Iteratively regularized Gauss–Newton method in the inverse problem of ionospheric radiosonding

The paper is concerned with the problem of reconstructing the vertical profile of the electron concentration of the ionosphere. The profile is reconstructed based on the results of measuring the incident phase of the probing signal from a moving satellite. The simplest measurement model with a single point of signal reception is adopted. The model under investigation takes into account the curvature of the probe beam when passing through the inhomogeneous ionosphere. The problem is reduced to a nonlinear integral equation. We prove that the resulting equation has a non–unique solution. To approximate the solution closest to the selected initial approximation, an iteratively regularized Gauss–Newton method is used with a projection on the set defined by a priori constraints on the solution. The results of numerical experiments are presented.