Modal analysis based beamforming for nearfield or farfield speaker localization in robotics

This paper describes a broadband beampattern synthesis method for sound source localization in the nearfield or in the farfield of a mobile robot, with a small-size linear array. The method is based on the theory of Modal Analysis and involves an original convex optimization procedure which benefits from the Parseval relation. The optimized beampattern is obtained by numerically minimizing the worst-case error between the modal coefficients of the array response and those of the reference beampattern, up to a finite rank of the series expansion, over a frequency grid. Simulations illustrate the analytical development.