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.
Index Terms: high-resolution multiple source localization,
second order cumulant, fourth order cumulant, non-stationary
source, non-Gaussian source and virtual array manifold matrix.