Bancroft's Algorithm is Global Nonlinear Least Squares

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.