May the Force Be Simple: Fourier-Based Radiation Pressure Models for all GNSS Spacecraft

Florian Dilssner and Tim Springer

Abstract:	Precise orbit determination and propagation of Global Navigation Satellite System (GNSS) spacecraft hinge on accurate modeling of non-conservative forces, such as solar radiation pressure (SRP), Earth radiation pressure (ERP), thermal reradiation (TRR), and antenna thrust (AT). Of the four forces mentioned, the radiation pressure forces—most notably SRP—are by far the most significant. Modeling them is intricate, as it requires detailed knowledge of spacecraft characteristics (attitude, geometry, surface properties, thermal design), as well as accurate Earth albedo and Earth infrared models. Even slight uncertainties, as small as a few nanometers per second squared, will significantly impact the satellite trajectories, altering them by tens of centimeters over a day. In this paper, we outline the development and testing of new empirically derived radiation pressure models for all GNSS, created independently of any spacecraft metadata. Our methodology involves dynamic long-arc (5-day) fitting to precise orbit data and the utilization of low-order Fourier functions of the Earth-spacecraft-Sun angle to represent the combined effect of the SRP, ERP, TRR, and AT forces as accurately as possible. The parameterization is similar to that of existing models, such as Rockwell’s ROCK and the Jet Propulsion Laboratory's (JPL) GPS Solar Pressure Model (GSPM). We iteratively adjust the Fourier coefficients along with a set of arc-dependent parameters—including the state vector, radiation pressure offset (D0), and one-constant-per-revolution (CPR) along-track terms—to best fit the data in a least-squares sense. Subsequently, we rigorously combine all 5-day arc solutions at the normal equation level to construct a robust, metadata-free set of force models for individual satellites or satellite groups. The new models offer several benefits: they are computationally efficient, easy to implement into any GNSS software, accurately reflect the satellites’ in-orbit behavior, eliminate the need for an additional Earth albedo/infrared model, and improve the accuracy of both the estimated and predicted orbits. Moreover, improved performance is evident in empirical radiation pressure estimates, laser ranging residuals, Earth rotation parameters, and narrow-lane double-difference residuals. The models are publicly available (https://gitlab.com/positim/RnR_models) and will be continuously updated, providing a powerful yet straightforward solution for the GNSS community.
Published in:	Proceedings of the 38th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2025) September 8 - 12, 2025 Hilton Baltimore Inner Harbor Baltimore, Maryland
Pages:	3251 - 3265
Cite this article:	Dilssner, Florian, Springer, Tim, "May the Force Be Simple: Fourier-Based Radiation Pressure Models for all GNSS Spacecraft," Proceedings of the 38th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2025), Baltimore, Maryland, September 2025, pp. 3251-3265. https://doi.org/10.33012/2025.20347
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