Equivalent Source Models for Altitude-Adaptive Magnetic Uncertainty and Anomaly Upward Continuation: A MagNav EKF Validation with Flight Test Data

Magnetic Anomaly Navigation (MagNav) performance is fundamentally dependent on the quality of the underlying magnetic anomaly map. Map generation is especially challenging when using poorly sampled historical data, such as the NOAA/NCEI database (NOAA/NCEI, nd), which often results in significant, spatially varying uncertainty that can introduce filter-breaking errors. Our previous research demonstrated that an uncertainty-aware Extended Kalman Filter (EKF) improves stability by selectively applying magnetic updates (Blakely et al., 2025, 2026). However, that approach relied on a 2D uncertainty grid fixed to the survey altitude, failing to account for the aircraft’s true flight altitude where uncertainty may differ significantly. This research expands on previous work by leveraging the Equivalent Sources (EQS) method to generate a continuous 3D model of magnetic sources. Unlike FFT-based methods, EQS solves the inverse problem to determine source strengths that replicate observed survey data, allowing for the upward propagation of both magnetic anomaly and uncertainty values to any 3D position. We integrate this EQS model into our EKF to obtain scalar, gradient, and uncertainty values at the aircraft’s specific latitude, longitude, and altitude. This provides a physically informed uncertainty value at the aircraft’s coordinates, enabling the EKF to dynamically and more accurately disregard or weight each magnetic update. We test this EQS-based, uncertainty-aware filter using real flight data across two geographic regions: offshore southern California (AngelWings) and the central Caribbean (CANREx (Saltus et al., 2023)). Tests comparing measured magnetic anomaly data with the magnetic map data at various flight altitudes demonstrates the ability of the EQS model to provide a more representative uncertainty value at flight altitude in comparison to the fixed-altitude uncertainty methods. Additionally, tests with both navigation and tactical grade IMUs in these regions demonstrate the ability to use this altitude-adaptive uncertainty in the navigation filter to improve stability in a meaningful way. This approach allows the filter to intelligently rely on accurate map regions while disregarding problematic areas by setting a different uncertainty threshold based on operation altitude, confirming the advantages of leveraging EQS to propagate map uncertainty to flight altitude.