Extending Temporal Disturbance Estimations For Magnetic Anomaly Navigation and Mapping

TL;DR

This work introduces the Extended Reference Station Model (ERSM) to extend magnetic anomaly navigation and mapping beyond the traditional 100 km ground-station limit by leveraging a distant extended reference station and a regression-based correction to estimate the local temporal disturbance field at a nearby reference. It evaluates three regression strategies—linear, kNN, and a neural-network ensemble—within a longitudinal-normalization framework, demonstrating typical RMSEs below $10$ nT and medians below $5$ nT across diverse geographies, including land, water, and polar regions. The results show ERSM is effective for mid-to-low latitude navigation and marine surveys but struggles near the poles due to magnetospheric and electrojet effects, and the method cannot forecast beyond the available ERS data. Practical implications include enabling long-range MagNav and anomaly-mapping campaigns with portable or land-based ERS deployments; future work could add forecasting capabilities or more portable station configurations to broaden real-time applicability.

Abstract

Slow-moving vehicles relying on crustal magnetic anomaly navigation (MagNav) or vehicles revisiting the same location in a short time - such as those used for surveys in magnetic anomaly mapping - require fixed ground stations within 100 km of the vehicle's trajectory to measure and remove the geomagnetic disturbance field from magnetic readings. This approach is impractical due to the limited network of fixed-ground magnetometer stations, making long-range (several hundred kilometers long) aeromagnetic surveys for anomaly map-making infeasible. To address these challenges, we developed the Extended Reference Station Model (ERSM). ERSM applies a longitudinal correction and regression model to an extended reference ground magnetometer station (ERS) to produce an estimate of the local temporal disturbance field. ERSM is regression model-agnostic, so we implemented a linear regression, a k-nearest neighbors (kNN) regression, and a neural-network regression model to assess performance benefits. Our results show typical performance below 10nT root mean square error and median performance below 5nT for typical use with the kNN and neural-net model for farther distances and below 5nT performance using the linear regression model on stations with proximity. We also consider how space-weather events, water-body separation, and proximity to polar regions affect the model performance based on ERS selection.

Figures (13)

• Figure 1: The Extended Reference Station Model (ERSM) inference pipeline. At a high level, ERSM has two components. 1) Longitude normalization is achieved by using a high-pass filter (HPF) and a low-pass filter (LPF) to shift low-frequency components to account for the Earth's rotation. 2) A regression model to account for shape and magnitude variations due to local geographic features. We also truncate the LRS's DV to ensure timestamp alignment during training of the regression model.
• Figure 2: The procedure for training and predicting with the kNN regression in ERSM. During training, we scale the features, tune the hyperparameter for the distance metric, and use this distance metric to make predictions.
• Figure 3: The neural-net model we implemented in ERSM. (a) The high-level representation of the architecture using 3 ERSM residual blocks. (b) Lower-level representation of each ERSM residual block. The block's output is the sum of the input and the output of the last linear layer.
• Figure 4: Features used in each model.
• Figure 5: The stations we used to evaluate ERSM. The central figure (Experiment Stations) provides a global view of the locations of the stations (dark blue dots) and how we selected a diverse range of stations. To identify the experiment in the central figure, we provide an alphabetical identification for each group of stations used in an experiment. The remaining figures show each experiment (with the alphabetical coding). In these figures, the red dot and light blue dots correspond to the LRS and ERSs, respectively. For experiments G and H, we provide the orthographic projections to illustrate the proximity between stations more clearly.