A Filtering of Incomplete GNSS Position Time Series with Probabilistic Principal Component Analysis

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.

What Causes the Common‐Mode Error in Array GPS Displacement Fields: Case Study for Taiwan in Relation to Atmospheric Mass Loading

“…Additionally, we calculate Lin's concordance correlation coefficient ( ρ c ) that is based on covariation and correspondence between two sets of scores in contrast to the linear covariation for the ρ (Gruszczynski et al, 2019; Lin, 1989; Tian & Shen, 2016). Unlike ρ that measures how far the data points are from the line, the ρ c evaluates the joint deviation of the data points from a 45° line through the origin representing perfect agreement.…”

“…The Kaiser‐Meyer‐Olkin (KMO) test statistically measures the suitability of selected GPS residuals to efficiently extract the CME using multivariate analysis such as EOF by estimating the proportion of variance among all the observed variables (Cerny & Kaiser, 1977; Gruszczynski et al, 2019; Santos et al, 2014). The resulting KMO index ranges from 0 and 1, where values close to 1 represent significant variance among the observed variables.…”

“…CME is traditionally extracted by applying the regional spatial processing (Ching et al, 2007; Wdowinski et al, 1997; Zhang et al, 2016; Zhu, Zhou, & Liu, 2017), for example, by estimating the mean of the stack of position residuals. This method has limitations when extended over extensive networks (maximum interstation distance of 600 km) where the assumption of spatial uniformity breaks down (Gruszczynski et al, 2019; Márquez‐Azúa & DeMets, 2003; Wdowinski et al, 1997; Williams et al, 2004). The CME can also be reduced via a similarity transformation algorithm (Blewitt et al, 2013).…”

“…However, Zhu, Zhou, Deng, et al (2017) used the regional stacking approach for the CME extraction which has limitations for the large region. Although the multichannel singular spectrum analysis extraction of CME used by Gruszczynski et al (2019) performed better than the regional stacking methods, it has limitations in the reliable extraction of CME for large regions. Despite some limitations, recent studies did provide insights into CME's relation with the environmental mass loading.…”

“…It is commonly known as the common‐mode errors (CMEs), or common‐mode signals depending on the context. It is thought to be the aggregative outcome of errors in the preprocessing techniques, alignment to reference frame, modeling of satellites (orbits, clocks, antenna phase center), modeling of tropospheric and ionospheric media, and geophysical phenomena such as thermal expansion and large‐scale atmospheric and hydrological effects (Dong et al, 2006; Gruszczynski et al, 2019; King et al, 2010; Wdowinski et al, 1997; Zhu, Zhou, Deng, et al, 2017).…”