Spatial-Temporal Hybrid Path Planning for Multi-UAV Methane Emission Rate Quantification

Accurate emission-rate quantification of methane point sources is essential for inventory verification and leak detection. UAV-borne sensing provides high-resolution, near-source measurements, but existing quantification methods mostly follow a predefined trajectory and rely on a single UAV. Building on a source receptor matrix (SRM) estimator and empirical observability Gramian (EMGR)-based path planning, this paper proposes a spatial-temporal hybrid path planning strategy for multi-UAV methane emission rate quantification. Measurements are time-averaged, and the forward Gaussian plume model is calibrated against a filament-based plume simulator (MOABS) to reduce model mismatch. Cooperating UAVs first spread out spatially to locate the source quickly, then switch to sequentially retracing a leader trajectory with a time lag to reduce quantification variance. Simulations show that the spatial stage localizes the source markedly faster than a single-UAV baseline, the temporal stage yields the lowest variance but converges slowly, and the proposed hybrid strategy converges substantially faster than the purely temporal strategy while matching its steady-state accuracy, with a narrower error band than the purely spatial strategy. A window-length study further shows that longer time-averaging windows exhibit diminishing returns, justifying the balance between spatial coverage and temporal averaging.