A High Resolution Multiple Source Localization Based on Generalized Cumulant Structure (GCS) Matrix

This paper considers a high-resolution multiple non-stationary and non-Gaussian source localization algorithm based on the proposed generalized cumulant structure (GCS) matrix that is constructed as a weighted sum of the second and fourth order cumulants of the sensor signals. The weight determines the rank and range space of the GCS matrix, and the range space of the GCS matrix should be same to the range space of the virtual array manifold matrix to estimate the true direction of arrival (DOA)s of the sources. To estimate the weight and the DOAs of sources, a rank constrained optimization problem is formulated. The optimal solution is computationally heavy, and for this reason a suboptimal solution is considered. With the weight set to an arbitrary value, singular value decomposition on the GCS matrix is performed to determine the singular matrix associated with the null space of the virtual array response matrix, and either this singular matrix or the singular matrix obtained using only the second order (SO) statistic is used to obtain the proposed spatial spectrum. Experimental results show that the proposed algorithm performs better than the recently proposed SO cumulant based algorithm for synthetic and real speech data.