On the Mátern covariance family:

a proposal for modeling temporal correlations based on turbulence theory

verfasst von: Gaël Kermarrec, Steffen Schön
Abstract: Current variance models for GPS carrier phases that take correlation due to tropospheric turbulence into account are mathematically difficult to handle due to numerical integrations. In this paper, a new model for temporal correlations of GPS phase measurements based on turbulence theory is proposed that overcomes this issue. Moreover, we show that the obtained model belongs to the Mátern covariance family with a smoothness of 5/6 as well as a correlation time between 125–175 s. For this purpose, the concept of separation distance between two lines-of-sight introduced by Schön and Brunner (J Geod 1:47–57, 2008a) is extended. The approximations made are highlighted as well as the turbulence parameters that should be taken into account in our modeling. Subsequently, fully populated covariance matrices are easily computed and integrated in the weighted least-squares model. Batch solutions of coordinates are derived to show the impact of fully populated covariance matrices on the least-squares adjustments as well as to study the influence of the smoothness and correlation time. Results for a specially designed network with weak multipath are presented by means of the coordinate scatter and the a posteriori coordinate precision. It is shown that the known overestimation of the coordinate precision is significantly reduced and the coordinate scatter slightly improved in the sub-millimeter level compared to solutions obtained with diagonal, elevation-dependent covariance matrices. Even if the variations are small, turbulence-based values for the smoothness and correlation time yield best results for the coordinate scatter.
Organisationseinheit(en): Institut für Erdmessung
Typ: Artikel
Journal: Journal of geodesy
Band: 88
ISSN: 0949-7714
Publikationsdatum: 02.07.2014
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Geophysik, Geochemie und Petrologie, Computer in den Geowissenschaften
Elektronische Version(en): https://doi.org/10.1007/s00190-014-0743-7 (Zugang: Geschlossen)
: Details im Forschungsportal „Research@Leibniz University“

BibTeX

@article{4ab097b1cbee46edb91110ef7ce62e04,
title = "On the M{\'a}tern covariance family:: a proposal for modeling temporal correlations based on turbulence theory",
abstract = "Current variance models for GPS carrier phases that take correlation due to tropospheric turbulence into account are mathematically difficult to handle due to numerical integrations. In this paper, a new model for temporal correlations of GPS phase measurements based on turbulence theory is proposed that overcomes this issue. Moreover, we show that the obtained model belongs to the M{\'a}tern covariance family with a smoothness of 5/6 as well as a correlation time between 125–175 s. For this purpose, the concept of separation distance between two lines-of-sight introduced by Sch{\"o}n and Brunner (J Geod 1:47–57, 2008a) is extended. The approximations made are highlighted as well as the turbulence parameters that should be taken into account in our modeling. Subsequently, fully populated covariance matrices are easily computed and integrated in the weighted least-squares model. Batch solutions of coordinates are derived to show the impact of fully populated covariance matrices on the least-squares adjustments as well as to study the influence of the smoothness and correlation time. Results for a specially designed network with weak multipath are presented by means of the coordinate scatter and the a posteriori coordinate precision. It is shown that the known overestimation of the coordinate precision is significantly reduced and the coordinate scatter slightly improved in the sub-millimeter level compared to solutions obtained with diagonal, elevation-dependent covariance matrices. Even if the variations are small, turbulence-based values for the smoothness and correlation time yield best results for the coordinate scatter.",
keywords = "GPS, M{\'a}tern covariance family, Physical correlations, Temporal correlations, Turbulence theory",
author = "Ga{\"e}l Kermarrec and Steffen Sch{\"o}n",
note = "Funding information: The authors gratefully acknowledge the funding by the DFG under the label SCHO1314/1-2. Fritz K. Brunner is warmly thanked for discussions on turbulence theory and for providing the GPS data of the Seewinkel Network. The valuable comments of three anonymous reviewers helped us improve significantly the manuscript.",
year = "2014",
month = jul,
day = "2",
doi = "10.1007/s00190-014-0743-7",
language = "English",
volume = "88",
journal = "Journal of geodesy",
issn = "0949-7714",
publisher = "Springer Verlag",
number = "11",
}