Mathematical Modeling of Radio Tomographic Ionospheres Monitoring Via Satellite Constellation

The reconstruction of the electronic components distribution functions in Earth's ionospheric layer is an actual problem of applied space research. The reason is that the ionosphere as a medium of propagation significantly affects the operation of the various systems of navigation, location and communication. The mathematical modeling technique of the electron density spatial distribution reconstruction in Earth's ionosphere spherical layer using a constellation of small satellites was developed by the author. It assumes twenty - four satellites, that are arranged uniformly on the circular orbit, sound a ring layer of ionosphere with radio emission at frequencies of (150 and 400) MHz. It is shown that under certain conditions, the problem can be reduced to a few-view tomographic problem, and the desired reconstruction of the electron density distribution by fast convolution algorithms can be evaluated. The applied software package allowing to perform a full cycle of mathematical modeling both for two-dimensional and three-dimensional problems was developed. The author also developed specialized “few-views dynamic kernel” that provides an opportunity to obtain satisfactory reconstruction of wide range input projection data for this class of problems.