Affine Structure from Sound

Abstract

We consider the problem of localizing a set of microphones together with a set of external acoustic events (e.g., hand claps), emitted at un- known times and unknown locations. We propose a solution that ap- proximates this problem under a far field approximation defined in the calculus of affine geometry, and that relies on singular value decompo- sition (SVD) to recover the affine structure of the problem. We then define low-dimensional optimization techniques for embedding the solu- tion into Euclidean geometry, and further techniques for recovering the locations and emission times of the acoustic events. The approach is use- ful for the calibration of ad-hoc microphone arrays and sensor networks.