Minimum variance spectral estimator fast algorithms based on covariance and modified covariance methods of linear prediction

The usual 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 and a doubly-block-Toeplitz structure in the 2D case. These inverses can be formulated in terms of triangular Toeplitz or block-triangular-Toeplitz matrix products which, when substituted into the MVSE formula, yield fast computational formulations for the 1D and 2D MUSE. This paper extends the class of 1D fast MUSE algorithms to the case of least squares data-only covariance and modified covariance formulations, which involve near-to-Toeplitz matrix inverses that also have special representations as products of triangular Toeplitz matrices. Due to space limitations, a future paper will provide the 1D MVSE versions.