Cross entropy approximation of structured Gaussian covariance matrices

We apply two variations of the principle of minimum cross entropy (the Kullback information measure) to fit parameterized probability density models to observed data densities. For an array beamforming problem with P incident narrowband point sources, N > P sensors, and colored noise, both approaches yield eigenvector fitting methods similar to that of the MUSIC algorithm and of the oblique transformation in factor analysis. Furthermore, the corresponding cross entropies (CE) are related to the MDL model order selection criterion.