Multi-Agent Adaptive Super-Resolution Sparse Source Localization for Advection-Diffusion Processes

This work presents a multi-agent system for the adaptive detection and localization of gas sources, based on sequentially collected concentration measurements. Gas distribution is modeled using stationary, non-homogeneous advection-diffusion Partial Differential Equation (PDE), driven by a superposition of unknown, arbitrarily located Dirac measures that represent the gas sources. To estimate both the number and locations of these sources, sparse Bayesian learning (SBL) is integrated with a combine-then-adapt gradient optimization strategy, resulting in an adaptive inversion algorithm capable of estimating both the source support and the concentration field in 2D. Unlike current approaches that require access to the full dataset, the proposed method operates adaptively, enabling real-time estimation achieving a similar estimation accuracy. This results in a more robust and efficient solution for gas source localization in complex environments using realistic sensors, while also offering greater flexibility in data collection.