The n-dimensional k-vector with Applications
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2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. This paper demonstrates how to extend the original, one-dimensional k-vector range searching technique, initially developed to solve the star identification problem of wide field-of-view star trackers, to n-dimensions. The technique is then compared to the current state-of-the-art technique, k-d tree, by comparing the time it takes for each technique to solve the nearest-neighbor problem and orthogonal range search problem. K-d tree completed the nearest-neighbor problem faster than n-dimensional k-vector but n-dimensional k-vector completed the orthogonal range search problem faster than k-d tree. Also, applications of the n-dimensional k-vector are demonstrated, which include: point-pairs closer than dmax, closest point-pair, satellite and orbital debris database search, star catalog database search, asteroid database search, satellite coverage, and observer position estimation with pulsars.
