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

• URL: http://arxiv.org/abs/2604.22526v1
• Date: Fri, 24 Apr 2026 13:12:14 GMT
• Title: Information-Theoretic Geometry Optimization and Physics-Aware Learning for Calibration-Free Magnetic Localization
• Abstract summary: This article presents a unified framework that combines information-theoretic sensor geometry optimization with physics-aware deep learning.<n>We show that a staggered split-array topology provides a substantially stronger observability foundation for localization.<n>We also propose Phy-GAANet, a calibration-free estimator trained entirely on hardware-aware synthetic data.
• Score: 10.338483096774063
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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