Information-Theoretic Geometry Optimization and Physics-Aware Learning for Calibration-Free Magnetic Localization

TL;DR

This paper introduces a physics-aware deep learning framework combined with optimized sensor geometry for calibration-free magnetic localization, achieving high accuracy and robustness in real-world medical guidance applications.

Contribution

It presents a Fisher Information Matrix-based sensor geometry optimization and a novel physics-informed deep learning estimator that bridges the Sim-to-Real gap in magnetic localization.

Findings

Achieved 1.84 mm position error and 3.18° orientation error in real experiments.

Staggered split-array topology improves observability for localization.

Proposed method outperforms classical solvers and baseline neural networks in robustness.

Abstract

Wireless localization of permanent magnets enables occlusion-free guidance for medical interventions, yet its practical accuracy is fundamentally limited by two coupled challenges: the poor observability of conventional planar sensor arrays and the simulation-to-reality (Sim-to-Real) gap of learning-based estimators. To address these issues, this article presents a unified framework that combines information-theoretic sensor geometry optimization with physics-aware deep learning. First, a rigorous Fisher Information Matrix (FIM)-based evaluation framework is established to quantify geometry-induced observability limitations. The results show that a staggered split-array topology provides a substantially stronger observability foundation for localization while remaining compatible with practical external deployment. Second, building on this optimized sensing configuration, we propose Phy-GAANet, a calibration-free estimator trained entirely on hardware-aware synthetic data. By incorporating Physics-Informed Features (PIF) for saturation modeling and Geometry-Aware Attention (GAA) for preserving cross-layer vector structure, the network effectively bridges the Sim-to-Real gap. Extensive real-world experiments demonstrate state-of-the-art performance, achieving a position error of 1.84 mm and an orientation error of 3.18 degrees at a refresh rate exceeding 270 Hz. The proposed method consistently outperforms classical Levenberg--Marquardt solvers and generic convolutional baselines, particularly in suppressing catastrophic outliers and maintaining robustness in challenging near-field boundary regions. Beyond the proposed network, the FIM-guided analysis also provides a framework for sensor geometry design in magnetic localization systems under practical deployment constraints.