A Weighted Image-Point-Measurement Method of Laser Altimetry Points for Improving Laser-Altimetry-Data-Assisted Positioning Accuracy of Small-Satellite Images

For small-satellite imagery, traditional image points derived from the direct back-projection of laser altimetry points onto the imagery often exhibit deviations of tens of pixels or more, owing to the relatively limited attitude and orbit determination accuracy of small-satellite platforms. Moreover, the diversity of imaging sensors, variations in image resolution, and inherently weak image geometric configurations further complicate the accurate acquisition of image-space coordinates for laser altimetry points. To facilitate the application of laser altimetry data for geometric positioning across multi-satellite, multi-sensor, and multi-resolution small-satellite imagery, this study proposes a measurement method for laser altimetry points tailored to small-satellite images and establishes a combined geometric positioning model that integrates virtual control points, laser altimetry points, and image-matching tie points. The framework comprises four key procedural components: (1) an image-point-measurement strategy for laser altimetry points; (2) the construction of a laser altimetry data-assisted geometric positioning model for small-satellite imagery; (3) the solution of the geometric positioning model using a total least squares approach based on the partial-EIV (errors-in-variables) models; and (4) a comprehensive accuracy assessment conducted under multiple image-combination scenarios, including single-satellite single-stereo, single-satellite multi-stereo, dual-satellite single-stereo, and multi-satellite multi-stereo imagery configurations. Experimental validation is carried out using Jilin-1 small-satellite panchromatic images (KF01A, GF02A, and GF02B) acquired over the Henan region of China. The experimental results demonstrate that, with the laser altimetry point-measurement method and the combined geometric positioning model, the vertical positioning accuracy is substantially improved across all tested image-combination scenarios. These findings further confirm the capability in enhancing the vertical geometric positioning performance of stereoscopic small-satellite imagery characterized by multi-satellite platforms, multi-sensors, and multi-resolutions over terrain conditions similar to those tested.