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