An inverse moving point source problem in electromagnetics

TL;DR

This paper presents a method to reconstruct the orbit of a moving point source in electromagnetics using magnetic field measurements at a few observation points, with proven stability and demonstrated effectiveness through numerical experiments.

Contribution

It introduces a novel approach to inverse moving source problems that requires minimal measurement data and establishes Lipschitz stability for the reconstruction.

Findings

Reconstruction accuracy depends linearly on noise level.

Four non-coplanar observation points suffice for orbit reconstruction.

Wave speed significantly impacts the relative error.

Abstract

This paper is concerned with an inverse moving point source problem in electromagnetics. The aim is to reconstruct the moving orbit from the tangential components of magnetic fields taken at a finite number of observation points. The distance function between each observation point and the moving point source is computed by solving a nonlinear ordinary differential equation with an initial value. This ODE system only involves the measurement data from the tangential trace of the magnetic field at observation points. As a consequence, the dynamical measurement data recorded at four non-coplanar points are sufficient to reconstruct the orbit function. A Lipschitz stability is established for the inverse problem, and numerical experiments are reported to demonstrate the effectiveness of the proposed method. Numerical examples have shown that the reconstructed error depends linearly on the noise level and that the wave speed is a critical factor affecting the relative error.