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 space. To obtain a tractable numerical 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 unknowns drastically. We use point-source Sensitivity Analysis of the SI objective function to initialize the resulting nonlinear optimization problem. To collect the required measurements, we control a mobile robot sensor through a sequence of waypoints that maximize the minimum-eigenvalue of the Fisher Information Matrix of the unknown source parameters. We formulate the path planning problem as a nonlinear Semi-Definite Program (SDP) and solve it iteratively using sequential SDP. We present numerical experiments that show that the ASI algorithm can efficiently identify sources in complex AD systems that live in non-convex domains.