Simultaneous Acoustic Echo Sorting and 3-D Room Geometry Inference

Room geometry estimation from multiple acoustic room impulse responses (RIRs) relies on being able to correctly identify first-order echoes corresponding to the same reflector. This can be done by exploiting the properties of various mathematical concepts but often results in needing to solve large combinatorial problems owing to the increased number of measurements these tools require for efficacy. A low-complexity iterative method is proposed for determining the boundaries in convex polygonal rooms using common tangent planes to sets of ellipsoids. Prior knowledge of the order of echoes is unnecessary and only three RIRs are required, which is one less than the minimum number typically needed to find a unique reflector in 3-D, allowing for simpler common tangent plane estimation and reducing possible echo combinations. Candidate partial rooms are built by checking whether expected second-order echoes appear in the RIRs, adding a reflector at each iterate until a room is found. The proposed method is validated by means of computer simulations.