Spatiotemporal Geomagnetic Intensity Mapping Using Gaussian Process for Underwater Vehicle Localization

Accurate geomagnetic field mapping plays a critical role in the navigation and localization of autonomous underwater vehicles (AUVs), especially in environments where traditional satellite navigation is unavailable. This paper introduces a spatiotemporal Gaussian process (GP) kernel for modeling spatial anomalies and temporal geomagnetic variations, integrating three distinct kernel functions: a radial basis function (RBF) for spatial dependence, a periodic kernel for diurnal fluctuations, and a Matérn-1/2 kernel for short-term disturbances. A simulation framework was developed to generate synthetic maritime magnetic field data, incorporating spatial anomalies and temporal variations derived from INTERMAGNET geomagnetic data. The proposed method was tested using multiple map sizes. The results revealed significant improvement in map regression accuracy over RBF-only models, with root-mean-square errors (RMSEs) in the 2–8 nT range and reconstruction errors consistently maintained within 10–20 nT. In addition, the proposed computational cost of the kernel was evaluated, revealing a trade-off between the map accuracy and processing time, particularly for larger mission areas. This study highlights the feasibility and practical advantages of using spatiotemporal GP models for real-time AUV geomagnetic mapping.