Detection and Estimation of Gas Sources With Arbitrary Locations Based on Poisson's Equation

Accurate estimation of the number and locations of dispersed material sources is critical for optimal disaster response in Chemical, Biological, Radiological, or Nuclear accidents. This paper introduces a novel approach to Gas Source Localization that uses sparse Bayesian learning adapted to models based on Partial Differential Equations for modeling gas dynamics. Using the method of Green's functions and the adjoint state method, a gradient-based optimization with respect to source locations is derived, allowing superresolving (arbitrary) source locations. By combing the latter with sparse Bayesian learning, a sparse source support can be identified, thus indirectly assessing the number of sources. Simulation results and comparisons with classical sparse estimators for linear models demonstrate the effectiveness of the proposed approach. The proposed sparsity-constrained gas source localization method offers thus a flexible solution for disaster response and robotic exploration in hazardous environments.