Time Correlation in GNSS Positioning over Short Baselines

Abstract

Ignoring the temporal correlations present within global navigation satellite systems (GNSS) observations can result in too much confidence being placed in the estimated positions. Temporally correlated errors occur when the magnitude of an error is similar over time. Treating temporally correlated GNSS errors as independent results in an overly optimistic variance-covariance (VCV) matrix, potentially resulting in an incorrect fix of the ambiguities and an overly optimistic estimated accuracy of the estimated positions. Unlike spatially correlated errors, temporally correlated errors are not mitigated or properly dealt with within most of today’s real-time kinematic (RTK) software. This paper reviews the theory of temporal correlations as well as previously developed solutions for obtaining more realistic position accuracies. A simulation is developed demonstrating the impact of neglecting temporal correlation. Using real data from five baselines up to 10 km in length, this paper then determines how long the L1 carrier phase observations remain correlated. By using the autocorrelation of the phase residuals, the L1 phase measurements are shown to be correlated for an average of 115 s. The length of temporal correlation varies according to receiver environment and satellite elevation angle. Trends in correlation time according to baseline length are also studied.