Harnessing Isochrons of Nonlinear Oscillators for High-Precision Ranging

Accurately determining the location of moving objects has posed a significant challenge in research for many years. The accuracy of time measurements, which are subsequently converted into distances, is the most vital component of ranging-based localization systems. In this work, we introduce a system designed to accurately measure the time of arrival (ToA) of incoming radio frequency (RF) signals through an innovative timing protocol. This protocol utilizes the phase shifts in limit cycle oscillators, drawing on the structure of their isochrons, to measure ToA. These measurements are then converted into distances and can be applied in any high-precision positioning system. Additionally, to tackle and improve the synchronization issues inherent in distance measurements, we suggest using a passive-round-trip-time (passive-RTT) protocol that employs retro-reflective tags. We evaluate the efficacy of our system through detailed simulations that mimic real-world conditions, utilizing operational parameters from commercially available semiconductor laser oscillators. Our numerical analyses reveal that our system can estimate distances with sub-millimeter precision, significantly surpassing the accuracy of current technologies by at least an order of magnitude.