Prediction of geodetic point velocity using MLPNN, GRNN, and RBFNN models: a comparative study

Abstract

The prediction of an accurate geodetic point velocity has great importance in geosciences. The purpose of this work is to explore the predictive capacity of three artificial neural network (ANN) models in predicting geodetic point velocities. First, the multi-layer perceptron neural network (MLPNN) model was developed with two hidden layers. The generalized regression neural network (GRNN) model was then applied for the first time. Afterwards, the radial basis function neural network (RBFNN) model was trained and tested with the same data. Latitude ( $$\varphi$$ ) and longitude (λ) were utilized as inputs and the geodetic point velocities ( $${V}_{X}$$ , $${V}_{Y}$$ , $${V}_{Z}$$ ) as outputs to the MLPNN, GRNN, and RBFNN models. The performances of all ANN models were evaluated using root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination ( $${\text{R}}^{2}$$ ). The first investigation demonstrated that it was possible to predict the geodetic point velocities by using all the components as output parameters simultaneously. The other result is that all ANN models were able to predict the geodetic point velocity with satisfactory accuracy; however, the GRNN model provided better accuracy than the MLPNN and RBFNN models. For example, the RMSE and MAE values were 1.77–1.88 mm and 1.44–1.51 mm, respectively, for the GRNN model.