Analysis of a GPS network based on Functional Data Analysis

Abstract

This work demonstrates the usefulness of approaching the dynamic study of the precise positioning of a network of GPS (Global Positioning Sys- tem) permanent stations through the Functional Data Analysis (FDA). The displacement data for each GPS station, obtained from observations of Global Navigation Satellite System, are a discrete sample of the positioning curve. The aim of this work is the reconstruction of the original functions in order to use it as functional data. In the methodology presented in this work, 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 Kalman filter. Finally, the original functions are reconstructed by using smoothing techniques and by evaluating several bases of functions. Moreover, these funcions are treated with statistical techniques for functional data. This procedure is applied to the permanent stations of SPINA network (South of the Iberian Peninsula and North of Africa). We analyze the topocen- tric series: East, North and Up. In the analysis of the positioning curves it is observed a synchronized behaviour of the functions in the periods of time with an important seismic activity. This behaviour also appears in the analysis of the second principal component of East and Up dimensions. Furthermore, the first two principal components of East coordinate enable us to make a classifi- cation of the stations in SPINA network. The classification made is consistent with the previous knowledge of the tectonic plates in the studied area.