Estimation of velocity uncertainties from GPS time series: Examples from the analysis of the South African TrigNet network

We present a method to derive velocity uncertainties from GPS position time series that are affected by time-correlated noise. This method is based on the Allan variance, which is widely used in the estimation of oscillator stability and requires neither spectral analysis nor maximum likelihood estimation (MLE). The Allan variance of the rate (AVR) is calculated in the time domain and hence is not too sensitive to gaps in the time series. We derived analytical expressions of the AVR for different kinds of noises like power law noise, white noise, flicker noise, and random walk and found an expression for the variance produced by an annual signal. These functional relations form the basis of error models that have to be fitted to the AVR in order to estimate the velocity uncertainty. Finally, we applied the method to the South Africa GPS network TrigNet. Most time series show noise characteristics that can be modeled by a power law noise plus an annual signal. The method is computationally very cheap, and the results are in good agreement with the ones obtained by methods based on MLE.