Adaptive hierarchical filtering particle swarm optimization for multiple magnetic dipoles modeling of space equipment

Accurate modeling of multiple magnetic dipoles is essential for characterizing spacecraft-generated magnetic fields and mitigating their interference with sensitive onboard instruments. To address the limitations of conventional multiple magnetic dipole modeling (MDM) methods facing local convergence and the curse of dimensionality in complex magnetic source scenarios, this work proposes an adaptive hierarchical filtering particle swarm optimization (AHFPSO) algorithm. The algorithm incorporates a hierarchical filtering mechanism and an adaptive adjustment mechanism to improve its capability in solving MDM problems. Extensive simulations under both noise-free and noisy conditions demonstrate that AHFPSO consistently outperforms eight state-of-the-art PSO variants in terms of accuracy, robustness, success rate, and execution time, particularly in high-dimensional, multi-dipole scenarios. Experimental validation using standard magnets and a spacecraft transponder further confirms its practical applicability and high modeling precision. AHFPSO effectively identifies equivalent magnetic dipole moments that closely match the measured magnetic fields of the transponder, with average errors of -0.3472 nT, 0.7445 nT, and -0.4141 nT in the X, Y, and Z-axis directions, respectively. The proposed method enhances the capability of PSO to address complex, ill-posed MDM inverse problems and offers a promising tool for magnetic characterization in space missions.