Application of the Generalized Method of Wavelet Moments to the analysis of daily position GNSS time series.

The modelling of the stochastic noise properties of GNSS daily coordinate time series allows to associate realistic uncertainties with the estimated geophysical parameters (e.g. tectonic rate, seasonal signal). Up to now, geodetic software based on Maximum Likelihood Estimation (MLE) jointly inverse a functional (i.e. geophysical parameters) and stochastic noise models. This method suffers from a computational time exponentially increasing  with the length of the GNSS time series, which becomes an issue when considering that the first permanent stations were installed in the late 80’s – early 90’s having recorded more than 25 years of geodetic data. Combining this issue with the tremendous number of permanent stations blanketing the world (i.e. more than 20,000 stations), the processing time in the analysis of large GNSS network is a key parameter. 

Here, we propose an alternative to the MLE called the Generalized Method of Wavelet Moments (GMWM). This method is based on the wavelet variance, i.e. a decomposition of the time series using the Haar wavelet. We show the first results and compare them with the MLE in terms of computational efficiency and absolute error on the estimated parameters. The versatility of this new method is its flexibility of choosing various stochastic noise models (e.g., Matérn, power law, flicker, white noise, random walk), and its robustness against outliers. Additional developments to account for deterministic components such as seasonal signal, offsets or post-seismic relaxation is easy. We explain the principle beyond the method and apply it to both simulated and real GNSS coordinate time series. Our first results are compared with the estimation using  the Hector software.