The use of fractional lower-order statistics in acoustical environments

Robust time delay estimation is necessary for many microphone array applications. Reverberant echoes and background noise can corrupt the estimates. Typically the signals and noise are modeled as Gaussian random processes and second moment information is used for time delay estimation. However, many signals are impulsive and should be modeled using alpha-stable distributions. Because of this impulsive nature, the second-order moments are theoretically undefined. This paper will review the important characteristics of alpha-stable random processes. Time delays will be found using lower order moments. Finally experimental evidence will show the superiority of lower order moments for TDE in real acoustical environments.