Generalized Burg algorithm for beamforming in correlated multipath field

Array beamforming employing nonlinear methods of spectral estimation presents a difficult problem when the spatial field is inhomogeneous, e.g., when correlated multipath is present, and hence, the corresponding cross-spectral (CS) matrix is non-Toeplitz. To overcome this difficulty in the maximum entropy (ME) beamforming, we present a generalization of the Burg algorithm for dealing with a non-Toeplitz CS matrix. The stability and minimum phase properties of the original Burg algorithm are retained. The use of the generalized Burg algorithm for elevation angle estimation is illustrated for the case of a passive sonar field. Statistical properties of the estimator are analyzed using (1) uncorrelated Gaussian noise only, and (2) the direct and specular multipath components of the target signal, embedded in uncorrelated noise and in directional ambient noise.