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\begin{document}

\title{A Fourier-series modeling approach to develop corrections to atmospheric
drag in orbit}



\author[1]{Vishal Ray}%
\author[1]{DANIEL SCHEERES}%
\author[1]{Eric Sutton}%
\affil[1]{University of Colorado Boulder}%


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  \date{May 18, 2024}


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\begin{abstract}
Atmospheric drag is one of the primary sources of error in the orbit
determination and prediction of satellites in the low altitude LEO
regime. Accurate modeling of the drag force is limited by uncertainties
in the atmospheric density model used in the filter and the assumption
of a constant drag coefficient, the so-called `cannonball' model. Over
the last two decades, various advances in density and drag-coefficient
modeling have been made possible through the development of empirical
and physics-based dynamical calibration techniques and machine-learning
methods respectively. But even with high-fidelity models for density and
drag coefficient, systematic uncertainties can remain in both due to the
lack of temporal and spatial resolution of data and insufficient
knowledge of parameters that feed into these models. In this work, we
develop an estimation-based Fourier expansion model that can provide
corrections to the nominal values of density and drag coefficient during
the orbit determination process. In an earlier work (Ray et al., 2018),
we demonstrated improved orbit prediction performance over the standard
cannonball model with Fourier series expansions of the drag coefficient
in body frame and orbit frame of a satellite. Whereas a body-fixed
Fourier model captures the dependence of the drag coefficient on
satellite attitude, the orbit-fixed model corrects for periodic changes
in the gas-surface interaction in orbit. Since changes in the
gas-surface interaction parameters in orbit are highly correlated with
atmospheric density, any existing errors in the density are absorbed in
the estimated orbit-fixed coefficients. Here, we derive a body-orbit
Fourier model such that the orbit-fixed terms provide corrections for
combined error variations of density and drag coefficient in orbit while
the body-fixed terms account for the drag coefficient attitude
dependence. We analyze the performance of the proposed approach with
various atmospheric models such as NRLMSISE-00 (Picone et al., 2002),
JB08 (Bowman et al., 2008), HASDM (Storz et al., 2002) and densities
derived by Mehta et al. (2017) for varying geomagnetic conditions for
the GRACE satellite.%
\end{abstract}%



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