Sequential Sensor Placement using Bayesian Compressed Sensing for Source Localization

This paper deals with the sensor placement problem for an array designed for source localization. When it involves the identification of a few sources, the compressed sensing framework is known to find directions effectively thanks to sparse approximation. The present contribution intends to provide an answer to the following question: given a set of observations, how should we make the next measurement to minimize (some form of) uncertainty on the localization of the sources? More specifically, we propose a methodology for sequential sensor placement inspired from the "Bayesian compressive sensing" framework introduced by Ji et al. Our method alternates between a step of sparse source localization estimation, and a step to choose the sensor position that minimizes the covariance of the estimation error. Numerical results show that an array designed by the proposed procedure leads to better performance than sensors positioned at random.