Analysis of a GPS Network Based on Functional Data Analysis

Abstract

This paper demonstrates the usefulness of approaching the dynamic study of the precise positioning of a network of permanent global positioning system (GPS) stations through functional data analysis. The displacement data for each GPS station, obtained from observations of the global navigation satellite system, are a discrete sample of the positioning curve. The aim of this paper is to reconstruct the original functions in order to use them as functional data. In the method presented in this paper, the geodetic series are obtained first by processing the GPS data with respect to a reference station. Second, for each station, a cleaning process is applied to eliminate the values considered as outliers, and the missing values are imputed by using a Kalman filter. Finally, the original functions are reconstructed by using smoothing techniques and by evaluating several bases of functions. Moreover, these functions are treated with statistical techniques for functional data. This procedure is applied to the permanent stations of the south of the Iberian peninsula and the north of Africa (SPINA) network. The topocentric series: east, north and up are analysed. In the analysis of the positioning curves, there is observed a synchronized behaviour of the functions in those periods of time with important seismic activity. This behaviour also appears in the analysis of the second principal component of the East and up dimensions. Furthermore, the first two principal components of the East coordinate enable us to make a classification of the stations in the SPINA network. The classification made is consistent with the previous knowledge of the tectonic plates in the studied area.