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

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.