A New Ionosphere Tomography Algorithm With Two-Grid Virtual Observations Constraints and Three-Dimensional Velocity Profile

Ionosphere tomography is a typical ill-posed problem, and using the ionosphere priori information as the constraints to improve the state of normal equation is an effective approach to solve this problem. In this paper, we impose priori constraints by increasing the virtual observations in $n$-dimensional space. Then, after the inversion region to be gridded, we can form a stable structure between the grids with loose constraints, which greatly improve the state of normal equation. Based on that, to obtain the real-time velocity information of ionosphere electron density, we introduce the grid electron density velocity parameters, which can be estimated with electron density parameters simultaneously. The authors use the new algorithm and the global navigation satellite system data in Europe to inverse the 12 ionosphere electron density and velocity images on August 15, 2003, which reflects the ionosphere changes of electron density and velocity in whole day; in addition, we compare the results with the traditional algorithm multiplicative algorithm reconstruction technique's results. Furthermore, we compare the results with the changes time series of plasma frequency observed by ionosphere ionosonde among different layers, and many types of analysis and comparison verify the effectiveness and reliability of the new algorithm. The related research provides a new way for the real-time detection and prediction of ionosphere changes.