Three-dimensional ionospheric tomography based on compressed sensing

Abstract

The insufficient number of low-elevation observations is a limitation of the three-dimensional ionospheric computer tomography (CT) based on the global navigation satellite system (GNSS). To solve this problem, accurate prior information on the regional ionosphere must be obtained. However, it is difficult to explicitly and accurately express prior ionospheric information. This study uses compressed sensing (CS) for ionospheric tomography for the first time. Specifically, the electron density obtained from the international reference ionosphere is used to build a dictionary to fully integrate the prior information into the dictionary. Then, the electron density is reconstructed by using the compressive sampling matching pursuit method. Subsequently, the GNSS data of China (Region I) and Europe (Region II) were utilized to validate this proposed method, and the results are compared with ionosonde observations. The mean and standard deviation (SD) of the difference with respect to the ionosonde result are 41 and 22 km, respectively. The mean and SD of relative deviation were 16% and 9%, respectively. In Region II, the mean and SD of the deviation between the reversed peak electron density and the result of the ionosonde were 1.9 × 1010 m−3 and 8.1 × 1010 m−3, respectively. The mean and SD of the relative deviation were 3% and 13%, respectively. The mean and SD of the peak height deviation were 33 and 19 km, and the mean and SD of the relative deviation were 11% and 7%. The electron density distribution and variation in these two regions showed a local time dependence, and the horizontal gradient of the electron density in the latitude was greater than that in the longitude. Moreover, CT by CS is efficient, taking about 6 s per inversion based on an desktop computer with 16 GB RAM and Intel (R) Core (TM) i7-8700 CPU.