Information-based Unified Design Framework for NMR Magnetic Tracking System

Seçkin Eren Yetim; Mehmet Efe Tiryaki

cs.ROOct 13, 2026

Information-based Unified Design Framework for NMR Magnetic Tracking System

Authors: Seçkin Eren Yetim, Mehmet Efe Tiryaki

Organizations: METU-ROMER, Center for Robotics and AI, Middle East Technical University, Ankara, Türkiye. · Department of Mechanical Engineering, Middle East Technical University, Ankara, Türkiye.

Abstract

Nuclear magnetic resonance (NMR) magnetic tracking offers a promising alternative to magnetic resonance imaging (MRI)-based localization for medical robotic guidance. However, scalar field measurements and field-aligned marker moments constrain position and orientation tracking, requiring careful configuration design. We present a unified information-based framework that uses local covariance analysis to evaluate receiver geometry, marker separation, and external source configuration in on/off-board NMR tracking. Numerical evaluation shows that planar-array precision depends jointly on receiver count and geometry, with triangular lattice arrays achieving the lowest best-case position uncertainty among the evaluated layouts for 9--20 receivers. Two spatially separated, field-aligned markers enable device-axis tracking, with predicted angular uncertainty below $2^\circ$ at the evaluated workspace center for suitable marker separations. We further establish point-dipole source--receiver duality, unifying the analysis of on/off-board NMR tracking. These

Figures & tables

Fig. 1: Magnetic-tracking architectures considered in this study.MRI setting and representative distance-dependent measurements $\delta B_{i}(r_{i})$ from seven receivers. (A) Off-board sensing of a device-mounted, field-aligned marker $\bm{m}$ by an external receiver array. (B) On-board sensing of fields $\delta B_{k}$ from independently activated external sources with moments $\bm{m}_{k}$ .

Fig. 2: (A) Single marker–receiver geometry with depth $z$ , lateral separation $\rho$ , and local field $\delta\bm{B}$ .(B) Two identical field-aligned markers separated by $L$ define the unoriented device axis $\bm{u}$ .

Fig. 3: Local 3-D position-uncertainty score for the three-receiver planar array. (A) Measurement geometry. (B) Top view of the equilateral reference array. (C) $A_{p}$ map in the $x=0$ plane. (D–F) $A_{p}$ maps at $z=5$ , 20, and 60 mm. All maps use a logarithmic scale with $A_{p}$ reported in millimeters.

Fig. 4: Planar receiver-array comparison with 20-mm minimum pairwise spacing. (A) Representative layouts from the four evaluated families. (B) Minimum sampled $A_{p}$ versus receiver count $N$ at $z=60$ mm over the $100\times 100$ mm 2 region; the inset enlarges $N=18$ –20.

Fig. 5: Worst-over-direction two-marker uncertainty. (A) $A_{u}$ workspace map at $z=60$ mm for $L=20$ mm; contours at $1^{\circ}$ and $2^{\circ}$ . (B) Corresponding $A_{p}$ map; contours at $0.1$ and $1$ mm. (C) Center-point $A_{u}$ versus $L$ . (D) Center-point $A_{p}$ versus $L$ . Open circles mark $L_{\mathrm{ref}}=20$ mm; (A–C) use logarithmic scales.

Fig. 6: Sequential scalar on-board sensing with three independently activated sources. (A) Distributed–parallel configuration. (B) Co-located–orthogonal configuration. (C) Distributed–parallel $A_{p}$ map in the $y=0$ plane. (D) Co-located–orthogonal $A_{p}$ map. Contours mark $0.01$ , $0.1$ , and $1$ mm; both maps share a 0–2 mm scale, with larger values saturated.

Robot Localization

Robot localization estimates a robot’s position and orientation from onboard sensors, maps, and observations of its surroundings.

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

Wenxuan Xie, Yuelin Zhang, Qingpeng Ding, Jianghua Chen+3

Department of Mechanical and Automation Engineering and T Stone Robotics Institute, The Chinese University of Hong Kong, Hong Kong.

Sim-to-Real Transfer Wireless Localization Physics-Informed ML

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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.

Abstract

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