 dataset gave better results than the other methods (RMSE=0.14173 m, MAE=0.09729 m, NSE=0.98986, and R2=0.99011. On the other hand, it has been observed that, the GRNN method exhibited the best performance, on average, with RMSE=0.18539 m, MAE=0.13676 m, NSE=0.98229, and R2=0.98249.