Details
| Original language | English |
|---|---|
| Journal | Journal of geodesy |
| Volume | 88 |
| Issue number | 11 |
| Publication status | Published - 2 Jul 2014 |
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.
Keywords
- GPS, Mátern covariance family, Physical correlations, Temporal correlations, Turbulence theory
ASJC Scopus subject areas
- Earth and Planetary Sciences(all)
- Geophysics
- Earth and Planetary Sciences(all)
- Geochemistry and Petrology
- Earth and Planetary Sciences(all)
- Computers in Earth Sciences
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In: Journal of geodesy, Vol. 88, No. 11, 02.07.2014.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the Mátern covariance family:
T2 - a proposal for modeling temporal correlations based on turbulence theory
AU - Kermarrec, Gaël
AU - Schön, Steffen
N1 - 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.
PY - 2014/7/2
Y1 - 2014/7/2
N2 - 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.
AB - 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.
KW - GPS
KW - Mátern covariance family
KW - Physical correlations
KW - Temporal correlations
KW - Turbulence theory
UR - http://www.scopus.com/inward/record.url?scp=84919465281&partnerID=8YFLogxK
U2 - 10.1007/s00190-014-0743-7
DO - 10.1007/s00190-014-0743-7
M3 - Article
AN - SCOPUS:84919465281
VL - 88
JO - Journal of geodesy
JF - Journal of geodesy
SN - 0949-7714
IS - 11
ER -