Position and Attitude Sensing by Directional Triangulation

P. Bierre

Abstract:	GPS owes its success to the geometry of distance triangulation (trilateration), but another distinct branch of positioning science uses direction-sensing of known points. Directional triangulation differs from distance-based methods in that the rotational attitude of the platform matters, i.e., directional observations superimpose the platform's current attitude, which may be unknown. An algorithm for directional positioning has been developed that works to position a platform having unknown, arbitrary attitude in space. The directions pointing toward three reference points are acquired as raw directions in local platform coordinates. The algorithm combines this information with the coordinate definitions of the three sighted reference points, and then solves for platform location. Once location is solved, the attitude of the platform is solved for using a new geometry result called the rotational inference algorithm. Rotational inference empowers a software gyro concept, based solely on camera-based tracking of known landmarks (or stars) to calculate a craft's 3D attitude. These results are achieved using a simplified approach to 3D algorithmic geometry, where angles are supplanted by direction vectors and rotators1. Directional triangulation gives the world of line-of-sight optics its own core positioning technology, analogous to the spherical intersection algorithms that undergird GPS. Patent pending, Cartesia USA2.
Published in:	Proceedings of the 2006 National Technical Meeting of The Institute of Navigation January 18 - 20, 2006 Hyatt Regency Hotel Monterey, CA
Pages:	629 - 641
Cite this article:	Bierre, P., "Position and Attitude Sensing by Directional Triangulation," Proceedings of the 2006 National Technical Meeting of The Institute of Navigation, Monterey, CA, January 2006, pp. 629-641.
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