A new least-squares-based minimum variance spectral estimator fast algorithm

The traditional formulation of the minimum variance spectral estimator (MVSE) depends on the inverse of the autocorrelation matrix, which has a Toeplitz structure in the 1D case. A fast computational algorithm exists that exploits this structure. This paper extends the class of fast MVSE algorithms to the case of a least-squares-based data-only formulation linked to the covariance case of linear prediction, which involves a near-to-Toeplitz matrix inverse. We show here that the inverse involves structures that yield fast computational formulations for the least-squares-based MVSE, in which the inverse has a special representation as sums of products of triangular Toeplitz matrices.