Alpha-Stable Modeling of Noise and Robust Time-Delay Estimation in the Presence of Impulsive Noise

A new representation of audio noise signals is proposed, based on symmetric -stable (S S) distributions in order to better model the outliers that exist in real signals. This representation addresses a shortcoming of the Gaussian model, namely, the fact that it is not well suited for describing signals with impulsive behavior. The -stable and Gaussian methods are used to model measured noise signals. It is demonstrated that the -stable distribution, which has heavier tails than the Gaussian distribution, gives a much better approximation to real-world audio signals. The significance of these results is shown by considering the time delay estimation (TDE) problem for source localization in teleimmersion applications. In order to achieve robust sound source localization, a novel time delay estimation approach is proposed. It is based on fractional lower order statistics (FLOS), which mitigate the effects of heavy-tailed noise. An improvement in TDE performance is demonstrated using FLOS that is up to a factor of four better than what can be achieved with second-order statistics.