Methods for Rapidly Estimating Velocity Precision from GNSS Time Series in the Presence of Temporal Correlation: A New Method and Comparison of Existing Methods

Abstract

Time series of position estimates from Global Navigational Satellite System (GNSS) are used to measure the velocities of points on the surface of the Earth. Along with the velocity estimates, a measure of the precision is needed to assess the quality of the velocity measurement. Here, I evaluate rate uncertainties provided by four different methods that have been applied to geodetic time series. The most rigorous approach uses a data covariance that incorporates a variety of noise processes relevant to geodetic time series but is computationally demanding. Two other approaches are efficient algorithms and are used widely, but both can provide less rigorous estimates of the rate uncertainty. I propose and evaluate a fourth method, which provides estimates of rate uncertainty closer to the rigorous approach but is significantly less computationally demanding. I have evaluated all three methods against the more rigorous method using both simulations and time series from 190 GNSS sites. For data best characterized as having a flicker type noise process, one of the widely used methods overestimates the uncertainty by up to a factor of 2, while the other widely used method underestimates the uncertainty by less than a factor of 2. For a random-walk process, both methods underestimate the rate uncertainty by a factor of 3 to 5.