An Alternative Closed Form Solution to the GPS Pseudorange Equations

Joseph Leva

Abstract:	The Global Positioning System (GPS) uses measurements from four satellites to form four nonlinear equations, the pseudorange equations, involving the unknown position coordinates of the user and the offset of the user’s clock relative to GPS time. These four equations are mathematically equivalent to a system of one pseudorange equation and three range difference equations. This paper shows that the range difference equations are equivalent to a system of two linear equations together with a range difference equation. This formulation represents the user’s position as the intersec- tion of two planes and a hyperbola branch of revolution. Gne readily solves for the user’s position and clock offset. The solution formulation results from a basic geometric fact concerning quadratic surfaces of revolution. It differs from related published works on hyperbolic systems by eliminating extraneous solutions in the formulation. The technique provides a stable algorithm for calculating GPS single point solutions. In addition, the 3-dimensional formulation provides significant geometric insight into the solution’s characteristics.
Published in:	Proceedings of the 1995 National Technical Meeting of The Institute of Navigation January 18 - 20, 1995 Disneyland Hotel Anaheim, CA
Pages:	269 - 275
Cite this article:	Leva, Joseph, "An Alternative Closed Form Solution to the GPS Pseudorange Equations," Proceedings of the 1995 National Technical Meeting of The Institute of Navigation, Anaheim, CA, January 1995, pp. 269-275.
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