Two-stage cylindrical magnetic localization with neural network calibration for wearable capsule endoscopy

Accurate localization of wireless capsule endoscopy is essential for reliable gastrointestinal diagnosis, yet magnetic tracking systems are often degraded by sensor distortions, misalignment, and patient motion in wearable settings. This study presents a magnetic localization framework that combines cylindrical magnetic field modelling with neural network-based sensor calibration to improve robustness under wearable operating conditions. By exploiting the structural properties of cylindrical magnetic field representations, the proposed approach decouples axial and transverse components of the magnetic field, enabling staged estimation of magnetic capsule position and orientation with improved numerical stability. A data-driven calibration model is employed to compensate for nonlinear sensor distortions arising from hard-iron effects, soft-iron effects, and dynamic misalignment. Experimental validation using a four-sensor wearable array demonstrates a mean static localization error of 0.12 cm and [Formula: see text], and a dynamic localization error of 0.20 cm and [Formula: see text], indicating improved performance under both stable and motion-affected conditions. These results suggest that accurate and robust magnetic capsule localization can be achieved with a minimal sensor configuration, supporting practical implementation in wearable capsule endoscopy systems.