Distance–Velocity Joint Extraction Method for Space Debris Based on Space-Based Single-Photon Ranging

Space-based single-photon ranging of space debris is affected by sparse signal photons, strong background noise, motion-induced echo broadening, and the amplification of local ranging errors during velocity estimation. To address these problems, this paper proposes a reliability-aware joint distance–velocity extraction framework that couples coded-echo processing with inter-window motion continuity. In each observation window, a phase-space trajectory matrix is constructed from the photon-counting echo, and fixed-rank truncated SVD is used as a front-end structural enhancement step to preserve the dominant temporal structure of the broadened coded echoes while suppressing part of the diffuse photon-count fluctuation. Coded cross-correlation is then used for coarse delay localization, followed by peak-neighborhood sub-bin estimation. A composite range-observation reliability measure is constructed from the retained singular-value-energy ratio, correlation-peak significance, and peak-to-sidelobe ratio. Reliability-weighted local polynomial fitting and distance–velocity joint optimization subsequently provide continuous range and radial-velocity estimates. In an orbital-reference simulation, the proposed method reduced the range RMSE, MAE, and MaxAE by 84.74%, 83.22%, and 83.83%, respectively, relative to VBSPC, and reduced the corresponding velocity errors by 89.36%, 89.04%, and 94.30% relative to IMMK. A 30-trial ablation study indicated the complementary contributions of SVD enhancement, sub-bin estimation, and joint optimization, while repeated tests under different coding conditions and 20–100% signal-photon levels demonstrated robustness to photon-count reduction. A scaled moving-target experiment further achieved range and velocity RMSEs of 0.066 m and 0.033 m/s, respectively. The experiment validates the measured-echo processing chain rather than the complete orbital optical link. The results demonstrate that jointly exploiting coded-echo structure, observation reliability, and motion continuity provides robust range-trajectory and radial-velocity extraction for photon-starved moving targets.