Identification of Black-Box Wave Propagation Models Using Large-Scale Convex Optimization

In this paper, we propose a novel approach to the identification of multiple-input multiple-output (MIMO) wave propagation models having a common-denominator pole-zero parametrization. We show how the traditional, purely data-based identification approach can be improved by incorporating a physical wave propagation model, in the form of a spatiotemporally discretized version of the wave equation. If the wave equation is discretized by means of the finite element method (FEM), a high-dimensional yet highly sparse linear set of equations is obtained that can be imposed at those frequencies where a high-resolution model estimate is desired. The proposed identification approach then consists in sequentially solving two large-scale convex optimization problems: a sparse approximation problem for estimating the point source positions required in the FEM, and an equality-constrained quadratic program (QP) for estimating the common-denominator pole-zero model parameters. A simulation example for the case of indoor acoustic wave propagation is provided to illustrate the benefits of the proposed approach.