On the reliability of the VCV Matrix: A case study based on GAMIT and Bernese GPS Software

Commonly, the variance-covariance (VCV) matrix derived from GPS processing software underestimates the magnitude of the error, mainly due to the fact that physical correlations are normally neglected. The GAMIT and Bernese software packages serve the scientific community as important tools for GPS measurement processing and analyzing, especially in precise applications. Therefore, the reliability of the VCV matrices derived by the GAMIT and Bernese packages is of great importance. Formal accuracies derived from both software need to be scaled by applying a scaling factor (SF) that multiplies the software-derived formal errors. However, to the best of our knowledge, no standard approach approved by the GPS community exists. In this report, an analysis is carried out in order to test the reliability and the validity of the VCV matrices in both software, and to provide SFs needed to calculate the realistic accuracies reflecting the actual error levels. The method applied in this study allows deriving SFs for formal accuracies obtained from GAMIT and Bernese. The results attained from the time series of eight days for eight baselines (lengths of 20–415 km) indicate that the overall SF for GAMIT is more than 10 times smaller than for Bernese (1.9 and 23.0, respectively). Although no distance-dependent SF was detected in either case, the session-duration dependence was detected for the Bernese software, while no clear session-duration dependence was observed for the GAMIT. Furthermore, no receiver/antenna dependence could be deduced from the results of this analysis.