A Physics-Informed Residual Learning Method for Real-Time 5-DoF Magnetic Localization in Capsule Endoscopy

Real-time localization is a requirement for the clinical application of magnetically actuated wireless capsule endoscopy. This study proposes a physics-informed deep learning framework to address the model-plant mismatch inherent in analytical methods and the data requirements of end-to-end learning. A dual-branch residual network, physics-informed residual network, computes corrections for the magnetic dipole model. Two operational paradigms are evaluated: a lookup-table-based approach and an end-to-end optimization approach. Experiments indicate that the framework achieves a mean position error of 0.69$\pm$0.29 mm and a mean orientation error of 0.70$\pm$0.37$^{\circ }$, utilizing less than 20% of the calibration configurations required by data-driven baselines. Validation includes an ex vivo signal propagation study through biological tissue and compatibility tests with an anti-interference filter, supplemented by a preliminary in vivo animal experiment. The results provide a methodology for sim-to-real transfer in robotic capsule tracking systems.