Localization of an Unknown Number of Magnetic Targets Based on 3-D Inversion Neural Network and Local Optimization Algorithm

Multiple magnetic target localization (MMTL) based on magnetic vector sensors has been widely used in unexploded ordnance (UXO) detection, medical applications, and marine target monitoring. However, locating an unknown number of noncooperative targets and targets with highly overlapping horizontal positions under sparse measurements is challenging. This study proposes an MMTL method that combines a 3-D inversion neural network with a local optimization algorithm. The method divides the inversion space into a fixed grid and employs a 3-D U-Net with a super-resolution module to reconstruct the 3-D magnetic moment distribution in space. Then, the reconstructed distribution is processed using a clustering method for preliminary positioning. Finally, the positions and magnetic moments of multiple targets are refined by the trust region reflective (TRR) algorithm. Compared with other methods, this method reduces the average positioning error of multiple targets, the magnetic moment estimation error, and the running time. Terrestrial experiments further demonstrate its effectiveness for an unknown number of multiple magnetic targets and targets with overlapping horizontal positions.