Prediction of geoid heights using the MLP ANN method at a regional scale

The aim of this study is to construct a regional geoid model using the MLP ANN method and to assess its accuracy with GNSS–levelling data for the Vinnytsia region, both within and without the application of the “Remove–Compute–Restore” procedure. Method. The construction of a geoid model using artificial neural networks (ANN) is a modern approach that integrates classical geodetic methods with intelligent data processing technologies. The main idea is to apply machine learning algorithms to establish nonlinear relationships between various input geophysical parameters and the geoid height. An ANN can be considered as a set of artificial neurons with local processing capability, which are connected according to a specific topology. This topology defines how these neurons are linked, and there is also a learning rule that governs the network's operation. Among various ANN models, the multilayer perceptron (MLP) is particularly popular. The MLP consists of an input layer (neurons that receive external stimulation, one or more hidden layers, and an output layer which provides the network’s result. When computing regional or local geoid models using the MLP ANN method, it is advisable to apply the “Remove–Compute–Restore” procedure. Results. A geoid model was computed using GNSS–levelling data for the Vinnytsia region, both with and without the “Remove–Compute–Restore” procedure. The accuracy of the resulting models was evaluated using independent datasets. The standard deviation of the model obtained with the “Remove–Compute–Restore” procedure, when compared with independent data, was approximately 1.8 cm, which corresponds well with the accuracy of the input data (geoid heights derived from GNSS–levelling). In contrast, the model constructed without applying this procedure showed significantly poorer accuracy, with a standard deviation of approximately 3.7 cm. Scientific novelty and practical significance of this work lie in assessing the accuracy of a regional geoid model constructed using the MLP ANN method, both with and without the “Remove–Compute–Restore” procedure. The proposed approach can be recommended for computing regional and local geoid models.