Time delay estimation for TDOA self-calibration using truncated nuclear norm regularization

Measurements with unknown time delays are common in different applications such as microphone array, radio antenna array calibration, where the sources (e.g. sounds) are transmitted in unknown time instants. In this paper, we present a method for estimating unknown time delays from Time-Difference-of-Arrival (TDOA) measurements. We propose a novel rank constraint on a matrix depending on the measurements and the unknown time delays. The time delays are recovered by solving a truncated nuclear norm minimization problem using alternating direction method of multipliers (ADMM). We show in synthetic experiments that the proposed method recovers the time delays with good accuracy for noisy and missing data.