Information-based Unified Design Framework for NMR Magnetic Tracking System

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.

Embedded magnetic tracking holds highly attractive prospects for remote navigation of endoluminal medical devices. However, existing six-degree-of-freedom pose recovery approaches often require pre-calibrated workspace field maps or iterative nonlinear optimization. This letter presents a Gradiometer-Based Electromagnetic Localization System (GELS), a closed-form tracking framework that uses a compact magnetometer array as an embedded quasi-gradiometer to estimate local magnetic fields and gradient tensors. These quantities are mapped by the Euler homogeneous relation to displacements between source and array, from which multi-source Procrustes registration recovers the array orientation and position using at least three non-collinear sources. The algorithm requires known source positions and array geometry, but no pre-calibrated workspace field maps, initial pose guesses, or calibrated excitation-source moments. The recovered pose also enables a proof-of-concept sub-level dipole localization task by serving as a mobile magnetic reference frame. Benchtop experiments across sensor-array configurations and excitation modes demonstrate sequence-averaged position errors of \SI{10.80}{\milli\meter}--\SI{15.57}{\milli\meter}, a fastest update rate of \SI{14.49}{\hertz}, and a median solver runtime of \SI{172.00}{\micro\second}. A perturbation-based error propagation analysis further identifies inter-sensor inconsistency and dipole-model mismatch as the dominant accuracy limits, thereby informing future sensor array and magnetic source design for further reducing pose-estimation error.

Robots that localize a radio transmitter need more than a point estimate: in cluttered rooms, one measurement is often consistent with several transmitter locations and, because upper-mid-band antennas are directional, several headings. We present MAGNETAR, which infers a joint posterior over planar transmitter position and heading from a single asynchronous radio-frequency (RF) multipath snapshot, represented by angle-of-arrival and signal-to-noise-ratio estimates, given the room layout and receiver pose. Among our five neural scorers, MAGNETAR adopts a shared 2D U-Net conditioned on each candidate heading, jointly normalizing scores over a discretized position-heading grid. Training uses real-to-sim-calibrated 10 GHz simulations and a small measured subset. Grid-based joint posteriors outperform parametric ones on held-out simulations, the heading-conditioned scorer transfers best to robotic measurements, and fusing joint posteriors improves on fusing position-only marginals.