Internal Variables in the Lattice for Cholesky Factorization. Kalman Filtering, and Model Identification.
Louis L. Scharf, Demeure,C · Defense Technical Information Center (DTIC) · 1984
The Levinson recursions provide an efficient algorithm for factoring the inverse of a Toeplitz correlation matrix R into its upper and lower triangular Cholesky factors. These factors produce a Gram-Schmidt orthogonalization of the underlying time series. The recursions are routinely used to compute reflection coefficients for implementing whitening and predicting filters in lattice form. These are also used to go back and forth between reflection coefficients, order-increasing whiteners, and correlations. One of this document's main purposes is to show how the Levinson recursion for going back and forth between correlations, reflection coefficients, and order-increasing whiteners may be replaced with a dual set of recursions for going back and forth between correlations, reflection coefficients, and order increasing synthesizers.