Hex-OSGM: Incremental Gravity Field Learning on Adaptive Hexagonal Meshes for Robust Passive Navigation

    Gravity-matching navigation—a self-contained and passive navigation modality—depends critically on the accuracy and resolution of the background gravity field and the adaptability of the matching algorithm，Current gravity modeling methods, however, are limited by slow model updates and inefficient storage under dynamic operating conditions. To overcome these challenges, we introduce a novel gravity-matching framework that integrates incremental learning with adaptive mesh optimization.

    Our approach proceeds in three key stages. First, a global gravity field is rapidly initialized using a spherical-harmonics model trained via an Extreme Learning Machine (ELM). We then employ an online sequential ELM (OS-ELM) to incrementally assimilate posterior gravity information—whether obtained in real time or fused from multi-source observations—thereby enabling timely model updates and continuous refinement of field fidelity.

    Second, we systematically evaluate the sensitivity of batch-matching algorithms (e.g., ICCP and contour matching) to interpolation density and derive an adaptive density-selection criterion that incorporates prior map information content, vehicle velocity, and inertial navigation system error growth. To improve storage and computational efficiency, we replace conventional rectilinear grids with a hexagonal tessellation for field discretization. Theoretical analysis and experimental results confirm that, at equal nominal resolution, the hexagonal lattice reduces both model and localization errors while its structural isotropy enhances the stability and convergence of batch matching across diverse heading angles.

    Third, we introduce an encrypted interpolation strategy centered on hexagonal cell centroids. This approach increases effective resolution with only a minor increase in storage, thereby improving the algorithm’s ability to resolve subtle gravity features. Numerical simulations and field data demonstrate that the proposed framework sustains high-precision matching performance while significantly reducing storage and computational burdens, offering a promising technical pathway toward long-endurance, robust gravity-matching navigation in complex environments.