Superresolution Multipoint Ranging With Optimized Sampling via Orthogonally Designed Golomb Rulers

We consider the problem of performing ranging measurements between a source and multiple receivers efficiently and accurately, as required by distance-based wireless localization systems. To this end, a new multipoint ranging algorithm is proposed, which is obtained by adapting superresolution techniques to the ranging problem, using for the sake of illustration the specific cases of time of arrival (ToA) and phase-difference of arrival (PDoA), unified under the same mathematical framework. The resulting nonparametric algorithm handles multipoint ranging in an efficient manner by employing an orthogonalized nonuniform sampling scheme optimized via Golomb rulers. Since the approach requires the design of mutually orthogonal sets of Golomb rulers with equivalent properties-a problem that founds no solution in current literature-a new genetic algorithm to accomplish this task is presented, which is also found to outperform the best known alternative when used to generate a single ruler. Finally, a Cramér-Rao lower bound (CRLB) analysis of the overall optimized multipoint ranging solution is performed, which together with a comparison against simulation results validates the proposed techniques.