A proposal for modelling physical correlations of GPS phase observations

Physical correlations are generally not considered in the stochastic model of GPS observations. Consequently, the resulting estimated parameters (such as station coordinates) are affected and their variances are too optimistic and therefore not appropriate to statistically test the significance of the estimates. Considering atmospheric physics, turbulent irregularities in the lower atmosphere cause physical correlations between GPS signals propagating through them. Based on turbulence theory, a variance–covariance model for double-differenced (DD) GPS phase observations is developed in this paper, termed SIGMA-C model. The resulting fully populated variance–covariance matrix depends not only on the satellite-station geometry but also on the prevailing atmospheric conditions. It is shown that especially the wind velocity and its direction play a key role for the adequate modelling of physical correlations. The comparison of the correlations predicted by the SIGMA-C model and the empirical auto- and cross-correlation functions of DD from a specially designed GPS test network shows good agreement between data and model. Consequently, the SIGMA-C model seems to be suited for the proper description of physical correlations in GPS phase data. Furthermore, the application of the SIGMA-C model now attenuates the unbounded decrease of formal coordinate variances when the number of observations is increased. Hence for small GPS networks, the new model yields more realistic formal coordinate variances—even for high sampling rates and longer observation sessions.