Physics-Informed Residual Network for Magnetic Dipole Model Correction and High-Accuracy Localization

Abstract

The magnetic dipole model exhibits significant deviations from real-world sensor data due to neglected material nonlinearities and environmental interference. This paper proposed a Physics-Informed Residual Network (PIRNet) that adaptively corrected simulated magnetic field data by integrating dipole theory with deep residual learning. The network took a 5×5 triaxial magnetic matrix as input and employed a dual-branch architecture: a convolutional residual branch extracted local sensor-level distortion features, while a physics-encoding branch models systematic position and orientation-related deviations. A gated fusion mechanism dynamically combined these features, with a divergence-free constraint (∇ B = 0) incorporated as a regularization term. The corrected data was processed through Levenberg-Marquardt (LM) optimization for pose estimation, with subsequent hybrid lookup table compensation combining distance-weighted trilinear interpolation for spatial coordinates and spherical linear interpolation (Slerp) for orientation vectors. Experimental results showed that the positioning error was reduced from 2.1 mm to 1.15 mm, the orientation error was reduced from 3.23<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">◦</sup> to 1.01<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">◦</sup>, and the average speed of magnet positioning reached 44.7 ms per frame. This approach provides a high-precision, low-cost sim-to-real transfer solution for magnetic navigation robots.