TY - JOUR

T1 - Common-clock GPS single differences

T2 - An improved correlation model for GPS phase observations based on turbulence theory

AU - Kermarrec, Gaël

AU - Schön, Steffen

N1 - Funding Information: Dr. Le Ren is warmly thanked for having processed the SD analyzed in this contribution. Dr. Thomas Krawinkel set up the GNSS measurements. We further thank Dr. Andreas Bauch und Julia Leute, both from PTB, for operating the common clock experiment. This study is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under the project KE2453/2-1, as a pre-step to the analysis of atmospheric noise from a terrestrial laser scanner. The data from the GPS experiment was captured within the research project “Surveying” funded by the European Metrology Research Program. Some analyses were made in the framework of the Collaborative Research Center TerraQ funded by the Deutsche Forschungsgemeinschaft – Project-ID 434617780 – SFB 1464.

PY - 2023/8/15

Y1 - 2023/8/15

N2 - Microwave signals, for example, those from Global Navigation Satellite System (GNSS) and Very Long Baseline Interferometry (VLBI), are affected by tropospheric turbulence in such a way that the random fluctuations of the atmospheric index of refractivity correlate the phase measurements. A proper modeling of correlations is mandatory to avoid biased analysis, particularly when statistical tests are used. In this contribution, we analyze single differences (SD) computed from Global Positioning System (GPS) phase observations for which the between receiver clock error could be strongly mitigated by a specific common clock setting. We estimate specific parameters from the power spectral density (psd), which is directly related to the correlation function, with the debiased Whittle maximum likelihood and investigate their dependencies with the satellite geometry (elevation, azimuth angles) and the time of the day. We show that (i) the estimated slopes of the psd follow the one predicted by the Kolmogorov turbulence theory and (ii) the cut-off at high frequencies shows daily variations that may be linked with the strength of the turbulence. Based on these findings, we derive an improved spectral density model for GPS phase SD. The results of this study contribute to improving the stochastic description of random effects impacting VLBI and GNSS phase observations by studying variations of parameters from the von Karman spectrum.

AB - Microwave signals, for example, those from Global Navigation Satellite System (GNSS) and Very Long Baseline Interferometry (VLBI), are affected by tropospheric turbulence in such a way that the random fluctuations of the atmospheric index of refractivity correlate the phase measurements. A proper modeling of correlations is mandatory to avoid biased analysis, particularly when statistical tests are used. In this contribution, we analyze single differences (SD) computed from Global Positioning System (GPS) phase observations for which the between receiver clock error could be strongly mitigated by a specific common clock setting. We estimate specific parameters from the power spectral density (psd), which is directly related to the correlation function, with the debiased Whittle maximum likelihood and investigate their dependencies with the satellite geometry (elevation, azimuth angles) and the time of the day. We show that (i) the estimated slopes of the psd follow the one predicted by the Kolmogorov turbulence theory and (ii) the cut-off at high frequencies shows daily variations that may be linked with the strength of the turbulence. Based on these findings, we derive an improved spectral density model for GPS phase SD. The results of this study contribute to improving the stochastic description of random effects impacting VLBI and GNSS phase observations by studying variations of parameters from the von Karman spectrum.

KW - atmospheric turbulence

KW - Common clock

KW - Correlation model

KW - GPS single difference

KW - Kolmogorov turbulence theory

KW - outer scale length

KW - VLBI

KW - Atmosphärische Turbulenz

KW - Common Clock

KW - Korrelationsmodell

KW - GPS Einfachdifferenzen

KW - Kolmogorov Turbulenz Theorie

KW - outer scale length

KW - VLBI

UR - http://www.scopus.com/inward/record.url?scp=85163368514&partnerID=8YFLogxK

U2 - 10.1016/j.asr.2023.05.042

DO - 10.1016/j.asr.2023.05.042

M3 - Article

AN - SCOPUS:85163368514

VL - 72

SP - 1081

EP - 1093

JO - Advances in space research

JF - Advances in space research

SN - 0273-1177

IS - 4

ER -