Higher-order statistics can be used for time delay estimation (TDE) to suppress spatially correlated Gaussian noise, since the higher-order cumulant of Gaussian signal is always zero. However, third-order statistics is invalid for those signals with zero skewness, speech signal as a typical one. In this paper, the fourth-order cumulant (FOC) spectrum is derived, based on which a TDE algorithm that is valid for speech signal and immune to spatially correlated Gaussian noise is proposed. This method can estimate the time delay between two sensor signals or simultaneously estimate the time delays between one sensor signal and other three. In addition, just like generalized cross correlation method, this spectrum domain algorithm is more robust than time domain FOC-based TDE algorithm, especially for speech signal due to its periodicity. Experiments verify the effectiveness of this TDE method for speech signal with spatially correlated Gaussian noise.

Index Terms: time delay estimation, FOC-spectrum, spatially correlated Gaussian noise, speech signal