Optimal GPS Attitude Determination without Ambiguity Resolution

Lawrence R. Weill

Abstract:	Recent research has determined that precise determination of platform orientation is possible using GPS carrier phase measurements from several antennas that are strategically placed on the platform. As the separation of the antennas is made larger, the accuracy of attitude estimation improves, but at a price. For example, using 3 antennas and the Ll carrier signals from 3 satellites, three-axis attitude can be estimated. However, when the antennas are separated by more than approximately 1 wavelength, multiple attitude solutions can occur, only one of which is the correct solution. Furthermore, the number of these multiple solutions grows larger as antenna separation increases. Thus, additional information is required to resolve the attitude ambiguity caused by the phase ambiguity of the Ll carrier. Most current techniques for attitude determination treat the problem as a two-step process: First obtain the set of possible attitude solutions that could reasonably produce the actual phase measurements observed, and then use least- squares fitting of additional measurements (such as extra satellites, extra antennas, or L2 carrier measurements) to resolve the ambiguities. While this approach is intuitively appealing, it is somewhat ad hoc and of questionable optimality. This paper shows that appropriate mathematical modeling of the attitude estimation problem leads directly to a maximum-likelihood solution or an optimum minimum mean-square error (MMSE) solution, neither of which requires a separate process of ambiguity resolution. The approach is generic and can be applied regardless of the available observables. It is also applicable when ambiguity resolution would otherwise be accomplished with redundant antennas instead of additional satellites or the use of the L2 carrier. A significant advantage of the MMSE solution is that, unlike conventional solutions involving ambiguity resolution, the attitude estimation error increases gracefully, rather than catastrophically, as the data quality degrades. Results will be given for several attitude estimation scenarios, and suggestions for further work will be presented.
Published in:	Proceedings of the 1994 National Technical Meeting of The Institute of Navigation January 24 - 26, 1994 Catamaran Resort Hotel San Diego, CA
Pages:	433 - 439
Cite this article:	Weill, Lawrence R., "Optimal GPS Attitude Determination without Ambiguity Resolution," Proceedings of the 1994 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 1994, pp. 433-439.
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