Star Covering Region Evaluation with Application to Star Tracker Design

Abstract

The performance of a star tracker is closely linked to the characteristics of the guide star catalog. It is an essential part of design to estimate the number of guide stars observed by the star tracker in any given boresight direction. This paper reports on the star covering region evaluation method, which is used to find ranges of orientation where the star tracker can observe a star. With this method, a conservative number of guide stars observed by the star tracker in any given boresight direction can be quantitatively evaluated and credible ranges of orientation can be found, where the star tracker can observe enough guide stars to perform autonomous star identification; thus, verifying the design of the star tracker. The celestial sphere is divided into 131,072 approximately congruent spherical triangles, such that the star’s covering region can be approximately depicted by triangles in which the circumcenters are close enough to the star. Then, the stars observed by the tracker, in which the boresight is located anywhere inside the circumcircle of the triangle, can be found by identifying where the triangle is located in a given star’s covering region. A guide star catalog containing 2,873 stars was generated and the star covering region evaluation was performed. It was found that the star tracker with a circular field of view (FOV) radius of 4° could measure at least three guide stars when its boresight direction was located in 63,554 spherical triangles. The evaluation results for 10,000 random orientations were used to compare the counting numbers of practically observed stars. The mean error is 0.6415 and the maximum error is 5, which results from the stars not considered because they are on the edge of the FOV. The results of a simulation have validated the method.