Direct Solution of the GPS Equations

Ilan Biton, Mark Koifman and Itzhack Bar-Itzhack

Abstract:	A known direct solution of the GPS equation which yields user position and clock bias is examined and tested using real GPS data. A comparison of the position computed using this solution with that obtained using the popular iterated least squares solution reveals that the direct solution is in errors of up to 4 meters. An improved direct solution is presented which takes in account the noise associated with the pseudo-range measurements. The position error obtained when using this solution is an order of magnitude smaller than that generated by the direct solution. Finally, an iterated solution, which is based on the improved direct solution, is presented. The accuracy of the latter is comparable to that of the iterated least squares solution of the GPS equation. The advantage of the new algorithm over that of the iterated least squares solution is in its fast convergence rate. Typically, the new algorithm converges in two iterations whereas the iterated least squares solution converges in five, both starting at the center of earth as the initial position guess. This advantage of the new algorithms is particularly important in extraterrestrial missions where the initial guess may be far off from the real position.
Published in:	Proceedings of the 9th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1996) September 17 - 20, 1996 Kansas City, MO
Pages:	1313 - 1320
Cite this article:	Biton, Ilan, Koifman, Mark, Bar-Itzhack, Itzhack, "Direct Solution of the GPS Equations," Proceedings of the 9th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1996), Kansas City, MO, September 1996, pp. 1313-1320.
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