A High‐Performance Method for Generating Ionospheric Tomographic Projection Matrix Using Spherical Triangles

Abstract

Projection‐matrix generation is an essential prerequisite for ionospheric tomographic inversion, and its computational speed determines the practicality of high‐resolution tomography. We developed and tested an algorithm that combines a fast ray‐voxel intersection test with the spherical‐triangle method. The algorithm was evaluated against the conventional formulation, the parametric‐equation approach, and the segmentation intersection and voxel tracking (SIVT) approach using two European GNSS epochs and voxel grids at different resolutions. Within these tested configurations, the spherical‐triangle method alone performed well for coarse grid configurations, whereas the combined “fast intersection test scheme II + spherical‐triangle method” gave the shortest runtime for the finest grid resolution. At a resolution of 0.1 (longitude) × 0.1 (latitude) × 1 km (altitude), the combined method completed the computations in approximately 3.88 and 8.45 s for 9,225 and 17,081 valid rays, respectively, corresponding to a 40%–50% reduction relative to using parametric equations alone in the same test setting. With five‐thread parallelization, the processing time was further reduced to 1.31 and 2.62 s. These results indicate that the proposed workflow can reduce the cost of projection‐matrix generation for the tested ionospheric tomography configurations without altering the numerical results.