Af ne Structure From Sound

We consider the problem of localizing a set of microphones together with a set of external acoustic events (e.g., hand claps), emitted at unknown times and unknown locations. We propose a solution that approximates this problem under a far eld approximation de ned in the calculus of af ne geometry, and that relies on singular value decomposition (SVD) to recover the af ne structure of the problem. We then de ne low-dimensional optimization techniques for embedding the solution into Euclidean geometry, and further techniques for recovering the locations and emission times of the acoustic events. The approach is useful for the calibration of ad-hoc microphone arrays and sensor networks.