Optimal sensor placement for sound field reconstruction

Sound field reconstruction aims at estimating acoustic fields over space from a limited number of measurements, typically in connection to the analysis, control, and reproduction of the measured fields. While the existing literature has focused on developing suitable acoustic models and estimation algorithms, less attention has been paid to the positioning of measurements. The present study investigates the optimal sensor placement for reconstructing sound fields over space. The reconstruction problem involves estimating a set of parameters used to describe the sound field. In this study, an optimization problem is formulated, in which the sensor positions that minimize the Bayesian Cramer-Rao bounds for the estimated parameters are chosen from a collection of candidates, while a constraint on the number of active sensors is imposed. An approximate solution to this problem is found via convex relaxation. Numerical results show that tight bounds can be obtained, thus the optimized positions can effectively reduce the mean-squared-error of the estimated parameters. Additionally, a bound on the best achievable performance by a selection of sensors can be calculated, making it possible to assess the optimality of the approximate, convex-relaxed solution. Experimental results indicate lower errors when the positions are optimized as compared to other selection methods.