Optimal Toeplitzification with a given rank constraint

A novel and appealing method is presented for estimating, from independent vector samples of a complex zero-mean circular Gaussian random process, an N×N covariance matrix R that belongs both to the vector space of Hermitian Toeplitz matrices and to the set of Hermitian matrices for which the minimum eigenvalue has a given multiplicity. The proposed algorithm is shown to yield an efficient estimator of the covariance matrix and thus behaves asymptotically like the maximum-likelihood estimator. It is shown by simulation and comparisons with the MUSIC and ITAM algorithms that the present method yield improvements in the estimation of the locations of multiple sources in passive sonar arrays