Session D4: Robust Navigation Using Alternative Navigation Sensors and Solutions

Factor Graph-Based Magnetic Anomaly Navigation: A Robust Bayesian Inference Approach
Shawn Whitney and Aaron Nielsen, USAF - AFIT
Location: Johnson (First Floor)
Date/Time: Thursday, Sep. 11, 2:12 p.m.

Global Navigation Satellite Systems (GNSS) provide effective aircraft positioning but are vulnerable to jamming and spoofing, necessitating alternative navigation methods. Magnetic Anomaly Navigation (MagNav) offers a passive, non-jammable solution by using spatially varying magnetic field measurements to correct drift in an Inertial Navigation Unit (INU). As a map-based technique, MagNav relies on pre-existing magnetic anomaly maps and real-time magnetic sensor data, which, when compared, provide position corrections within an extended Kalman filter (EKF) or similar framework. While MagNav can achieve navigation accuracies down to 200 meters, its effectiveness depends on high-quality maps, precise vehicle magnetic calibration, and optimized filter initialization. Conventional MagNav, however, is limited by its reliance on single-point measurements, making it susceptible to errors if foundational system prerequisites are incomplete.
Factor graphs provide a structured optimization framework that can enhance MagNav by addressing its limitations. Many optimization problems involve objectives composed of multiple factors, each dependent on only a subset of variables. This locality is common in applications like object tracking, where each frame contributes only momentary information about a target’s position. Factor graphs capture these relationships explicitly by representing unknown variables and their interdependencies through factor nodes. This structure enables efficient computation and improved estimation, making factor graphs a powerful tool for state estimation problems.
This research develops a factor graph-based approach to MagNav, leveraging its ability to optimize past and present navigation states simultaneously while incorporating all available measurements. The factor graph framework integrates magnetic observation constraints, aircraft kinematic and dynamic models, and auxiliary sensor data such as barometric altitude. To maintain real-time performance, past states will be marginalized, reducing computational complexity while preserving key information for accurate navigation. By structuring MagNav as a factor graph, this research aims to improve positional accuracy, reduce drift, and enhance resilience against GNSS-denied environments.
To evaluate the approach, simulation studies are conducted using synthetic data with controlled noise and bias conditions, assessing the factor graph’s ability to mitigate measurement known error types. The key performance metrics is localization accuracy, but other metrics may be used such as covariance estimation likelihoods and computational efficiency. Results should demonstrate that the factor graph formulation provides more stable and accurate positioning compared to extended Kalman filter (EKF) implementations, particularly in degraded magnetic regions and in the presence of significant bias sources.
Beyond simulation, real-world flight test data is analyzed to further assess the factor graph’s effectiveness in operational conditions. Data from historical magnetic surveys and instrumented flight campaigns validate the approach’s ability to leverage measurement redundancy over time, improving robustness against transient anomalies. The results highlight the potential for factor graph-based MagNav to enhance aircraft positioning in GPS-denied environments.
This work advances MagNav by demonstrating the benefits of factor graph optimization for handling nonlinear, noisy measurement relationships in a computationally feasible manner. The findings should suggest that this approach provides a scalable and effective method for aiding INU-based navigation, with implications for aircraft, underwater vehicles, and other autonomous platforms operating in GNSS-denied environments. Future work will explore real-time implementation and adaptive bias modeling to further enhance operational robustness.