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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2021, Volume 18, Issue 2, Pages 1153–1164
DOI: https://doi.org/10.33048/semi.2021.18.087
(Mi semr1428)
 

Computational mathematics

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

M. Yu. Kokurin, A. E. Nedopekin

Mari State University, 1, Lenin sqr., Yoshkar-Ola, 424001, Russia
References:
Abstract: 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.
Keywords: nonlinear equation, irregular equation, iterative regularization, ionosphere, radiotomography.
Funding agency Grant number
Russian Science Foundation 20-11-20085
The work was supported by the Russian Science Foundation (project 20–11–20085).
Received April 1, 2021, published October 27, 2021
Bibliographic databases:
Document Type: Article
UDC: 519.642.6
Language: English
Citation: M. Yu. Kokurin, A. E. Nedopekin, “Iteratively regularized Gauss–Newton method in the inverse problem of ionospheric radiosonding”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 1153–1164
Citation in format AMSBIB
\Bibitem{KokNed21}
\by M.~Yu.~Kokurin, A.~E.~Nedopekin
\paper Iteratively regularized Gauss--Newton method in the inverse problem of ionospheric radiosonding
\jour Sib. \`Elektron. Mat. Izv.
\yr 2021
\vol 18
\issue 2
\pages 1153--1164
\mathnet{http://mi.mathnet.ru/semr1428}
\crossref{https://doi.org/10.33048/semi.2021.18.087}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000734395000007}
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