A Rapid Linear Localization Method for Multiple Magnetic Dipole Sources

This article addresses the simultaneous localization problem of multiple magnetic dipole sources distributed at varying heights in space. To overcome the limitations of traditional optimization-based methods, which are time-consuming and prone to local optima, we propose a fast multidipole linear localization (MDLL) method. After performing 2-D grid measurements, the MDLL method first determines the number of magnetic sources, their initial positions, and magnetic moments by calculating the magnetic gradient tensor (MGT) and tilt angle. It then filters effective measurement points for each source using the Voronoi diagram and iteratively refines the results through a single-source linear localization scheme to approach the true values. The simulation and experimental results demonstrate that the MDLL method significantly outperforms the benchmark one-step localization (OSL) and differential evolution (DE) methods in both localization accuracy and computational efficiency. In noise-free simulations, the localization error of MDLL is reduced by over 99% compared to OSL and DE, and its computation speed is more than 20 000 times faster than DE in the scenario with 30 magnetic sources, with the advantage becoming more evident as the number of sources increases. In experiment, the average localization error of MDLL are only 4.55% and 36.94% of that of OSL and DE methods, respectively, and its computation time remains significantly shorter than that of the DE method.