Global Positioning on Earth
Metric Geometry
2025-05-08 v1
Abstract
Contrary to popular belief, the global positioning problem on earth may have more than one solutions even if the user position is restricted to a sphere. With 3 satellites, we show that there can be up to 4 solutions on a sphere. With 4 or more satellites, we show that, for any pair of points on a sphere, there is a family of hyperboloids of revolution such that if the satellites are placed on one sheet of one of these hyperboloid, then the global positioning problem has both points as solutions. We give solution methods that yield the correct number of solutions on/near a sphere.
Cite
@article{arxiv.2505.04344,
title = {Global Positioning on Earth},
author = {Mireille Boutin and Rob Eggermont and Gregor Kemper},
journal= {arXiv preprint arXiv:2505.04344},
year = {2025}
}