Organizations: Department of Mechanical and Automation Engineering and T Stone Robotics Institute, The Chinese University of Hong Kong, Hong Kong.
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.
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.
Learning-based wireless localizers often fail to utilize geometric information about the propagation environment, limiting their ability to exploit non-line-of-sight (NLoS) propagation and generalize across scenes. To bridge this gap, we propose GLocFM, a Geometry-aware Localization Foundation Model, which jointly exploits WiFi measurements and scene geometry represented as a 3D point cloud. We formulate localization as a maximum-likelihood (ML) estimation problem, where the goal is to find a transmitter position that maximizes the likelihood of the wireless observations conditioned on the scene geometry. The likelihood of a candidate transmitter position is calculated by a learned scoring function that matches the observed delay--angle-of-arrival (AoA) spectrum against the spectrum predicted for that candidate. A hierarchical scene encoder extracts propagation-relevant features to produce geometric priors for LoS and one-bounce reflection paths. For scenarios with imperfect synchronization, we further introduce a time-of-flight (ToF)-robust GLocFM model to handle unknown ToF offsets. GLocFM is trained on a multi-modal synthetic indoor localization dataset comprising 221 diverse scenes whose associated wireless signals are generated using Sionna RT. On both synthetic and the NeRF2 dataset based on real measurements, GLocFM reduces mean 3D localization error relative to one of the state-of-the-art localization baselines by 49.5% and 48.8%, respectively. Ablations across different number of receiver, bandwidths, and array sizes further demonstrate the effectiveness and robustness of the proposed framework.
Indoor positioning is an essential technology for a wide range of applications in GNSS-denied environments, including indoor navigation and IoT systems. Combining convolutional neural networks (CNNs) and magnetic field-based features offers a low-cost, infrastructure-free solution for precise positioning. While magnetic fingerprints are a promising approach for indoor positioning, models trained on raw 3D magnetometer data are highly sensitive to device orientation. We address this by using two rotation invariant features derived from the 3D magnetic field: the norm (Mn) and the projection onto the gravity axis (Mg). We train a lightweight 7-layer dilated CNN (MagNetS/XL) on magnetic sequences to directly regress (x, y) positions. Using the MagPie dataset (three buildings, handheld trajectories), we systematically evaluate fixed and random rotations of test and/or train data. Raw 3D inputs (Mx, My , Mz) exhibit isotropic error increases under fixed 90° rotations and further degrade with growing random rotations. In contrast, 2D (Mn, Mg) inputs maintain rotation invariant accuracy and surpass the 3D inputs once rotation exceeds building-specific thresholds for three reference buildings: 0° for Loomis (large), 5° for Talbot (medium), and 6° for CSL (small). MagNetXL achieves or exceeds state-of-the-art accuracy on the MagPie dataset, and MagNetS delivers similar performance with roughly one third of the parameters, favoring mobile deployment. These results show that the robustness gained from rotation invariant inputs outweighs the loss of input dimensionality in realistic usage, allowing mapping and localization without orientation alignment or added infrastructure.