It has been known since 1981 at least, that the Levinson (and Shur) algorithm can be applied to a non-stationary process with its associated arbitrary non-Toeplitz covariance matrix. However, in general case this generalized Levinson algorithm involves O(N 3 ) computations, so that there are no particular advantages over the usual methods of Choleski decomposition or of matrix inversion. Therefore, the main attention devoted to a special class of non-stationary processes with covariance matrices that have a finite "displacement rank" (or equivalently "Toeplitz distance"). For this class of non-stationary processes, adaptive lattice filters retained most of their computational and structural advantages. Another type of approximations for an arbitrary Hermitian covariance matrices that is based upon the so-called bandinverse extension, developed by H. Dym and I. Gohberg in Yet, long before these results of H. Dym and I. Gohberg were considered for applications in adaptive processing in [5]
