Convex optimization and modal analysis for beamforming in robotics: Theoretical and implementation issues

This paper deals with sound source localization in mobile robotics. This context opens new areas of research as it involves some specific constraints such as real time performance or embeddability. Quite often, broadband beamforming techniques are sought for, exploiting small-sized microphone arrays. A new approach to the design of broadband nearfield or farfield beamformers is first described, based on modal analysis and convex optimization. Original considerations related to the involvement of the theoretical beam-pattern into the real integrated acoustic sensor are then presented, which lead to alleviate some constraints during the optimization process and enable the use of smaller arrays. The whole method is illustrated on an example.