Common-clock GPS single differences: An improved correlation model for GPS phase observations based on turbulence theory

Microwave signals, for example, those from Global Navigation Satellite System (GNSS) and Very Long Baseline Interferometry oVLBI thorn , are affected by tropospheric turbulence in such a way that the random fluctuations of the atmospheric index of refractivity correlate the phase measurements. A proper modeling of correlations is mandatory to avoid biased analysis, particularly when statistical tests are used. In this contribution, we analyze single differences (SD) computed from Global Positioning System (GPS) phase observations for which the between receiver clock error could be strongly mitigated by a specific common clock setting. We estimate specific parameters from the power spectral density (psd), which is directly related to the correlation function, with the debiased Whittle maximum likelihood and investigate their dependencies with the satellite geometry (elevation, azimuth angles) and the time of the day. We show that (i) the estimated slopes of the psd follow the one predicted by the Kolmogorov turbulence theory and (ii) the cut-off at high frequencies shows daily variations that may be linked with the strength of the turbulence. Based on these findings, we derive an improved spectral density model for GPS phase SD. The results of this study contribute to improving the stochastic description of random effects impacting VLBI and GNSS phase observations by studying variations of parameters from the von Karman spectrum. & COPY; 2023 COSPAR. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/