Scaling of the variance covariance matrix obtained from Bernese software

Abstract

Global positioning system (GPS) refers positioning, timing and navigation services for different engineering applications. GPS positioning accuracies vary depending on the several parameters such as surveying method, data processing strategy and software packages. Bernese v5.2 software package is an important tool for processing and analyzing of the GPS measurements especially for the precise applications in scientific community. Although the accuracies of the estimated coordinates are sufficient, Variance–Covariance (VCV) matrices obtained from Bernese v5.2 are very optimistic because the correlations between different observables may be ignored by choosing identical weights for each measurement type in the analysis. This situation causes wrong interpretations for statistical analyses based on these VCV matrices. Therefore, the VCV matrices obtained from software should be scaled. In this study, the VCV matrices obtained from Bernese v5.2 were investigated for GPS measurements to estimate appropriate scale factor (SF) values. Baselines whose lengths ranging from 55 to 268 km and session durations between 2 and 24 h were processed with single baseline strategy for 31 consecutive days. According to the results, SF values do not depend on baseline lengths; but they vary depending on the session durations. A logarithmic function was defined for time-dependent SF values. This function has been tested in deformation analysis at the global test step and the obtained results, when the SF values are taken into account, are more reliable than the results when the unscaled VCV matrices are implemented.