An EM-Algorithm for Band-Toeplitz Covariance Matrix Estimation

Toeplitz covariance matrix estimation has many uses in statistical signal processing due to the stationarity assumption of many signals. For some applications, further constraints may exist on the maximum lag at which the correlation function is non-zero and thereby giving rise to a band-Toeplitz covariance matrix. In this paper, an existing EM-algorithm for Toeplitz estimation is generalized to the case of band-Toeplitz estimation. In addition, the Cramer-Rao lower-bound for unbiased band-Toeplitz covariance matrix estimation is derived and through simulations it is shown that the proposed estimator achieves the bound for medium and large sample-sizes.