An Efficient Algorithm for Performing Orbital Celestial Navigation

Franz D. Busse

Abstract:	Navigation of satellites when GPS signals are not available is an important and enduring problem, with several possible solutions. This work introduces State-spaced Orbital Celestial Navigation (SSOCN), an efficient state-space algorithm for determining a satellite’s position in a terrestrial frame to within 100 m, utilizing only a star-tracker and horizon sensor. The vehicle calculates its present location by measuring the angle between three or more stars and the horizon. Other algorithms exist which are similar (most notably, sailors using sextants, see also Kaplan’s authoritative rhumb-line algorithms), but the algorithm presented here uses a state-space formulation that is not dependent on the observer’s altitude, and can be readily implemented in modern navigation routines. In this paper, an explicit, step-by-step description of the SSOCN algorithm is presented. The algorithm is given in three forms: a Kalman filter implementation, a least-squares implementation, and a non-real-time batch fit. A subroutine for selecting stars to use for measurements is also presented. Results from Monte Carlo simulations are also presented, where sensor noise and initial conditions are randomly varied. Sensor accuracy is parametrically varied, and position accuracy is measured. SSOCN is very robust to poor initial state estimates. The largest error source is the accuracy of the measurement of the angle between the star and the horizon. Results show that measurements with 200 arcsec accuracy provide position solutions within about 3 km error, while 5 arcsec accuracy provides solutions with less than 100 m error.
Published in:	Proceedings of the 2010 International Technical Meeting of The Institute of Navigation January 25 - 27, 2010 Catamaran Resort Hotel San Diego, CA
Pages:	514 - 519
Cite this article:	Busse, Franz D., "An Efficient Algorithm for Performing Orbital Celestial Navigation," Proceedings of the 2010 International Technical Meeting of The Institute of Navigation, San Diego, CA, January 2010, pp. 514-519.
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