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.
