Review of tomographic reconstruction methods of the ionosphere using GNSS

Abstract

Spatial and temporal variation of the electron density in the atmosphere makes the ionosphere a difficult region to model. A major difficulty arises due to the incomplete geometrical coverage of the Global Navigation Satellite System (GNSS) for tomographic applications, making the ionospheric tomographic systeman ill-conditioned problem. Although the tomographic system is ill-conditioned, several techniques have been developed to partially overcome the problem. There is great interest in using tomographic techniques for ionospheric imaging, because it allows describing the ionosphere in terms of electron density, which is an important parameter for studying the behavior of the physical processes that occur in the upper atmosphere. In Brazil, there are additional interests in the tomographic techniques, due to the peculiar characteristics of the ionosphere and of the geomagnetic field over the region. In this direction, methods of ionospheric tomographic reconstruction are presented and discussed in this review. Particular emphasis is given to the mathematical formulation from grid-based and function-based methods and some of their main advantages and limitations are presented.