Direct computation of sound and microphone locations from time-difference-of-arrival data

In this paper we present a novel approach to directly recover the location of both microphones and sound sources from time-difference-of-arrival measurements only. No approximation solution is required for initialization and in the absence of noise our approach is guaranteed to always recover the exact solution. Our approach only requires solving linear equations and matrix factorization. We demonstrate the feasibility of our approach with synthetic data.