Impact of estimating position offsets on the uncertainties of GNSS site velocity estimates

We study the impact of estimating offsets within GNSS position time series on the uncertainties of site velocity estimates. Site velocity uncertainties are estimated by assuming different observational noise types, including white noise, fractal white noise, flicker noise, first-order Gauss-Markov noise, random walk, fractal random walk, and mixture of flicker noise, and white noise. For each noise type, we assess the sensitivity of the velocity uncertainty to offsets numerically by computing the inflation rate of the uncertainty as the number of offset parameters increases. We show that the sensitivity reduces when the noise becomes more temporally correlated. For the mixture of flicker noise plus white noise, which has been concluded as an appropriate noise model for the majority of current GNSS position time series, the rate uncertainty increases by about 11% as the number of offset parameters doubles from 1 to 2 provided that the white noise does not dominate the flicker noise. Based on the analysis of the Plate Boundary Observatory position time series, we find that adding one additional offset parameter would increase the median velocity standard deviation by 14%, consistent with the result of the simulation study. Such increase is much smaller than the conclusion of a 40% by a previous study. Therefore, given the noise characteristics of current GNSS site position estimates, position offsets have limited impact on uncertainties of site velocity estimates. This result implies that improving instrumentation, even though may introduce position offsets, is the best approach for improving reference frame stability.