Bifurcation of Pseudorange Equations

James W. Chaffee, Jonathan S. Abel

Abstract:	Given four measured pseudoranges, a position-bias pair almost always exists which exactly satisfies all four pseudorange equations. In this paper, we study such exact solutions, with a focus on the question of solution uniqueness. We show that GPS solu- tions may bifurcate into two solutions, each so- lution exactly reproducing the pseudoranges. We also propose simple geometric conditions for so lution uniqueness. The conditions are developed by analyzing a direct ,solution to the pseudorange equations, and involves the sign of a Lorentz inner product. As a side benefit, the difference between ranging systems and pseudoranging systems is made clear. Finally, examples are given showing that a bi- furcation can occur when the user is near a satellite or pseudolite, independent of GDOP.
Published in:	Proceedings of the 1993 National Technical Meeting of The Institute of Navigation January 20 - 22, 1993 Parc 55 Hotel San Francisco, CA
Pages:	203 - 211
Cite this article:	Chaffee, James W., Abel, Jonathan S., "Bifurcation of Pseudorange Equations," Proceedings of the 1993 National Technical Meeting of The Institute of Navigation, San Francisco, CA, January 1993, pp. 203-211.
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