2023/10/13 by Mireille Boutin, Gregor Kemper, Boutin, Mireille +1
Computer Science · Engineering · #13P10 #13P25 #51K99 #Coding theory and cryptography #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Signal Processing (eess.SP) #Wireless Communication Networks Research #electronic engineering #graph theory and CDMA systems #information engineering
paper · pdf · doi:10.48550/arxiv.2310.09261
openalex publication_date 2023/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a new algebraic solution procedure for the global positioning problem in n dimensions using m satellites. We also give a geometric characterization of the situations in which the problem does not have a unique solution. This characterization shows that such cases can happen in any dimension and with any number of satellites, leading to counterexamples to some open conjectures. We fill a gap in the literature by giving a proof for the long-held belief that when m ≥ n+2, the solution is unique for almost all user positions. Even better, when m ≥ 2n+2, almost all satellite configurations will guarantee a unique solution for all user positions. Some of our results are obtained using tools from algebraic geometry.