Transect-Based Magnetic Navigation Using Confidence Likelihood Estimation

Magnetic anomaly navigation (MagNav) offers a passive, globally available alternative to Global Navigation Satellite System (GNSS) positioning, but practical deployment remains limited by ambiguity in map matching and the absence of principled confidence measures that transfer cleanly into sequential estimators. Trackline-based magnetic map matching mitigates some limitations of single-measurement filtering by exploiting spatial context across a sequence of measurements; however, commonly used scores—such as Mean Absolute Difference (MAD), Mean Squared Difference (MSD), and correlation—are heuristic and provide no intrinsic notion of uncertainty. This paper introduces Covariance Likelihood Estimation (CLE), a likelihood-based formulation of transect matching that evaluates a Gaussian negative log-likelihood over candidate positions. The resulting likelihood field yields both a maximumlikelihood position estimate and a local, data-driven measure of confidence derived from the field’s curvature. To mitigate sensitivity to additive bias from residual aircraft interference, compensation error, or map bias, a gradient-domain formulation (CLE-Grad) is developed and used as the primary estimator. A structured Design of Experiments (DOE) is conducted using AngelWings flight data while varying independently generated magnetic anomaly maps of differing fidelity to isolate map-driven ambiguity. Results show that likelihood-field curvature from CLE tracks realized localization error more consistently than curvature proxies derived from classical scores. While pointestimation accuracy remains comparable to established methods, CLE provides a principled mechanism for forming adaptive measurement covariances by exploiting the local Hessian curvature of the negative log-likelihood at the maximum-likelihood solution. Empirically, the log-determinant of this Hessian is shown to correlate with realized DRMS error, yielding a data-driven confidence metric enables direct integration into an Extended Kalman Filter (EKF) without scenario-specific tuning.