Physics-guided multi-branch deep network for footprint localization in full-waveform spaceborne laser altimetry

Real-time processing capability is a key enabler for the next generation of intelligent satellites. Full-waveform spaceborne laser altimetry has become an indispensable tool in a wide range of scientific and engineering applications, including terrain mapping, biomass estimation, and Earth system monitoring. Within this context, accurate and efficient laser footprint localization is essential for ensuring the geometric reliability of altimetric measurements. However, conventional waveform-matching methods suffer from severe computational burdens, rendering them unsuitable for high-frequency on-orbit calibration and difficult to deploy in real-time onboard scenarios. To address these challenges, this paper proposes SLA-FLNet – a physics-guided deep learning framework that integrates key physical mechanisms of laser pulse propagation, terrain modulation, and echo formation through a multi-branch spatiotemporal architecture. Each module of SLA-FLNet explicitly encodes a physically interpretable process, enabling accurate, interpretable, and scalable footprint localization. To support supervised training in the absence of ground-truth labels, pseudo-labels were generated using a classical waveform-matching algorithm. The model was evaluated on 2379 laser footprints from 18 beams of the GaoFen-7 (GF-7) satellite, spanning 12 U.S. states with diverse terrain. SLA-FLNet achieved high prediction accuracy and delivered footprint localization results consistent with waveform matching, even in unseen geographic regions. An ablation study further highlighted the critical role of terrain-encoding in enhancing structural fidelity and cross-regional generalization. Compared to traditional methods, SLA-FLNet achieved over 100,000 × inference speedup on modern GPUs, demonstrating strong potential for real-time onboard processing. In summary, SLA-FLNet provides a physically consistent, computationally efficient, and deployment-ready solution for full-waveform footprint localization and on-orbit calibration, supporting future autonomous Earth observation missions.