Model-Based Active Source Identification in Complex Environments

In this paper we consider the problem of Active Source Identification (ASI) in steady-state Advection-Diffusion (AD) transport systems. Specifically, given a set of noisy concentration measurements, we formulate the Source Identification (SI) problem as a PDE-constrained optimization in function spaces. To obtain a tractable solution, we employ Proper Orthogonal Decomposition to approximate the concentration field by a low dimensional subspace. We also model the unknown source field using nonlinear basis functions, which decreases the number of source parameters drastically. We use the Sensitivity Analysis of the SI objective to initialize the resulting nonlinear optimization problem. To collect the measurements, we control a robot sensor through a sequence of waypoints that maximize the minimum-eigenvalue of the Fisher Information Matrix of the unknown source parameters. Specifically, with every new measurement, the solution of the SI problem is used to determine the next waypoint in a feedback loop. We present numerical simulations and real-world experiments that show that the proposed ASI algorithm can efficiently identify sources in complex AD systems and non-convex domains.