On time delay estimation with unknown spatially correlated Gaussian noise using fourth-order cumulants and cross cumulants

The problem of estimating the difference in arrival times of a linear non-Gaussian signal at two spatially separated sensors is considered. The signal is assumed to be corrupted by spatially correlated Gaussian noises of unknown cross correlation. A parameter estimation approach is adopted, and the fourth-order cumulant statistics of the noisy measurements are exploited to obtain the time delay estimate. Specific and mild sufficient conditions are given for time delay identifiability via a persistence of excitation condition. Illustrative Monte Carlo simulation examples are also presented