The Global Positioning Problem: Geometry and Algebra

Every GPS enabled device must solve the global positioning problem multiple times. So it seems surprising that the question of when this problem has a unique solution has so far not been properly understood. This talk is about joint work with Mireille Boutin, and focuses on the uniqueness question, giving a geometric understanding of it. This leads to a proof of the long-held belief that if at least five satellites are in view, then there is a unique solution for almost all device positions. Even better, almost all configurations of at least eight satellites in view will guarantee a unique solution for ALL device positions. If time permits, I will show how a very modest amount of algebraic geometry plays an essential part in the proof of the "five is enough" result.