Bancroft's Algorithm is Global Nonlinear Least Squares

James Chalfee and Karl Kovach

Abstract:	It is shown that Bancroft’s closed-form solution for the GPS pseudorange equations is global nonlinear least squares. The metric is not the usual Euclidean metric, but is instead the Lorentz metric of hyperbolic space. This is the natural metric since GPS is a hyperbolic system. A geometric interpretation is given, including not only the solution geometty but also the effect of noise on pseudoranges as well as on satellite positions.
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:	431 - 437
Cite this article:	Chalfee, James, Kovach, Karl, "Bancroft's Algorithm is Global Nonlinear Least Squares," 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. 431-437.
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