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\begin{document}

\title{The Atmospheric Scale Lengths of Turbulence and Its Dependencies Derived
from GPS Single Difference with a Common Clock}



\author[1]{Gaël Kermarrec}%
\author[2]{Steffen Schön}%
\affil[1]{Leibniz University Hanover}%
\affil[2]{Leibniz Universität Hannover}%


\vspace{-1em}



  
  \date{May 23, 2024}


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\begin{abstract}
Microwave signals, for example, those from Global Navigation Satellite
Systems (GNSS) and very long baseline interferometry, are affected by
tropospheric turbulence in such a way that the random fluctuations of
the atmospheric index of refraction correlate the phase measurements.
These atmospheric correlations are an important error source in space
geodetic techniques. For computational reasons, they are neglected in
positioning applications, to the detriment of a trustworthy description
of the precision, and rigorous test statistics. Fortunately, modelling
such correlations is possible by combining concepts from electromagnetic
wave propagation in a random medium and the Kolmogorov turbulence
theory. In this contribution, we will process single differences GNSS
phase observations from a 300 m baseline between two different receivers
linked to a common clock. After a preprocessing to filter additional
error contributions, such as multipath, we will study the power spectral
density of the phase residuals. We will estimate its low and high cutoff
frequencies with an adapted unbiased Whittle maximum likelihood
estimator. These cutoff frequencies -- as predicted by turbulence theory
-- are related directly to the scale lengths of turbulence, i.e. the
size of the eddies that correlate the GNSS observations. The study of
their dependencies with the satellite geometry, day of the year, or time
of the day provides new insights into the two- and three-dimensional
atmospheric turbulence in the atmosphere. In addition, it contributes to
improving the stochastic description of random effects impacting GNSS
phase observations.%
\end{abstract}%



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\textbf{Hosted file}

\verb`essoar.10507630.1.docx`  available at \url{https://authorea.com/users/529761/articles/602325-the-atmospheric-scale-lengths-of-turbulence-and-its-dependencies-derived-from-gps-single-difference-with-a-common-clock}

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