Extracting and filtering the Common Mode Signal of GNSS coordinate time series via Independent Component Analysis and Multiresolution analysis

Abstract

Time series related to a GNSS network at regional scale, or larger, generally show a spatially correlated component, called common-mode signal (CMS), related to both unmodelled geophysical processes, including environmental loading effects, and technique-dependent systematic errors that persist after data processing. The CMS estimation is very useful for two reasons: (i) untreated CMS leads to long-period noise in coordinate time series which induces bias and higher uncertainty in velocity estimates, so that many authors prefer the term CME (Common Mode Error) instead of CMS; (ii) whether it is possible to adequately discriminate between the components of the CMS, it is then possible to obtain relevant information regarding some geophysical phenomena. Independent Component Analysis (ICA) is particularly useful for estimating the CMS because the ICA components show insightful correlations, e.g., with atmospheric and non-tidal ocean loading displacements. For this reason, we propose a small MATLAB toolbox, partially compatible with GNU Octave, for ICA-based CMS estimation and, if required, filtering. The ICA is implemented using a FastICA algorithm in which data whitening is carried out using a Principal Component Analysis (PCA) modified in order to allow the use of incomplete time series. In this way, in the case of short periods of data loss (a few days or also some weeks), the ICA is obtained without use of data interpolation. The only used preprocessing technique is detrending. The spectral content of each ICA component can be studied by means of both frequency and time-frequency analysis and the filtering can be carried out either in the frequency domain or by means of Multiresolution analysis (MRA), according to the user’s choice. This filtering requires continuity of the time series and, therefore, in the case of short periods of data loss (a few days, at most a few weeks), interpolation is needed to build the required continuity; for non-short periods of data loss, no interpolation is implemented. The fact that the interpolation occurs after the CMS analysis, and therefore has no possible effect on its estimate, should be noted. The toolbox, which is designed to be used both independently and together with the StaVel/GridStrain toolbox developed by the same authors, will soon be made available on the Harvard Dataverse. Development of the Python version is planned. In order to test the validity of the proposed approach in the case of real data, it is applied to vertical data related to a network of some dozens of GNSS stations located in Southern Italy (Sicily and Calabria) and Greece (North-Western Greece and Peloponnese).