Fast approximation algorithm to noise components estimation in long-term GPS coordinate time series

Tehranchi, Ramin; Moghtased-Azar, Khosro; Safari, Abdolreza

doi:10.1007/s00190-021-01473-0

Cited by 12 publications

(6 citation statements)

References 64 publications

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“… 2008 ) or closely related estimators such as the restricted MLE (see, e.g., Tehranchi et al. 2021 ). In this section, we briefly review how maximum likelihood estimators can be constructed in this setting.…”

Section: Problem Formulationmentioning

confidence: 99%

“…The standard approach for the estimation of the problem defined in (1) is based on the MLE (see, e.g., Bos et al 2008) or closely related estimators such as the restricted MLE (see, e.g., Tehranchi et al 2021). In this section, we briefly review how maximum likelihood estimators can be constructed in this setting.…”

Section: Standard Likelihood-based Approachmentioning

confidence: 99%

“…Tehranchi et al. ( 2021 ) further improved the computational aspect of the method using restricted MLE. Despite these computational improvements, the analysis of crustal deformation or geodynamical activity on a large scale that (i) includes hundreds to thousands of GNSS stations (He et al.…”

Section: Introductionmentioning

confidence: 99%

“…Bos et al (2008Bos et al ( , 2013 reduced the computation time of a factor of 10-100 compared to the standard MLE method (depending on the length of the real time series) initially developed by Williams (2008). Tehranchi et al (2021) further improved the computational aspect of the method using restricted MLE. Despite these computational improve-ments, the analysis of crustal deformation or geodynamical activity on a large scale that (i) includes hundreds to thousands of GNSS stations (He et al 2021), (ii) with some of them recording more than 25 years of continuous observations and (iii) when different noise models must be tested, becomes impractical due to the large amount (e.g., weeks) of processing time required (He et al 2019;Bos et al 2020).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Generalized Method of Wavelet Moments with eXogenous inputs: a fast approach for the analysis of GNSS position time series

Cucci

Voirol

Kermarrec

et al. 2023

J Geod

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The global navigation satellite system (GNSS) daily position time series are often described as the sum of stochastic processes and geophysical signals which allow to study global and local geodynamical effects such as plate tectonics, earthquakes, or ground water variations. In this work, we propose to extend the Generalized Method of Wavelet Moments (GMWM) to estimate the parameters of linear models with correlated residuals. This statistical inferential framework is applied to GNSS daily position time-series data to jointly estimate functional (geophysical) as well as stochastic noise models. Our method is called GMWMX, with X standing for eXogenous variables: it is semi-parametric, computationally efficient and scalable. Unlike standard methods such as the widely used maximum likelihood estimator (MLE), our methodology offers statistical guarantees, such as consistency and asymptotic normality, without relying on strong parametric assumptions. At the Gaussian model, our results (theoretical and obtained in simulations) show that the estimated parameters are similar to the ones obtained with the MLE. The computational performances of our approach have important practical implications. Indeed, the estimation of the parameters of large networks of thousands of GNSS stations (some of them being recorded over several decades) quickly becomes computationally prohibitive. Compared to standard likelihood-based methods, the GMWMX has a considerably reduced algorithmic complexity of order $$\mathcal {O}\{\log (n) n\}$$ O { log ( n ) n } for a time series of length n. Thus, the GMWMX appears to provide a reduction in processing time of a factor of 10–1000 compared to likelihood-based methods depending on the considered stochastic model, the length of the time series and the amount of missing data. As a consequence, the proposed method allows the estimation of large-scale problems within minutes on a standard computer. We validate the performances of our method via Monte Carlo simulations by generating GNSS daily position time series with missing observations and we consider composite stochastic noise models including processes presenting long-range dependence such as power law or Matérn processes. The advantages of our method are also illustrated using real time series from GNSS stations located in the Eastern part of the USA.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Standard Likelihood-based Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Generalized Method of Wavelet Moments with eXogenous inputs: a fast approach for the analysis of GNSS position time series

Cucci

Voirol

Kermarrec

et al. 2023

J Geod

View full text Add to dashboard Cite

show abstract

“…Bos et al (2008Bos et al ( , 2013 reduced the computation time of a factor of 10 to 100 compared to the standard MLE method (depending on the length of the real time series) initially developed by Williams (2008). Tehranchi et al (2021) further improved the computational aspect of the method using restricted MLE. Despite these computational improvements, the analysis of crustal deformation or geodynamical activity on a large scale that (i) includes hundreds to thousands of GNSS stations (He et al, 2021), (ii) with some of them recording more than 25 years of continuous observations and (iii) when different noise models must be tested, becomes impractical due to the large amount (e.g., weeks) of processing time required (He et al, 2019;Bos et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

The Generalized Method of Wavelet Moments with Exogenous Inputs: a Fast Approach for the Analysis of GNSS Position Time Series

Cucci¹,

Voirol²,

Kermarrec³

et al. 2022

Preprint

View full text Add to dashboard Cite

The Global Navigation Satellite System (GNSS) daily position time series are often described as the sum of stochastic processes and geophysical signals which allow studying global and local geodynamical effects such as plate tectonics, earthquakes, or ground water variations. In this work we propose to extend the Generalized Method of Wavelet Moments (GMWM) to estimate the parameters of linear models with correlated residuals. This statistical inferential framework is applied to GNSS daily position time series data to jointly estimate functional (geophysical) as well as stochastic noise models. Our method is called GMWMX, with X standing for eXogeneous variables: it is semiparametric, computationally efficient and scalable. Unlike standard methods such as the widely used Maximum Likelihood Estimator (MLE), our methodology offers statistical guarantees, such as consistency and asymptotic normality, without relying on strong parametric assumptions. At the Gaussian model, our results (theoretical and obtained in simulations) show that the estimated parameters are similar to the ones obtained with the MLE. The computational performances of our approach have important practical implications. Indeed, the estimation of the parameters of large networks of thousands of GNSS stations (some of them being recorded over several decades) quickly becomes computationally prohibitive. Compared to standard methods, the processing time of the GMWMX is over 1000 times faster considering time series recorded over 20 years and allows the estimation of large scale problems within minutes on a standard computer. We validate the performances of our method via Monte-Carlo simulations by generating GNSS daily position time series with missing observations and we consider composite stochastic noise models including processes presenting long-range dependence such as power-law or Matérn processes. The advantages of our method are also illustrated using real time series from GNSS stations located in the Eastern part of the USA.

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Efficient variance component estimation for large-scale least-squares problems in satellite geodesy

Nie

Shen

Pail

et al. 2022

J Geod

View full text Add to dashboard Cite

Fast approximation algorithm to noise components estimation in long-term GPS coordinate time series

Cited by 12 publications

References 64 publications

The Generalized Method of Wavelet Moments with eXogenous inputs: a fast approach for the analysis of GNSS position time series

The Generalized Method of Wavelet Moments with eXogenous inputs: a fast approach for the analysis of GNSS position time series

The Generalized Method of Wavelet Moments with Exogenous Inputs: a Fast Approach for the Analysis of GNSS Position Time Series

Efficient variance component estimation for large-scale least-squares problems in satellite geodesy

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