An Analytical Approach to Star Identification Reliability
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abstract
We consider the problem of real-time, on-board star pattern identification which must precede any spacecraft attitude estimation algorithm based upon measured line of sight directions to stars. Following the use of the search-less k-vector method1,2to access the feasible candidate stars for each measured pair, a tiered logical structure is introduced in which inter-star angles for pairs, triples, quadruples and generalized elementary polygons are used to match measured star patterns to corresponding patterns in a star catalog. The fundamental innovation of this paper is the following: 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 and the large number of stars in the catalog. This expected frequency of a random invalid match can be used to rigorously terminate the star pattern matching process with a virtually certain star identification. The analytical method to characterize the frequency of an incorrect star identification is an innovation of significant theoretical and practical importance since the expected frequencies derived are general functions of the measurement precision, number of stars the camera can image, and the measured inter-star angles. These general formulas will hereafter negate the need for expensive and often inconclusive Monte Carlo simulations for each variation of star sensor design. All of these developments are supported by simulations and by a few ground test experimental results. 2008 by Mrinal Kumar.
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AIAA Guidance, Navigation and Control Conference and Exhibit
