Ill-posed formulation of the emission source localization in the radio-detection experiments of extensive air showers

TL;DR

This paper discusses the challenges of localizing emission sources in radio-detection experiments of air showers, highlighting issues with non-linear minimization and proposing a simple method to improve source localization accuracy.

Contribution

It introduces a new straightforward approach to estimate the emission source location, addressing convergence and bias issues in existing minimization algorithms.

Findings

Identifies problems with solution degeneration and bias in current minimization methods.

Proposes a simple method that improves the estimation of the emission source location.

Abstract

Reconstruction of the curvatures of radio wavefronts of air showers initiated by ultra high energy cosmic rays is discussed based on minimization algorithms commonly used. We emphasize the importance of the convergence process induced by the minimization of a non-linear least squares function that affects the results in terms of degeneration of the solutions and bias. We derive a simple method to obtain a satisfactory estimate of the location of the main point of emission source, which mitigates the problems previously encountered.