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

Abstract

[1] 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.Citation: Hackl, M., R. Malservisi, U. Hugentobler, and R. Wonnacott (2011), Estimation of velocity uncertainties from GPS time series: Examples from the analysis of the South African TrigNet network,

Slow slip events in Costa Rica detected by continuous GPS observations, 2002–2011

“…Sample GPS time series and model fits are shown in Figure 8. [18] To quantify the noise level in our CGPS time series, we calculated the noise amplitude by applying the Allan Variance of the Rate (AVR) to the time series [Hackl et al, 2011]. The AVR has been fit with an error model accounting for white noise, flicker noise, random walk and an annual signal:…”

Fast error analysis of continuous GNSS observations with missing data

“…The influence of time correlated noise on time series and the presence of reasonably fast method to include coloured noise in the analysis of timeseries, such as shown in this paper and by Hackl et al (2011), strongly suggest that people should routinely add time correlated noise analysis in Table 1: The results of the time-series analysis using both CATS and the new algorithm, East and North component. Giventhe uncertainties estimation.…”

“…However, Hackl et al (2011) also mention that MLE gives more robust results. Therefore, it is desirable to lower the computation time of MLE to have the best results in a time comparable to heuristic methods.…”

“…Williams (2003) noted that the computation time for analysing 10 years of data was around 6 hours. Computers have become much more powerful since then but Hackl et al (2011) still mention a computation time of several days to analyse 50 IGS stations using the CATS software (Williams, 2008) that employs the MLE method. They use this result as an argument in favour of their more rapid Allan Variance of the Rate method.…”

Design of a web-based GNSS data management system at HartRAO: preliminary results

“…These velocities are used in studying Earth phenomena such as plate kinematics, strain and estimating rheology properties (Hackl et al, 2011). The velocity data archived at HartRAO can be used for incorporation into global plate tectonics models such as NUVEL-1, NUVEL-1A and MORVEL (DeMets et ah, 2010).…”