New forms of Levinson and Schur algorithms

The Levinson and Schur solutions to the adaptive filtering and parameter estimation problem of recursive least squares processing are described. Unnormalized versions of a newly developed Schur RLS adaptive filter are presented. A systolic array of the Schur RL adaptive filter is devised and its performance is illustrated with a typical example. The classical Levinson and Schur algorithms drop out as special cases of the more general Levinson and Schur RLS adaptive filtering algorithms. The recently introduced split Levinson and Schur algorithms, which are obtained by exploiting the symmetry in the Toeplitz-structured extended normal equations, are reviewed.>