Star trackers, star catalogs, and attitude determination - Probabilistic aspects of system design

Abstract

Optimizing spacecraft attitude determination systems that use onboard star trackers requires analysis and evaluation of some probabilistic aspects of system design. This paper discusses methods of constructing or compiling optimum star catalogs, which are defined as uniform distributions on a sphere. Both local and global measures of uniformity on a sphere are defined. Application of these methods and measures to a specific problem is also discussed. In addition, Poisson models of star tracker acquisition probabilities are formulated to provide a useful analytical basis for designing and optimizing attitude determination systems. These analytical models and methods lead to rapid and realistic quantitative results and should therefore facilitate making system performance trades. The use of such methods should also reduce the need for performing tedious computer simulations to obtain analogous results. TTITUDE determination of both Earth-orbiting satel- lites, as well as planetary spacecraft, can be performed autonomously using one or more onboard star trackers. An essential part of such an attitude determination system is the onboard star catalog, and the performance of the attitude determination system is closely linked to the characteristics of this catalog. In particular, the total number of stars in the catalog and their spatial distribution largely determine the probability of a given number of stars appearing in a tracker's field of view (FOV); this includes the possibility of there being zero stars from the catalog in the FOV. The purpose of this paper is to apply some analytic methods of probability theory to the following problems: generating optimum star catalogs of any given size and, given such a catalog, evaluating some of the characteristics of the star cata- log/star tracker interaction that are of particular interest when designing attitude determination systems. Evaluating such characteristics will entail some analytical modeling. We shall formulate some simple analytical models that lead to excellent estimates of such quantities as star acquisition probabilities as a function of the number of stars in the catalog, number of operating star trackers, and size of the FOV. Another kind of performance parameter that can be analytically estimated is the duration of intervals during which none of the stars in the catalog appears in a star tracker's FOV. These analytical mod- els should be useful for quantitatively evaluating design and performance trades involving these variables, and for star tracker system engineering in general. Their use may obviate doing tedious computer simulations to obtain quantitative esti- mates of such parameters. Although some related efforts have been reported,1 such efforts have focused more strongly on star tracker hardware than analytical aspects of performance.