Analysis of the movement of permanent GNSS stations in Spain with directional statistics

Global Navigation Satellite System (GNSS), such as Galileo, GPS, GLONASS, and BeiDou, provide essential global positioning, navigation, and timing data used across a wide range of scientific and engineering applications. These systems enable precise monitoring of civil infrastructure, crustal deformations, and geodetic reference frame updates. In particular, the European Reference Frame (EUREF) Permanent Network (EPN) offers a long-term dataset of GNSS measurements valuable for multi-disciplinary analyses. This paper explores the use of circular statistics to analyze directional data derived from EPN stations distributed across Spain. Our study provides both numerical and graphical representations of GNSS vector data to uncover temporal trends and spatial patterns in station movements. The visual interpretation of directional data enhances the understanding of GNSS-derived displacement behavior. This work aims to make such analyses more accessible by promoting intuitive, graphical tools over traditional, often proprietary statistical software, thereby supporting broader engagement in GNSS-based geospatial research. Among the findings, the study reveals that all permanent stations exhibit a northeastward shift of [Formula: see text] (2.53cm/y) with an angle of [Formula: see text], approximately 1 mm every 14 days.