Correction of Laser Footprint Positioning Errors in Mountainous Forest Areas Based on the Minimizing the Sum of Satellite–Earth Laser Ranging Residuals

The correction of spaceborne laser footprint positioning errors in forested areas is the primary task required to improve the reliability of laser data and ensure the accuracy of large-scale forestry surveys based on laser data. Currently, this correction largely requires high-precision terrain data, which are difficult to obtain over mountainous forests. Therefore, a method for correcting spaceborne laser footprint positioning errors in mountainous forest areas by minimizing the sum of satellite‒Earth ranging residuals is proposed. In this method, a satellite digital surface model (DSM) is used to calculate satellite‒Earth laser ranges at different ground locations, and the laser footprint positioning error is corrected based on the principle of minimizing the sum of the ranging residual between the satellite‒Earth laser ranging and the actual ranging. The proposed method was subsequently tested on the GF7-01 satellite laser, and the corrected laser footprint positions were compared with the true positions of the laser footprints captured by laser detectors. The results indicated that the laser footprint positioning accuracy was 4.16 m for beam 1 of the GF7-01 satellite, while beam 2 achieved an accuracy greater than 3.96 m. Overall, these outcomes clearly demonstrate the effectiveness of the proposed method.