Robust maximum-likelihood estimation of structured covariance matrices

In many situations some information about the structure of the covariance matrix of a random process is known beyond the fact that it is symmetric and positive definite; for instance, the matrix is frequently Toeplitz. Many people have considered the structured covariance matrix estimation problem for Gaussian processes. However, in actual practice, random signals are seldom, if ever, Gaussian. By using a generalization to processes with known non-Gaussian densities, the authors demonstrate how to find the maximum-likelihood estimate of complex Toeplitz covariance matrices and then evaluate the use of this estimate in some passive array beamforming algorithms. There is substantial improvement in the performance of these bearing estimation algorithms when the authors' estimate is used, especially when non-Gaussian noise is present.<
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