Monte Carlo SSA to detect time-variable seasonal oscillations from GPS-derived site position time series

Xu, Chang; Yue, Dongjie

doi:10.1016/j.tecto.2015.09.029

Cited by 38 publications

(13 citation statements)

References 31 publications

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“…Zerbini et al (2013) used SSA to analyze the inter-annual variability of different series. Recently, Xu and Yue (2015) used daily GPS vertical coordinate time series, to investigate seasonal SSA-filtered signals. Although it was not quantified, they concluded that SSA might absorb a part of the colored noise.…”

Section: Singular Spectrum Analysis: Ssamentioning

confidence: 99%

“…Although the noise level may have a significant impact on the precision of the estimated seasonal signals, up until now, no special attention has been paid to its influence on the effectiveness of each method. Only recently, Xu and Yue (2015) emphasized that the seasonal signals filtered with SSA may contain an artificial signal driven by colored noise. Therefore, some of the power may be artificially removed from power spectra of the residuals, leading to imprecise estimates of the noise level.…”

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confidence: 99%

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Detecting time-varying seasonal signal in GPS position time series with different noise levels

2017

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The coordinate time series determined with the Global Positioning System (GPS) contain annual and semi-annual periods that are routinely modeled by two periodic signals with constant amplitude and phase-lag. However, the amplitude and phaselag of the seasonal signals vary slightly over time. Various methods have been proposed to model these variations such as Wavelet Decomposition (WD), writing the amplitude of the seasonal signal as a Chebyshev polynomial that is a function of time (CP), Singular Spectrum Analysis (SSA), and using a Kalman Filter (KF). Using synthetic time series, we investigate the ability of each method to capture the time-varying seasonal signal in time series with different noise levels. We demonstrate that the precision by which the varying seasonal signal can be estimated depends on the ratio of the variations in the seasonal signal to the noise level. For most GPS time series, this ratio is between 0.05 and 0.1. Within this range, the WD and CP have the most trouble in separating the seasonal signal from the noise. The most precise estimates of the variations are given by the SSA and KF methods. For real GPS data, SSA and KF can model 49-84 and 77-90% of the variance of the true varying seasonal signal, respectively.

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Section: Singular Spectrum Analysis: Ssamentioning

confidence: 99%

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confidence: 99%

Detecting time-varying seasonal signal in GPS position time series with different noise levels

2017

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“…In the latter, the authors proved that SSA has the ability to extract time-variable seasonal signals (annual and semiannual) and non-linear trend from GPS time series. More recently, Xu and Yue (2015) used Monte Carlo SSA (MCSSA) to extract the time-variable seasonal signal from daily GPS position time series and conducted statistical analysis on the colored noise. MSSA, which we employ in this research, has been only recently used in geodesy field.…”

Section: Multichannel Singular Spectrum Analysismentioning

confidence: 99%

Deriving common seasonal signals in GPS position time series: by using multichannel singular spectrum analysis

Gruszczyńska¹

2017

Acta Geodynamica Et Geomaterialia

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We estimated the common seasonal signal (annual oscillation) included in the Global Positioning System (GPS) vertical position time series by using Multichannel Singular Spectrum Analysis (MSSA). We employed time series from 24 International GNSS Service (IGS) stations located in Europe which contributed to the newest ITRF2014 (International Terrestrial Reference Frame). The MSSA method has an advantage over the traditional modelling of seasonal signals by the Least-Squares Estimation (LSE) and Singular Spectrum Analysis (SSA) approaches because it can extract time-varying and common seasonal oscillations for stations located in the considered area. Having estimated the annual curve with LSE, we may make a misfit of 3 mm when a peakto-peak variations of seasonal signals are to be estimated due to the time-variability of seasonal signal. A variance of data modelled as annual signal with SSA and MSSA differs of 3 % at average what proves that the MSSA-curves contain only time-varying and common seasonal signal and leave the station-specific part, local phenomena and power-law noise intact. In contrast to MSSA, these effects are modelled by SSA. The differences in spectral indices of power-law noise between MSSA and LSE estimated with Maximum Likelihood Estimation (MLE) are closer to zero than the ones between SSA and LSE, which means that MSSA curves do not contain site-specific noise as much as the SSA curves do. ARTICLE INFO

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“…Beyond wavelet decomposition, the SSA approach has also been previously applied to the GPS (e.g. Zerbini et al 2013;Xu and Yue 2015) and DORIS data (Khelifa et al 2012) and followed by a noise analysis with wavelet decomposition (Khelifa et al 2012). This paper focuses on the analysis of the stochastic properties of the DORIS time series; however, the deterministic part of the DORIS data is also examined.…”

Section: Electronic Supplementary Materialsmentioning

confidence: 99%

Stochastic models in the DORIS position time series: estimates for IDS contribution to ITRF2014

Kłos

Bogusz

Moreaux

2017

J Geod

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This paper focuses on the investigation of the deterministic and stochastic parts of the Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) weekly time series aligned to the newest release of ITRF2014. A set of 90 stations was divided into three groups depending on when the data were collected at an individual station. To reliably describe the DORIS time series, we employed a mathematical model that included the long-term nonlinear signal, linear trend, seasonal oscillations and a stochastic part, all being estimated with maximum likelihood estimation. We proved that the values of the parameters delivered for DORIS data are strictly correlated with the time span of the observations. The quality of the most recent data has significantly improved. Not only did the seasonal amplitudes decrease over the years, but also, and most importantly, the noise level and its type changed significantly. Among several tested models, the power-law process may be chosen as the preferred one for most of the DORIS data. Moreover, the preferred noise model has changed through the years from an autoregressive process to pure power-law noise with few stations characterised by a positive spectral index. For the latest observations, the medians of the velocity errors were equal to 0.3, 0.3 and 0.4 mm/year, respectively, for the North, East and Up components. In the best cases, a velocity uncertainty of DORIS sites of 0.1 mm/year is achievable when the appropriate coloured noise model is taken into consideration.

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Monte Carlo SSA to detect time-variable seasonal oscillations from GPS-derived site position time series

Cited by 38 publications

References 31 publications

Detecting time-varying seasonal signal in GPS position time series with different noise levels

Detecting time-varying seasonal signal in GPS position time series with different noise levels

Deriving common seasonal signals in GPS position time series: by using multichannel singular spectrum analysis

Stochastic models in the DORIS position time series: estimates for IDS contribution to ITRF2014

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