Language-goal aerial navigation requires an agent to local- ize a potentially unobserved target from relational instruc- tions and partial observations, and translate this inference into metric actions in large-scale continuous environments. Existing methods often reduce language grounding to one single waypoint or action, prematurely collapsing the spatial uncertainty inherent in incomplete evidence and ambiguous relations. To address this limitation, we introduce SBFNav, a closed-loop navigation framework centered on a language- conditioned Spatial Belief Field (SBF). Unlike ego-centric maps that primarily record what has been observed, SBF rep- resents a task-conditioned distribution over plausible target locations, preserving multiple spatial hypotheses under par- tial evidence. At each step, this distribution is updated from accumulated observations as new evidence becomes avail- able. Built on this representation, SBFNav selects the goal that best aligns with the instruction and observations as a met- ric waypoint for control. Experiments on both the original and revised CityNav benchmarks achieve the best reported overall performance. On the Test Unseen split, our method improves SR from 25.91% to 32.29% and SPL from 19.63% to 30.43%. Ablation studies further confirm the advantages of spatial-belief modeling over single-point prediction.

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