Sensor Planning for Model-Based Acoustic Source Identification
In this paper we propose an online active sensor planning strategy for model-based acoustic source identification (SI) in non-convex domains utilizing the three-dimensional Helmholtz partial differential equation (PDE). After discretizing the PDE using the finite element method, we formulate the SI problem as a PDE-constrained optimization problem. To make the solution computationally tractable, we employ proper orthogonal decomposition to reduce the dimension of the pressure field. Given a set of initial measurements, we solve the SI and sensor planning problems in a feedback loop. Specifically, given a set of measurements, we first solve the SI problem to get an estimate of the source field. We then fit a set of nonlinear basis functions to the solution in order to reduce the number of unknowns required to describe the source field. We finally utilize the Fisher information matrix (FIM) along with the current source parameter estimates to select the next best measurement location. Specifically, we choose a sequence of waypoints that sequentially maximize the minimum eigenvalue of the FIM with respect to the unknown source parameters. We present numerical and experimental results that showcase our proposed method. This work presents the first active sensor planning method for PDE-based acoustic SI that is investigated in practice.
