  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.
