Adaptive Regularization Method for 3-D GNSS Ionospheric Tomography Based on the U-Curve

Computerized ionospheric tomography is a highly ill-posed inverse problem, and regularization tends to stabilize the problem to provide a unique solution. When a regularization method is used, the choice of an optimal parameter is a key issue. In this article, we propose an adaptive regularization method for 3-D ionospheric tomography based on the U-curve. The proposed approach uses a U-curve method to determine the optimal regularization parameter from Global Navigation Satellite Systems (GNSS) observation data. Comparative case studies are investigated based on GNSS simulated observations and real measurements. The simulation results indicate that the proposed method is superior to the adaptive regularization method based on the L-curve. In addition, we further validate the tomographic results with actual ionosonde station data. The results demonstrate the reliability and superiority of the proposed method compared to traditional methods.