Robust Unsupervised Spatial-Kinematic Coupling for Satellite Laser Ranging Signal Extraction

In satellite and space debris laser ranging, photon-counting time-of-flight sequences exhibit spatio-temporal echo coherence and deterministic orbital constraints. We propose an unsupervised framework exploiting this spatial-kinematic coupling to extract weak returns under high background noise. First, a fuzzy clustering regression employs a dynamic energy functional and cross-entropy-regularized photon attribution, guided by target motion priors. To enhance low signal-to-noise ratio sensitivity, we introduce a low-gradient sampling strategy that theoretically guarantees a signal-to-background ratio exceeding 1/2. Furthermore, a dual-stream autoencoder fuses orbital kinematic parameters and multi-scale echo densities via noise-adaptive latent gating. Validation on 88 satellite and 24 debris datasets achieves F1-scores of 0.73 and 0.93, respectively. The sampling strategy reduces computational latency by ∼5.2% with no loss in tracking precision. This label-free, physically grounded approach enables robust weak signal detection in ground-based photon-counting lidar.