Attentive Neural Processes for Few-Shot Learning Anomaly-Based Vessel Localization Using Magnetic Sensor Data

Underwater vessel localization using passive magnetic anomaly sensing is a challenging problem due to the variability in vessel magnetic signatures and operational conditions. Data-based approaches may fail to generalize even to slightly different conditions. Thus, we propose an Attentive Neural Process (ANP) approach, in order to take advantage of its few-shot capabilities to generalize, for robust localization of underwater vessels based on magnetic anomaly measurements. Our ANP models the mapping from multi-sensor magnetic readings to position as a stochastic function: it cross-attends to a variable-size set of context points and fuses these with a global latent code that captures trajectory-level factors. The decoder outputs a Gaussian over coordinates, providing both point estimates and well-calibrated predictive variance. We validate our approach using a comprehensive dataset of magnetic disturbance fields, covering 64 distinct vessel configurations (combinations of varying hull sizes, submersion depths (water-column height over a seabed array), and total numbers of available sensors). Six magnetometer sensors in a fixed circular arrangement record the magnetic field perturbations as a vessel traverses sinusoidal trajectories. We compare the ANP against baseline multilayer perceptron (MLP) models: (1) base MLPs trained separately on each vessel configuration, and (2) a domain-randomized search (DRS) MLP trained on the aggregate of all configurations to evaluate generalization across domains. The results demonstrate that the ANP achieves superior generalization to new vessel conditions, matching the accuracy of configuration-specific MLPs while providing well-calibrated uncertainty quantification. This uncertainty-aware prediction capability is crucial for real-world deployments, as it can inform adaptive sensing and decision-making. Across various in-distribution scenarios, the ANP halves the mean absolute error versus a domain-randomized MLP (0.43 m vs. 0.84 m). The model is even able to generalize to out-of-distribution data, which means that our approach has the potential to facilitate transferability from offline training to real-world conditions.