Airborne Magnetic Anomaly Navigation with Neural-Network-Augmented Online Calibration

Antonia Hager; Sven Nebendahl; Alexej Klushyn; Jasper Krauser; Torleiv H. Bryne; Tor Arne Johansen

cs.LGMar 9, 2026

Airborne Magnetic Anomaly Navigation with Neural-Network-Augmented Online Calibration

Authors: Antonia Hager, Sven Nebendahl, Alexej Klushyn, Jasper Krauser, Torleiv H. Bryne, Tor Arne Johansen

Organizations: Airbus, 82024 Taufkirchen, Germany. · Norwegian University of Science and Technology, 7034 Trondheim, Norway.

Abstract

Airborne Magnetic Anomaly Navigation (MagNav) provides a jamming-resistant and robust alternative to satellite navigation but requires the real-time compensation of the aircraft platform's large and dynamic magnetic interference. State-of-the-art solutions often rely on extensive offline calibration flights or pre-training, creating a logistical barrier to operational deployment. We present a fully adaptive MagNav architecture featuring a "cold-start" capability that identifies and compensates for the aircraft's magnetic signature entirely in-flight. The proposed method utilizes an extended Kalman filter with an augmented state vector that simultaneously estimates the aircraft's kinematic states as well as the coefficients of the physics-based Tolles-Lawson calibration model and the parameters of a Neural Network to model aircraft interferences. The Kalman filter update is mathematically equivalent to an online Natural Gradient descent, integrating superior convergence and data efficiency of state-of-the-art second-order optimization directly into the navigation filter. To enhance operational robustness, the neural network is constrained to a residual learning role, modeling only the nonlinearities uncorrected by the explainable physics-based calibration baseline. Validated on the MagNav Challenge dataset, our framework effectively bounds inertial drift using a magnetometer-only feature set. The results demonstrate navigation accuracy comparable to state-of-the-art models trained offline, without requiring prior calibration flights or dedicated maneuvers.

Figures & tables

Panel of Figure 1 — Figure 1: Hybrid MagNav Architecture with NN -augmented calibration model.

Figure 2: Mean position error distribution and average runtimes from 100 Monte Carlo simulations for input parameter sets $\bm{\phi}_{\text{m}}$ , $\bm{\phi}_{\text{mv}}$ , and $\bm{\phi}_{\text{all}}$ for different numbers of hidden neurons.

Figure 3: Magnetic-Anomaly aided odometry with NN -online-learning based platform interference compensation for four trajectories ( $\bm{\phi}=\bm{\phi}_{\text{m}}$ , $N_{h}=8$ ).

Panel of Figure 4 — Figure 4: NN-EKF performance on the lawnmower trajectory ( $\bm{\phi}_{\text{m}}$ ) for $N_{h}=2$ and $N_{h}=8$ showing position RMSE improvement compared to odometry in (a) and platform interference approximation in (b).

Panel of Figure 5 — Figure 5: EKF-based online adaptation of the NN parameters $\bm{x}_{\text{NN}}$ for $\bm{\phi}=\bm{\phi}_{\text{m}}$ , $N_{h}=8$ for the (a) Figure Eight, (b) Irregular, (c) Lawnmower, and (d) Spiral trajectories.

Figure 6: GNSS trajectory of flight line 1007.06.

Figure 7: Magnetic aiding performance results using magnetometer 1 to 5 and different hidden layer sizes $N_{h}$ .

Panel of Figure 8 — Figure 8: Positioning accuracy in cold and warm start scenarios using Magnetometer 2 ( $N_{h}=5$ ). (a) Our hybrid approach combining TL and NN calibration ( DRMS cold start $51\text{\,}\mathrm{m}$ / warm start $48\text{\,}\mathrm{m}$ ) (b) TL online calibration ( $N_{h}=0$ ), DRMS cold start $107\text{\,}\mathrm{m}$ / warm start $86\text{\,}\mathrm{m}$ ).

Panel of Figure 9 — Figure 9: Evolution of the NN parameter variance $\bm{\mathcal{P}}_{\text{NN}}$ using Magnetometer 2 ( $N_{h}=5$ ), comparing (a) cold start and (b) warm start.

Panel of Figure 10 — Figure 10: Evolution of NN (top) and TL (bottom) model parameters using Magnetometer 2 ( $N_{h}=5$ ), comparing (a), (c) cold start and (b), (d) warm start.

Panel of Figure 11 — Figure 11: Comparison between the (a) TL model compensation components (including the bias state $S_{CB}$ ) and the (b) learned NN output using Magnetometer 2 in the cold start scenario.

Appendix figures & tables21 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 12 — Figure 12: CRLBs along the lawnmower-trajectory for (a) small $N_{h}=4$ and (b) large $N_{h}=32$ .

Panel of Figure 13 — Figure 13: Evolution of the positioning accuracy in cold and warm start scenarios using Magnetometer 1 ( $N_{h}=5$ ). (a) Our hybrid approach combining TL and NN calibration ( DRMS cold-start $17\text{\,}\mathrm{m}$ / warm-start $17\text{\,}\mathrm{m}$ ) (b) TL online calibration ( DRMS cold-start $17\text{\,}\mathrm{m}$ / warm-start $17\text{\,}\mathrm{m}$ ).

Panel of Figure 14 — Figure 14: Evolution of NN (top) and TL model (bottom) parameters using Magnetometer 1 ( $N_{h}=5$ ), comparing (a), (c) cold start and (b), (d) warm start.

Panel of Figure 15 — Figure 15: Comparison between the (a) TL model compensation components (including the bias state $S_{CB}$ ) and the (b) learned NN output using Magnetometer 1 in the cold start scenario.

Panel of Figure 16 — Figure 16: Comparison of INS and MagNav position errors (north, east, and down) for Magnetometer 1 in (a) our hybrid TL + NN cold-start and (b) the TL -only cold-start scenarios.

Panel of Figure 17 — Figure 17: Comparison of INS and MagNav position errors (north, east, and down) for Magnetometer 2 in (a) our hybrid TL + NN cold-start and (b) the TL -only cold-start scenarios.

Panel of Figure 18 — Figure 18: Evolution of the positioning accuracy in cold and warm start scenarios using Magnetometer 3 ( $N_{h}=2$ ). (a) Hybrid approach combining TL and NN calibration ( DRMS cold-start $42\text{\,}\mathrm{m}$ / warm-start $36\text{\,}\mathrm{m}$ ) (b) TL online calibration ( DRMS cold-start $46\text{\,}\mathrm{m}$ / warm-start $45\text{\,}\mathrm{m}$ ).

Panel of Figure 19 — Figure 19: Evolution of NN (top) and TL model (bottom) parameters using Magnetometer 3 ( $N_{h}=5$ ), comparing (a), (c) cold start and (b), (d) warm start.

Panel of Figure 20 — Figure 20: Comparison between the (a) TL model compensation components (including the bias state $S_{CB}$ ) and the (b) learned NN output using Magnetometer 3 in the cold start scenario.

Panel of Figure 21 — Figure 21: Comparison of INS and MagNav position errors (north, east, and down) for Magnetometer 3 in (a) our hybrid TL + NN cold-start and (b) the TL -only cold-start scenarios.

Panel of Figure 22 — Figure 22: Evolution of the positioning accuracy in cold and warm start scenarios using Magnetometer 4 ( $N_{h}=5$ ). (a) Hybrid approach combining TL and NN calibration ( DRMS cold-start $37\text{\,}\mathrm{m}$ / warm-start $46\text{\,}\mathrm{m}$ ) (b) TL online calibration ( DRMS cold-start $58\text{\,}\mathrm{m}$ / warm-start $54\text{\,}\mathrm{m}$ ).

Panel of Figure 23 — Figure 23: Evolution of NN (top) and TL model (bottom) parameters using Magnetometer 4 ( $N_{h}=5$ ), comparing (a), (c) cold start and (b), (d) warm start.

Panel of Figure 24 — Figure 24: Comparison between the (a) TL model compensation components (including the bias state $S_{CB}$ ) and the (b) learned NN output using Magnetometer 4 in the cold start scenario.

Panel of Figure 25 — Figure 25: Comparison of INS and MagNav position errors (north, east, and down) for Magnetometer 4 in (a) our hybrid TL + NN cold-start and (b) the TL -only cold-start scenarios.

Panel of Figure 26 — Figure 26: Evolution of the positioning accuracy in cold and warm start scenarios using Magnetometer 5 ( $N_{h}=5$ ). (a) Hybrid approach combining TL and NN calibration ( DRMS cold-start $14\text{\,}\mathrm{m}$ / warm-start $15\text{\,}\mathrm{m}$ ) (b) TL online calibration ( DRMS cold-start $15\text{\,}\mathrm{m}$ / warm-start $15\text{\,}\mathrm{m}$ ).

Panel of Figure 27 — Figure 27: Evolution of NN (top) and TL model (bottom) parameters using Magnetometer 5 ( $N_{h}=5$ ), comparing (a), (c) cold start and (b), (d) warm start.

Panel of Figure 28 — Figure 28: Comparison between the (a) TL model compensation components (including the bias state $S_{CB}$ ) and the (b) learned NN output using Magnetometer 5 in the cold start scenario.

Panel of Figure 29 — Figure 29: Comparison of INS and MagNav position errors (north, east, and down) for Magnetometer 5 in (a) our hybrid TL + NN cold-start and (b) the TL -only cold-start scenarios.

Figure 30: Evolution of the innovation using (

N_{h}=5

), comparing (a) Magnetometer 4 (C), (b) Magnetometer 4 (W), (c) Magnetometer 5 (C), and (d) Magnetometer 5 (W).

Figure 31: GNSS trajectory of all segments of flight line 1003.01 to 1003.09.

Panel of Figure 32 — Figure 32: Evolution of the positioning accuracy for our hybrid approach combining TL and NN calibration using Magnetometer 3 ( $N_{h}=2$ ) in the (a) cold-start ( DRMS $142\text{\,}\mathrm{m}$ ) and (b) warm-start ( DRMS $70\text{\,}\mathrm{m}$ ) scenarios.

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Neural Aided Adaptive Innovation-Based Invariant Kalman Filter

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Kalman Filtering Invariant EKF Autonomous Underwater Navigation

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Autonomous platforms require accurate positioning to complete their tasks. To this end, a Kalman filter-based algorithms, such as the extended Kalman filter or invariant Kalman filter, utilizing inertial and external sensor fusion are applied. To cope with real-world scenarios, adaptive noise estimation methods have been developed primarily for classical Euclidean formulations. However, these methods remain largely unexplored in the tangent Lie space, despite it provides a principled geometric framework with favorable error dynamics on Lie groups. To fill this gap, we combine invariant filtering theory with neural-aided adaptive noise estimation in real-world settings. To this end, we derive a novel theoretical extension of classical innovation-based process noise adaptation formulated directly within the Lie-group framework. We further propose a lightweight neural network that estimates the process noise covariance parameters directly from raw inertial data. Trained entirely in a sim2real framework via domain adaptation, the network captures motion-dependent and sensor-dependent noise characteristics without requiring labeled real-world data. To examine our proposed neural-aided adaptive invariant Kalman filter, we focus on the challenging real-world scenario of autonomous underwater navigation. Experimental results demonstrate superior performance compared to existing methods in terms of position root mean square error. These results validate our sim2real pipeline and further confirm that geometric invariance significantly enhances learning-based adaptation and that adaptive noise estimation in the tangent Lie space offers a powerful mechanism for improving navigation accuracy in nonlinear autonomous platforms.

Abstract

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