The Effect of the Ballistic Coefficient on Satellite Orbit Prediction

Madeline McDougal, Scott Martin, Kip Underwood

Abstract:	Determining the location of LEO satellites in orbit is important when using them for navigation. Because of the altitude that LEO satellites orbit, a large perturbation affecting them is atmospheric drag. This variable, unlike gravity, can be difficult to model accurately due to the variations in density and the ballistic coefficient. While in orbit, a satellite equipped with an on-board GPS receiver could possibly malfunction and lose measurements. In this case, the satellite has to integrate its position forward in time to relay that information to a ground user. This paper studies the effect that error on the ballistic coefficient estimate has on the orbit propagation error. The process was run for error between -100% and 1200% of the real coefficient value, and the mean error over these runs is compared. Results are shown for three satellites modeled off current or former LEO satellites: AAUSat3 CubeSat, OneWeb, and Iridium chosen for the variation in ballistic coefficients. After analysis, it was determined that the ballistic coefficient effect on the integration error was largely dependent on the measurement noise. This is because the ballistic coefficient is below the noise floor of the measurements which until it exceeds this error, it has no effect on the orbit. Adding error to the ballistic coefficient directly effected the drag, and it was found that the atmospheric drag needed to outweigh the effect of gravitational acceleration for an effect on the solution to be had. The ability to estimate the coefficient from GPS measurements is also studied. Once again, it was found that the ballistic coefficient was highly sensitive to the noise in the measurements. The estimation method extracts the atmospheric drag from a total acceleration that was estimated using the GPS measurements. Because the measurements had a large amount of noise compared to the value of the ballistic coefficient, the atmospheric drag and subsequently the coefficient could not be estimated with much accuracy. It is theorized that adding an IMU to the measurements to obtain total acceleration would greatly improve the estimation.
Published in:	Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023) September 11 - 15, 2023 Hyatt Regency Denver Denver, Colorado
Pages:	3282 - 3295
Cite this article:	McDougal, Madeline, Martin, Scott, Underwood, Kip, "The Effect of the Ballistic Coefficient on Satellite Orbit Prediction," Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023), Denver, Colorado, September 2023, pp. 3282-3295. https://doi.org/10.33012/2023.19175
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