Velocity-based sparse photon clustering for space debris ranging by single-photon Lidar

Single-photon Lidar (SPL) offers unprecedented sensitivity and time resolution, which enables Satellite Laser Ranging (SLR) systems to identify space debris from distances spanning thousands of kilometers. However, existing SPL systems face limitations in distance-trajectory extraction due to the widespread and undifferentiated noise photons. In this paper, we propose a novel velocity-based sparse photon clustering algorithm, leveraging the velocity correlation of the target's echo signal photons in the distance-time dimension, by computing and searching the velocity and acceleration of photon distance points between adjacent pulses over a period of time and subsequently clustering photons with the same velocity and acceleration. Our algorithm can extract object trajectories from sparse photon data, even in low signal-to-noise ratio (SNR) conditions. To verify our method, we establish a ground simulation experimental setup for a single-photon ranging Lidar system. The experimental results show that our algorithm can extract the quadratic track with over 99 percent accuracy in only tens of milliseconds, with a signal photon counting rate of 5 percent at -20 dB SNR. Our method provides an effective approach for detecting and sensing extremely weak signals at the sub-photon level in space.