On Error Modeling in GNSS-based Frequency Transfer: Effects of Temperature Variations and Satellite Orbit Repeat Times

authored by

Ahmed Elmaghraby, Thomas Krawinkel, Steffen Schön, Dirk Piester, Andreas Bauch

Abstract

Frequency transfer is essential in various geodetic applications, where accuracy and low uncertainty are needed. The low uncertainty provides rigorous means to model and monitor the sea level, the atmosphere and the Earth’s gravitational field, where clock frequency comparison is a tool to measure the gravity potential differences. The remote oscillators’ frequency can be transferred/compared using many methods. In this paper, the focus is Global Navigation Satellite System (GNSS) based frequency transfer. Although GNSS-based frequency transfer is a well-established method, it suffers from disturbances degrading its stability which often are not properly modeled nor compensated. We analyze here the data acquired from a dedicated common-clock experiment done at Physikalisch-Technische Bundesanstalt (PTB), Germany’s national meteorology institute. In which the GNSS receivers were located at two sites approximately 295 m apart, and the clock signal generated at one site is transported via an optical fiber link to the other site. So the analysis deals with a type of common-clock configuration. Correlations are discussed for the available fiber link used during the experiment for the same baseline. Furthermore, we inspect the fiber link data to correct the estimated receiver clock differences. Both links, GNSS and the fiber, show the deviation modeled with 3 degrees polynomial. We discuss the impact of local temperature and of the repeatability of GNSS constellations GPS and Galileo as reasons for such disturbances. Hence, we investigate the temperature variations effect especially on the GNSS receivers by analyzing the indoor temperature data logged at both stations. Moreover, we introduce a glimpse on the GPS and Galileo constellation repeatability and how this could influence the estimated receiver clock differences. The fiber link data is correlated with the estimated clock signal differences with values reaching 94% of maximum correlation. In addition, we employ fiber link correction data recorded at PTB in parallel to our GNSS experiment. We use these data to compensate for residual deviations between the two clock signals involved. We investigate precisely the ambient temperature data collected inside the laboratories where the GNSS receivers were installed. The differential temperature data show high correlations values of 60% with the estimated receiver clock variations on the day, when a temperature drop happened. Furthermore, a temperature coefficient of the overall indoor setup could be estimated to be in the range of 25 ps/

^◦C in this experiment. As expected, for the fiber link corrected time series, the data show better long-term instability than without the correction applied. This approach leads, however, to a marginally worse short-term instability. The temperature sensitivity is estimated from the linear regression applied on the highly correlated data set. We apply this further on the clock difference showing slight improvement in the computed modified Allan deviation. Concerning the GNSS constellation, the number of used satellites in the estimation process is used to indicate the repeatability of the GNSS constellation on one hand. On the other hand, we discuss the effect of number changes on the estimated receiver clock differences.

Organisation(s)

Institute of Geodesy
CRC 1464: Relativistic and Quantum-Based Geodesy (TerraQ)
QUEST-Leibniz Research School

Type

Conference contribution

Pages

23-37

No. of pages

Publication date

15.02.2023

Publication status

Published

Electronic version(s)

https://doi.org/10.33012/2023.18699 (Access: Closed)

BibTeX

@inproceedings{7cf8f15aea364c948c047525ce545de6,
title = "On Error Modeling in GNSS-based Frequency Transfer: Effects of Temperature Variations and Satellite Orbit Repeat Times",
abstract = "Frequency transfer is essential in various geodetic applications, where accuracy and low uncertainty are needed. The low uncertainty provides rigorous means to model and monitor the sea level, the atmosphere and the Earth{\textquoteright}s gravitational field, where clock frequency comparison is a tool to measure the gravity potential differences. The remote oscillators{\textquoteright} frequency can be transferred/compared using many methods. In this paper, the focus is Global Navigation Satellite System (GNSS) based frequency transfer. Although GNSS-based frequency transfer is a well-established method, it suffers from disturbances degrading its stability which often are not properly modeled nor compensated. We analyze here the data acquired from a dedicated common-clock experiment done at Physikalisch-Technische Bundesanstalt (PTB), Germany{\textquoteright}s national meteorology institute. In which the GNSS receivers were located at two sites approximately 295 m apart, and the clock signal generated at one site is transported via an optical fiber link to the other site. So the analysis deals with a type of common-clock configuration. Correlations are discussed for the available fiber link used during the experiment for the same baseline. Furthermore, we inspect the fiber link data to correct the estimated receiver clock differences. Both links, GNSS and the fiber, show the deviation modeled with 3 degrees polynomial. We discuss the impact of local temperature and of the repeatability of GNSS constellations GPS and Galileo as reasons for such disturbances. Hence, we investigate the temperature variations effect especially on the GNSS receivers by analyzing the indoor temperature data logged at both stations. Moreover, we introduce a glimpse on the GPS and Galileo constellation repeatability and how this could influence the estimated receiver clock differences. The fiber link data is correlated with the estimated clock signal differences with values reaching 94% of maximum correlation. In addition, we employ fiber link correction data recorded at PTB in parallel to our GNSS experiment. We use these data to compensate for residual deviations between the two clock signals involved. We investigate precisely the ambient temperature data collected inside the laboratories where the GNSS receivers were installed. The differential temperature data show high correlations values of 60% with the estimated receiver clock variations on the day, when a temperature drop happened. Furthermore, a temperature coefficient of the overall indoor setup could be estimated to be in the range of 25 ps/ ◦C in this experiment. As expected, for the fiber link corrected time series, the data show better long-term instability than without the correction applied. This approach leads, however, to a marginally worse short-term instability. The temperature sensitivity is estimated from the linear regression applied on the highly correlated data set. We apply this further on the clock difference showing slight improvement in the computed modified Allan deviation. Concerning the GNSS constellation, the number of used satellites in the estimation process is used to indicate the repeatability of the GNSS constellation on one hand. On the other hand, we discuss the effect of number changes on the estimated receiver clock differences.",
author = "Ahmed Elmaghraby and Thomas Krawinkel and Steffen Sch{\"o}n and Dirk Piester and Andreas Bauch",
note = "Funding Information: This research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 434617780 – SFB 1464.; 54th Annual Precise Time and Time Interval Systems and Applications Meeting ; Conference date: 23-01-2023 Through 26-01-2023",
year = "2023",
month = feb,
day = "15",
doi = "10.33012/2023.18699",
language = "English",
series = "Proceedings of the Annual Precise Time and Time Interval Systems and Applications Meeting, PTTI",
pages = "23--37",
booktitle = "Proceedings of the 54th Annual Precise Time and Time Interval Systems and Applications Meeting",
}