Correcting Laser Footprint Geolocation Errors in Mountainous Forests by Minimizing the Sum of Spaceborne-Airborne Collaborative Distances

Spaceborne laser has been widely used for global forest canopy height retrieval, carbon stock estimation, and other forestry surveys, owing to its excellent vertical detection capability. However, its effectiveness in mountainous forest regions is highly dependent on the geolocation accuracy of laser footprints. In such regions, footprints are prone to significant geolocation errors caused by the long-term thermal effects of the laser, satellite jitter, and terrain–vegetation characteristics. Existing studies have struggled to achieve high-accuracy corrections under such complex conditions. To address this challenge, we propose a method to correct laser footprint geolocation errors in mountainous forests by minimizing the sum of spaceborne–airborne collaborative distances. First, a weighting parameter of the order of 10⁻³ is introduced to weight the horizontal coordinates of both spaceborne laser footprints and airborne LiDAR-derived terrain data. Second, using these weighted coordinates, spaceborne–airborne collaborative distances between footprints and terrain grids are computed and summed. The optimal target grid is identified by minimizing this total distance. Finally, within the target grid, a residual function is constructed from the summed spaceborne–airborne distances. The optimal footprint position is determined by minimizing this function using a least-squares approach. Experiments were conducted using Global Ecosystem Dynamics Investigation (GEDI) and Gaofen-7 (GF-7) laser footprints across four typical terrain–vegetation regions. The results indicate that the proposed method significantly improves both geolocation and elevation accuracy. For GEDI footprints, elevation accuracy improved from 3.14 m to 2.18 m. For GF-7 dual-beam laser footprints, average geolocation accuracy improved from 6.79 m to 3.13 m, a 53.9% gain. Beam 1 improved from 6.76 m to 2.68 m (a 60.4% improvement), and Beam 2 from 6.82 m to 3.58 m (a 47.5% improvement). In addition, the proposed method effectively extrapolates GEDI error corrections across beams, greatly reducing reliance on high-precision terrain data.