Global localization from 3D point clouds remains challenging under limited or asymmetric fields of view (FOV), which fail to provide the dense, symmetric coverage that place recognition methods assume. We present G-PROBE, a learning-free global localization framework that removes this assumption. A virtual sensor decomposition runs the same pipeline, by design, on configurations ranging from a narrow-FOV sensor to a panoramic or multi-sensor rig. The front-end enumerates cross-FOV branch ensembles that encode heading hypotheses for heading-invariant place recognition. A score-scale-invariant, tuning-free gamma-SGRT suppresses heading aliasing under partial FOV and provably becomes inert at symmetric 360 degrees. The back-end, CG-GICP, refines a coarse full-cloud GICP with a pass restricted to high-certainty co-observed points selected by a bird's-eye-view certainty map (a by-product of front-end scoring). This certainty coupling links descriptor evaluation to 6-DoF metric pose estimation without an external verification module. Evaluated on five LiDAR datasets and three modalities (mechanical, solid-state, FMCW), G-PROBE attains the highest learning-free multi-session F1 on average and is competitive in panoramic single-session settings. Where hand-crafted and zero-shot supervised baselines collapse under wide-to-narrow cross-sensor pairing, it remains usable end-to-end (up to 55.0% vs. no more than 6.8% success), and under FOV asymmetry (360 to 60 degrees) it retains about 54% Recall@1, about 18x the strongest learning-free baseline.

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