Abstract
For the first time, we introduced the probabilistic principal component analysis (pPCA) regarding the spatio-temporal filtering of Global Navigation Satellite System (GNSS) position time series to estimate and remove Common Mode Error (CME) without the interpolation of missing values. We used data from the International GNSS Service (IGS) stations which contributed to the latest International Terrestrial Reference Frame (ITRF2014). The efficiency of the proposed algorithm was tested on the simulated incomplete time series, then CME was estimated for a set of 25 stations located in Central Europe. The newly applied pPCA was compared with previously used algorithms, which showed that this method is capable of resolving the problem of proper spatio-temporal filtering of GNSS time series characterized by different observation time span. We showed, that filtering can be carried out with pPCA method when there exist two time series in the dataset having less than 100 common epoch of observations. The 1st Principal Component (PC) explained more than 36% of the total variance represented by time series residuals’ (series with deterministic model removed), what compared to the other PCs variances (less than 8%) means that common signals are significant in GNSS residuals. A clear improvement in the spectral indices of the power-law noise was noticed for the Up component, which is reflected by an average shift towards white noise from − 0.98 to − 0.67 (30%). We observed a significant average reduction in the accuracy of stations’ velocity estimated for filtered residuals by 35, 28 and 69% for the North, East, and Up components, respectively. CME series were also subjected to analysis in the context of environmental mass loading influences of the filtering results. Subtraction of the environmental loading models from GNSS residuals provides to reduction of the estimated CME variance by 20 and 65% for horizontal and vertical components, respectively.
Highlights
We found that only the first Principal Component (PC) is significant when deterministic model was subtracted prior the principal component analysis (pPCA) analysis, which is consistent with the considerations of other authors (Dong et al 2006; Shen et al 2013)
On the basis of the results presented we may conclude that the pPCA method is able to be directly applied to the Global Navigation Satellite System (GNSS) position time series with no need to interpolate the data before spatio-temporal filtering
We proposed probabilistic Principal Component Analysis (PCA)-based filtering method for the GNSS time series highly affected by missing values or for a situation where stations started and ended operation at different times
Summary
The advantages of reliable coordinates provided by the globally distributed Global Navigation Satellite System (GNSS) stations have been appreciated by scientists since the early 90s. We applied the pPCA method to resolve the problem of a proper spatio-temporal filtering of GNSS position time series when gaps occur at the same time in the regional network and the series do not necessarily have the same observation time span. This method is presented as an alternative to the classic PCA approach and its modifications: mPCA and iPCA. That the methodology presented in this research, applied to the GNSS position time series, is universal and can be successfully adapted to data having spatial relationships gathered by GNSS, as e.g. ZTD (Zenith Total Delay), or any other geodetic instruments such as GRACE (Gravity Recovery and Climate Experiment) or altimetric satellites
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