TY - JOUR

T1 - The Generalized Method of Wavelet Moments with eXogenous inputs

T2 - a fast approach for the analysis of GNSS position time series

AU - Cucci, Davide A.

AU - Voirol, Lionel

AU - Kermarrec, Gaël

AU - Montillet, Jean Philippe

AU - Guerrier, Stéphane

N1 - Funding Information: The data for PANGA/CWU processing center are available freely at https://data.unavco.org/archive/gnss/products/position/ . In this study, we used, e.g., https://YORK/YORK.pbo.igs14.pos for the YORK station. The PBO velocity solutions are available at https://data.unavco.org/archive/gnss/products/velocity/ . We choose the solutions https://cwu.final_igs14.vel. D. A. Cucci and S. Guerrier were supported by the SNSF Professorships Grant #176843 and by the Innosuisse-Boomerang Grant #37308.1 IP-ENG. L. Voirol was supported by SNSF Grant #182684. G. Kermarrec is supported by the Deutsche Forschungsgemeinschaft under the project KE2453/2-1. We thank Roberto Molinari, Maria-Pia Victoria-Feser, Haotian Xu and Yuming Zhang for their valuable inputs and suggestions throughout the development of this work as well as for their comments on the final draft. We thank the Assistant Editor-in-Chief Professor Peiliang Xu and the two anonymous referees for their valuable inputs and suggestions that have allowed us to greatly improve the quality of this work. All simulations were performed on the high-performance computing clusters Yggdrasil and Baobab of the University of Geneva. We thank the maintenance team and the University of Geneva for the access to this computing cluster. The GMWMX method is available in the R package gmwmx, which is available on Github https://github.com/SMAC-Group/gmwmx and on the Comprehensive R Archive Network (CRAN) https://cran.r-project.org/web/packages/gmwmx/index.html .

PY - 2023/2/6

Y1 - 2023/2/6

N2 - 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 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.

AB - 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 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.

KW - Geodynamics

KW - Long-range dependence

KW - Maximum likelihood estimator

KW - Tectonic

KW - Two-step estimation

KW - Variance decomposition

UR - http://www.scopus.com/inward/record.url?scp=85147506855&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2206.09668

DO - 10.48550/arXiv.2206.09668

M3 - Article

AN - SCOPUS:85147506855

VL - 97

JO - Journal of geodesy

JF - Journal of geodesy

SN - 0949-7714

IS - 2

M1 - 14

ER -