Robust time delay estimation for speech signals using information theory: A comparison study

Abstract

Time delay estimation (TDE) is a fundamental subsystem for a speaker localization and tracking system. Most of the traditional TDE methods are based on second-order statistics (SOS) under Gaussian assumption for the source. This article resolves the TDE problem using two information-theoretic measures, joint entropy and mutual information (MI), which can be considered to indirectly include higher order statistics (HOS). The TDE solutions using the two measures are presented for both Gaussian and Laplacian models. We show that, for stationary signals, the two measures are equivalent for TDE. However, for non-stationary signals (e.g., noisy speech signals), maximizing MI gives more consistent estimate than minimizing joint entropy. Moreover, an existing idea of using modified MI to embed information about reverberation is generalized to the multiple microphones case. From the experimental results for speech signals, this scheme with Gaussian model shows the most robust performance in various noisy and reverberant environments.