Exact Localization of Planar Acoustic Reflectors in Three-Dimensional Geometries

In this paper we propose a methodology for localizing acoustic planar reflectors in a 3D geometry, using acoustic measurements acquired by a set of microphones. An acoustic source emitting a known signal is placed close to the wall to be identified, and is used for estimating the source-to-microphone impulse responses. In a preliminary step, such estimates are employed for localizing the source. After that, the Times Of Arrival (TOAs) associated to the first order reflective paths are extracted from the impulse responses and converted into quadratic constraints (ellipsoids) acting on the reflective plane. The constraints are then collected into a cost function, whose exact minimization leads to the searched plane. A theoretical analysis is performed for predicting the impact of measurement errors on the estimation. Moreover, experimental results in a real meeting room prove the effectiveness of the method.