Accounting for spatiotemporal correlations of GNSS coordinate time series to estimate station velocities

Abstract

It is well known that GNSS permanent station coordinate time series exhibit time-correlated noise. Spatial correlations between coordinate time series of nearby stations are also long-established and generally handled by means of spatial filtering techniques. Accounting for both the temporal and spatial correlations of the noise via a spatiotemporal covariance model is however not yet a common practice. We demonstrate in this paper the interest of using such a spatiotemporal covariance model of the stochastic variations in GNSS time series in order to estimate long-term station coordinates and especially velocities.We provide a methodology to rigorously assess the covariances between horizontal coordinate variations and use it to derive a simple exponential spatiotemporal covariance model for the stochastic variations in the IGS repro2 station coordinate time series. We then use this model to estimate station velocities for two selected datasets of 10 time series in Europe and 11 time series in the USA. We show that coordinate prediction as well as velocity determination from short time series are improved when using this spatiotemporal model, as compared with the case where spatiotemporal correlations are ignored.