Isochrons in Photonic Oscillators

Precisely measuring the location of moving objects has been a long-standing research challenge. Here, we present a highly accurate three-dimensional positioning system named LIO: Localization using Isochrons in Oscillators. LIO precisely measures the time of arrival (ToA) of incoming radio frequency (RF) signals employing a novel timing protocol. The proposed protocol measures ToA leveraging the phase shifts of limit cycle oscillators based on their isochrons’ structure. These ToA measurements are then translated into distances and are employed in LIO for high-accuracy three-dimensional positioning. Moreover, LIO utilizes a passive-round-trip-time (passive-RTT) protocol leveraging retro-reflective tags to address and enhance the synchronization challenge. We derive LIO’s positioning error bound (PEB) and attribute the localization error to ranging- and geometry-induced errors. While our primary objective in this work is to address the former source of error, we also provide a novel optimization framework to mitigate the geometry-induced errors by proposing optimal anchor placements. Lastly, we assess the performance of LIO by designing comprehensive simulations using real-world operational parameters for commercially available semiconductor laser oscillators. Our numerical results indicate that LIO achieves distance estimation with the accuracy of sub-tenth of the millimeter (mm) and overall three-dimensional localization with sub-1 mm accuracy. This is at least an order of magnitude better compared to the existing technologies.