Implementation and evaluation of nonparametric methods to detect abrupt variations in gnss time series
Keywords:
GNSS, detection of discontinuities, Geodesy, Time Series analysisAbstract
Global Navigation Satellite Systems (GNSS) provide users with high precision coordinate time series and enable measurements to be easily link to the International Terrestrial Reference Frame (ITRF). They also give a significant tool to the scientific community to observe and model the dynamics of planet Earth. To better understand geodetic phenomena at the regional level, there is an increasing demand on detecting milimetric to sub-milimetric displacements. This situation requires improvements in the sensitivity of GNSS time series and emphasizes the importance of maintaining the solutions consistency over time. In order to contribute to the localization of abrupt discontinuities automatically, it was decided to use non-parametric methods instead of functional approximations, since they do not require knowing the behaviour of the signal beforehand. Different mathematical algorithms of regime shift and changepoint analysis were implemented to detect offset changes in the time series, called Block Average, Sequential Average and Cumulative Sum. Subsequently, an analysis of the obtained results was made, as well as a comparison with a classical method of maximization, referred here as estimator F, proposed by Basseville and Nikiforov.
The algorithms were applied to time series of 21 stations belonging to the SIRGAS-CON network. Each one of them presented known discontinuities of different magnitudes. After applying the algorithms, additional conditions were imposed on the results in order to minimize the amount of false positives detected, without sacrificing the detection sensitivity. All the proposed algorithms were able to detect the jumps in the great majority of the analyzed stations. Its application becomes more robust when combining the techniques, and when comparing, for each station the locations of the offsets in the three components. The Sequential Average method was effective in 87% of the cases analyzed, while the Block Average was successful in 95% of them. The Average Block algorithm was the most efficient method for finding and quantifying jumps in GNSS coordinate time series.
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