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

Gruszczynski, Maciej; Kłos, Anna; Bogusz, Janusz

doi:10.1007/s00024-018-1856-3

Cited by 23 publications

(34 citation statements)

References 67 publications

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“…Similarly to Klos and Bogusz [23], and Gruszczynski et al [28], we also observed a distinguished spatial pattern in the distribution of the parameters describing the stochastic part, i.e., the spectral index and the amplitudes of the power-law noise with an impact for the Baltic countries. These parameters influence the velocity uncertainty, as in Equation (4).…”

Section: Discussionsupporting

confidence: 87%

“…It may arise from large-scale phenomena which were insufficiently modelled at the processing stage of the observations. Similar spatial patterns were noticed by Gruszczynski et al [28] from the analysis based on the empirical orthogonal functions (EOFs) computed for the non-tidal environmental loading models. They found an evident impact of the Baltic Sea, concluding that this area is mostly affected by large-scale phenomena; this impact will occur as the common mode error when computed for the European sites.…”

Section: Noise Analysissupporting

confidence: 81%

“…Based on these uncertainties, we decide about the statistical significance of the GPS vertical rates. As shown by [28] with empirical orthogonal functions, areas of central and northern Europe, i.e., especially those surrounding the Baltic coasts, are significantly impacted by non-tidal atmospheric loading, which is for now not included within the GPS processing. We argue that this loading may mostly affect the character of the position time series, i.e., the amplitudes of power-law noises, and also, the character of the noise, and the velocity uncertainties, consequently.…”

Section: Discussionmentioning

confidence: 99%

“…A flicker noise arises from the mis-modelling of large-scale effects has a spectral index of −1. This mis-modelling of hydrospheric effects or satellite orbits and clocks is considered the common mode error (CME, [26]) and has already been effectively modelled and removed from the position time series [27], leading to its impact on the velocity uncertainty being reduced [28]. A white noise component with a spectral index of 0 arises from the high-frequency temporally uncorrelated errors introduced at the stage of data processing.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Strategy of a GPS Position Time Series Analysis for Post-Glacial Rebound Investigation in Europe

2019

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We describe a comprehensive analysis of the 469 European Global Positioning System (GPS) vertical position time series. The assumptions we present should be employed to perform the post-glacial rebound (PGR)-oriented comparison. We prove that the proper treatment of either deterministic or stochastic components of the time series is indispensable to obtain reliable vertical velocities along with their uncertainties. The statistical significance of the vertical velocities is examined; due to their small vertical rates, 172 velocities from central and western Europe are found to fall below their uncertainties and excluded from analyses. The GPS vertical velocities reach the maximum values for Scandinavia with the maximal uplift equal to 11.0 mm/yr. Moreover, a comparison between the GPS-derived rates and the present-day motion predicted by the newest Glacial Isostatic Adjustment (GIA) ICE-6G_C (VM5a) model is provided. We prove that these rates agree at a 0.5 mm/yr level on average; the Sweden area with the most significant uplift observed agrees within 0.2 mm/yr. The largest discrepancies between GIA-predicted uplift and the GPS vertical rates are found for Svalbard; the difference is equal to 6.7 mm/yr and arises mainly from the present-day ice melting. The GPS-derived vertical rates estimated for the southern coast of the Baltic Sea are systematically underestimated by the GIA prediction by up to 2 mm/yr. The northern British Isles vertical rates are overestimated by the GIA model by about 0.5 mm/yr. The area of the Netherlands and the coastal area of Belgium are both subsiding faster than it is predicted by the GIA model of around 1 mm/yr. The inland part of Belgium, Luxemburg and the western part of Germany show strong positive velocities when compared to the GIA model. Most of these stations uplift of more than 1 mm/yr. It may be caused by present-day elastic deformation due to terrestrial hydrology, especially for Rhein basin, or non-tidal atmospheric loading, for Belgium and Luxembourg.

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Section: Discussionsupporting

confidence: 87%

Section: Noise Analysissupporting

confidence: 81%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Strategy of a GPS Position Time Series Analysis for Post-Glacial Rebound Investigation in Europe

2019

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“…This has already been widely described in numerous studies by Zhang et al (1997), Mao et al (1999), Williams et al (2004), Bos et al (2010) and Klos et al (2016), that a power-law process being close to flicker noise with a spectral index of −1 is the optimum noise model to describe the stochastic part of the GPS data. The impact of this phenomena on the velocity uncertainties may be reduced by spatial filtering using different methods, such as stacking or principal component analysis (PCA), which help to estimate a common mode error (CME; Dong et al 2006;Bogusz et al 2015b;Gruszczynski et al 2018). Some authors observed that the instability of monuments may be another contributor to site-specific noise.…”

Section: Introductionmentioning

confidence: 99%

Noise-Dependent Adaption of the Wiener Filter for the GPS Position Time Series

et al. 2018

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Various methods have been used to model the time-varying curves within the global positioning system (GPS) position time series. However, very few consider the level of noise a priori before the seasonal curves are estimated. This study is the first to consider the Wiener filter (WF), already used in geodesy to denoise gravity records, to model the seasonal signals in the GPS position time series. To model the time-varying part of the signal, a first-order autoregressive process is employed. The WF is then adapted to the noise level of the data to model only those time variabilities which are significant. Synthetic and real GPS data is used to demonstrate that this variation of the WF leaves the underlying noise properties intact and provides optimal modeling of seasonal signals. This methodology is referred to as the adaptive WF (AWF) and is both easy to implement and fast, due to the use of the fast Fourier transform method.

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Modelling the GNSS Time Series: Different Approaches to Extract Seasonal Signals

Kłos

Bogusz

Bos

et al. 2019

Geodetic Time Series Analysis in Earth Sciences

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

Cited by 23 publications

References 67 publications

Optimal Strategy of a GPS Position Time Series Analysis for Post-Glacial Rebound Investigation in Europe

Optimal Strategy of a GPS Position Time Series Analysis for Post-Glacial Rebound Investigation in Europe

Noise-Dependent Adaption of the Wiener Filter for the GPS Position Time Series

Modelling the GNSS Time Series: Different Approaches to Extract Seasonal Signals

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