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Localization of an Electromagnetic Source with Magnitude Only Measurements in a 2D Metallic Cavity with Scatterers
  • Varatharajan Meenakshi Sundaram,
  • Bharath Bhikkaji
Varatharajan Meenakshi Sundaram

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Bharath Bhikkaji

Abstract

A time harmonic electromagnetic (EM) source inside a 2D metallic cavity is considered. Scatterers of known geometry and dielectric constants are present inside the cavity. These scatterers alter the fields in the cavity. The coordinates of the source are unknown, while those of the scatterers are given. The magnitude of the resulting electric field is measured at certain locations in the cavity. The goal is to locate the source from these magnitude-only measurements. As there is only one source, its localization is formulated as a sparse source reconstruction problem. The 2D metallic cavity is discretized using a Finite Difference scheme. Determination of the source location is posed as a constrained minimization problem with the cost being the norm of the error between the measured and the simulated sumulated (obtained using the discretized Maxwell's equation). An additional L1 regularization is added to the cost to impose sparsity. Linear constraints based on the principle of Electromagnetic Time Reversal (EMTR) are derived and enforced. Numerical results are presented for random choices of measurement locations. Numerical experiments suggest that the source can be localised with measurements taken at 5% of the total points on the search grid.
01 Jun 2024Submitted to TechRxiv
07 Jun 2024Published in TechRxiv