Tracking Beyond the Unambiguous Range with Modulo Single-Photon Lidar

In single photon lidar (SPL), the laser repetition rate sets the maximum distance that can be recovered unambiguously. Conventional SPL extends this maximum recordable depth by reducing the repetition rate; however, the slower acquisition speed limits the number of received photons, which may be insufficient to track fast-moving objects. Inspired by recent successes in modulo sensing, we leverage the smoothness of typical trajectories to achieve long-range tracking beyond the unambiguous range. Although SPL naturally acquires modulo time-of-flight measurements, it introduces several challenges—including random sampling times, multiple noise sources, and absolute distance uncertainty—that are not addressed by the current modulo sensing literature. Hence, we propose an interpolation and denoising method that operates directly over the modulo samples. We further disambiguate the absolute distance based on the changing reflectivity fall-off. Monte Carlo simulations considering realistic trajectories under practical conditions show that, when properly unwrapped, the normalized mean squared error of our depth estimate decreases by over 20 dB with respect to a lidar setup whose repetition period leads to no ambiguity.