Investigation of Random Walk Noise in GNSS Time-series

Abstract:

The fact that GNSS time-series contain power-law noise with a spectral index around -1, also called flicker noise, is well known and taken into account in current state-of-the-art analyses. However, with the ever-increasing length of the time-series, small random-walk noise component is being observed in the GNSS time-series. As Langbein (2012) recently has pointed out, a small random-walk noise component can have a significant effect on the estimated trend error and it is there important to quantify the magnitude of the random-walk noise. Maximum likelihood estimation methods are a popular choice to investigate the stochastic properties of the noise in GNSS time-series but have the disadvantage to be computational intensive and therefore rather slow. Bos et al. (2013) made advantage of symmetries present in the covariance matrices to speed up the analysis. However, this method only handles weakly non-stationary noise. Random walk is highly non-stationary and we have used another approach, based on auto-regressive noise models, to deal with this situation. The new method is also faster in most cases and it can deal with missing data in a convenient way.

Using synthetic data, we first demonstrate that random walk can be detected in data that also contains flicker and white noise. Finally, we apply our new method to data of a set of around 300 globally distributed GNSS stations to evaluate the improvement on the estimation of the uncertainties of the computed time-series.