Efficient and High-Accuracy Ray Tracing in Discretized Ionospheric Models
arXiv:2506.18579 · doi:10.1109/TAP.2026.3681396
Abstract
High-frequency (HF) ray tracing in complex ionospheric media generally involves a fundamental trade-off between path accuracy and computational efficiency, which directly affects practical applications such as over-the-horizon radar, ionospheric monitoring, and HF skywave communication systems. This paper presents RTM-GD, a ray-tracing framework that combines Hamiltonian ray integration with a continuously differentiable Galerkin--Difference (GD) interpolation strategy. Under discretized ionospheric grid conditions, the electron density is reconstructed as a -continuous function within each grid cell, yielding an everywhere differentiable electron-density field for stable numerical integration and improved propagation-path accuracy. Numerical simulations and validations using measured HF oblique sounding data are conducted under diverse conditions, including different ionospheric states, low- and high-elevation angles, multiple operating frequencies, and both ordinary (O) and extraordinary (X) wave modes. Results show that RTM-GD consistently achieves sub-kilometer RMSE in both group-path and ground-distance metrics and sub-0.01-degree azimuth deviation relative to Richardson extrapolation, while reducing computational time by 98\%. Compared with Catmull--Rom interpolation, RTM-GD reduces the RMSEs of ray parameters by approximately one order of magnitude with less than 4\% additional computational cost. Measured-data validation based on ionogram synthesis further shows that the mean relative group-path error remains within 7\%, confirming reliable reproduction of practical HF oblique propagation characteristics. Overall, RTM-GD provides an accurate and computationally efficient framework for HF ray tracing in discretized ionospheric environments.
12 pages, 10 figures. Revised to correspond to the accepted manuscript after peer review. Published in IEEE Transactions on Antennas and Propagation as an Early Access article. DOI: 10.1109/TAP.2026.3681396