SVD approach based on fourth-order cumulants and cross cumulants for time delay estimation

This paper discusses the problem of time delay estimation in spatially correlated colored Gaussian noises. Fourth-order cumulant-based SVD (singular value decomposition) approach is suggested which uses higher-order statistics of measurements. This approach is based on the idea of "comparing the similarities" between the two sensor measurements in higher-order spectrum domains (trispectrum) rather than in the cross-correlation domain One of the fundamental properties of higher-order spectra which will be explored in this paper is the fact that for Gaussian processes only, all polyspectra of order greater than two are identically zero in theory. Thus can suppress the effect of correlated Gaussian noises, and also preserve information of non-Gaussian stationary random processes. Simulations have shown that this approach is effective and accurate to estimate time delay in unknown spatially correlated Gaussian noises. When SNR (signal-to-noise) is -2.5 dB, the parametric trispectrum method suppresses the correlated Gaussian noises even with not longer data length, so improves the resolution. The new approach has two outstanding advantages. One is that it improves performance over generalized cross-correlation methods, including improved the resolution and stability of spectral estimation, guaranteed the parameter identifiability. The other is that it almost needs no preknowledge about colored noises, but suppresses the effect of colored Gaussian noises.