On the analysis of the earth’s surface vertical change by GNSS residual position time series prediction and analysis using radial basis function networks machine learning

Abstract

In this paper, the method of radial basis function machine learning is employed to analyze and predict the GNSS residual position time series. Based on four different types of radial basis functions, which are the linear, Gaussian, multiquadratic, and inverse multiquadratic the centroids of which are determined by the method of kmeans clustering, two methods of estimation, namely least squares and ridge regression, and two schemes of prediction-batch and auto regressive-the residual positions of the time series are predicted and compared with their observed values. A case study is presented for the permanent GNSS station in Almeria, Spain. In this study, residual positions over time spanning from 1094.857 to 2070.857 in GPS time are analyzed. In the batch mode, the first 4641 points are used for training the network and 2000 points for the prediction phase. In the auto-regressive mode, for different steps, the residual positions are computed and compared with the observed values. It is shown that the best performance of the machine learning algorithms occurs when the linear basis functions, 200 centroids, least squares method, and batch scheme are used.