An analytical approach to star identification reliability

The problem of real-time, on-board star pattern identification is considered which must precede any spacecraft attitude estimation algorithm based on measured line of sight directions to stars. Following the use of the search-less k-vector method[1, 2] to access feasible candidate stars, a tiered logical structure is introduced in which inter-star angles for pairs, triples and general elementary polygons are used to match measured star patterns to corresponding patterns in a star catalog. The fundamental innovation of this paper is that analytical expressions are developed for the expected frequency of matching an observed star pattern with an incorrect pattern in the star catalog due to measurement error. Such knowledge of erroneous match frequencies can be used to rigorously terminate the star identification process with a virtually certain match, while obviating the need for expensive Monte-Carlo simulations. Developments shown are supported with a few simulation results.