TIME-DELAY ESTIMATION USING THE CROSS BISPECTRUM

The cross bispectrum phase can be effectively used to estimate the time required for a non-Gaussian signal to propagate between a pair of spatially separated sensors in the presence of highly correlated Gaussian noise. In this paper we present a consistent estimator of the phase of the cross bispectrum, derive the exact distribution of the phase of a complex Gaussian sample bispectrum, and show that in most cases the exact distribution can be approximated by a Gaussian distribution. Using this Gaussian approximation, we derive the variance of the time delay estimate computed from the sample cross bispectrum of a signal in additive correlated noise. These results allow the performance of time delay estimators based on the cross bispectrum phase to be quantified as a function of the sample size, the skewness of the signal, the signal-to-noise ratio (SNR), and the noise correlation.