A “true” maximum likelihood method for directional wave spectra estimation and matched-field source localization
Arthur B. Baggeroer · The Journal of the Acoustical Society of America · 1990
Most methods of estimating directional spectra involve a step wherein the cross spectral covariance of the signal field over the array elements must be estimated, When the arrays are large and the data sparse, this estimate is singular or poorly conditioned. Several methods of mitigating this, including diagonal loading, eigenvalue thresholding, and subspaces have been traditionally used to circumvent these singularities. The fundamental problem is that an arbitrary covariance matrix has many more degrees of freedom than the data can constrain. A new algorithm is introduced that starts directly from the data to form an estimate of the covariance matrix that is constrained by the wave equation describing the propagation of the directional signals. It is found that a “true” maximum likelihood estimate (not a minimum variance, distortionless filter in the guise of maximum likelihood) can be specified and an iterative algorithm for implementing it can be derived. The results are similar in structure to those derived by Snyder and Miller (Proc. IEEE, July 1987) for estimating power densities by imposing a Toeplitz constraint. The algorithm can be extended to matched-field processing for localizing-independent sources. One of the advantages is that a priori information about the sources can be used in estimating their distribution.