Sp-search star pattern recognition for multiple fields of view star trackers
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This paper presents the extension of the Spherical-Polygon Search technique, to accomplish the star pattern recognition, to the recently proposed multiple field-of-view star trackers DIGISTAR II and III which observe star fields in orthogonal directions, thus providing substantial gain in both the attitude estimation accuracy and in the operating time. The main idea of the proposed algorithm, which extensively uses the k-vector technique (a new range searching approach which does not require of searching phases), is based on the fact that any star direction can always be expressed as a linear combination of two star directions (star pair basis) together with their vector cross product. Using this property, which does not depend on the used system of coordinates, the problem of accessing candidate stars is then transformed into one of accessing the stars falling within a cone about a given direction. The cone observed surface is approximated herein as a spherical polygon, and its aperture is set to be h times of the star image centroiding accuracy standard deviation . Linear Error Theory is then applied for to establish an analytical approximation of h while, for fast applications, an empirical formula, is also presented. The resulting algorithm is very fast and has a high probability of quickly identifying the imaged stars. This we validate by numerical tests reported herein. This approach has the additional capability to identify and discard spurious images and we have validated that it is a suitable and reliable concept to perform star pattern recognition in the most general lost-in-space case, that is, when no attitude information is available.