Iterated Toeplitz approximation of covariance matrices

For a signal consisting of p complex exponentials in white noise, it is well known that the true covariance matrix will have the Hermitian Toeplitz structure and that its minimum eigenvalue will have a dimension of M-p (where M is the dimension of the matrix). When the covariance matrix is estimated from such a signal, it will not generally satisfy these constraints. Two algorithms are presented for imposing these constraints on a covariance matrix. It is shown that the second algorithm generalizes easily to the two-dimensional case. Examples are given to demonstrate the improvement that these algorithms offer for the harmonic retrieval problem.<>