Physics-Informed Calibration of Aeromagnetic Compensation in Magnetic Navigation Systems using Liquid Time-Constant Networks

Magnetic navigation (MagNav) is a rising alternative to the Global Positioning System (GPS) and has proven useful for aircraft navigation. Traditional aircraft navigation systems, while effective, face limitations in precision and reliability in certain environments and against attacks. Airborne MagNav leverages the Earth's magnetic field to provide accurate positional information. However, external magnetic fields induced by aircraft electronics and Earth's large-scale magnetic fields disrupt the weaker signal of interest. We introduce a physics-informed approach using Tolles-Lawson coefficients for compensation and Liquid Time-Constant Networks (LTCs) to remove complex, noisy signals derived from the aircraft's magnetic sources. Using real flight data with magnetometer measurements and aircraft measurements, we observe up to a 64% reduction in aeromagnetic compensation error (RMSE nT), outperforming conventional models. This significant improvement underscores the potential of a physics-informed, machine learning approach for extracting clean, reliable, and accurate magnetic signals for MagNav positional estimation.

An Explainable Geometric-Weighted Graph Attention Network for Identifying Functional Networks Associated with Gait Impairment

One of the hallmark symptoms of Parkinson's Disease (PD) is the progressive loss of postural reflexes, which eventually leads to gait difficulties and balance problems. Identifying disruptions in brain function associated with gait impairment could be crucial in better understanding PD motor progression, thus advancing the development of more effective and personalized therapeutics. In this work, we present an explainable, geometric, weighted-graph attention neural network (xGW-GAT) to identify functional networks predictive of the progression of gait difficulties in individuals with PD. xGW-GAT predicts the multi-class gait impairment on the MDS Unified PD Rating Scale (MDS-UPDRS). Our computational- and data-efficient model represents functional connectomes as symmetric positive definite (SPD) matrices on a Riemannian manifold to explicitly encode pairwise interactions of entire connectomes, based on which we learn an attention mask yielding individual- and group-level explainability. Applied to our resting-state functional MRI (rs-fMRI) dataset of individuals with PD, xGW-GAT identifies functional connectivity patterns associated with gait impairment in PD and offers interpretable explanations of functional subnetworks associated with motor impairment. Our model successfully outperforms several existing methods while simultaneously revealing clinically-relevant connectivity patterns. The source code is available at https://github.com/favour-nerrise/xGW-GAT .