Delta Levinson and Schur-type RLS algorithms for adaptive signal processing

In this paper, we develop delta operator based Levinson and Schur type on-line RLS algorithms. Such algorithms have the potential of improved numerical behavior for ill-conditioned input data. These new algorithms are obtained by a unified transformation on the existing q operator based ones. We first show that the conventional lattice structure can be naturally derived when the backward delta operator is used. With this operator, Levinson and Schur algorithms for the stationary stochastic model in q-domain can easily be transformed into the delta domain. Then, same transformation, will be applied to the q-domain on-line Levinson and Schur type RLS algorithms to obtain the delta-domain counterparts. Their normalized versions as well as a systolic array architecture implementing the new delta Schur RLS algorithm are proposed. Extension to the equal length multichannel case is also given. Computer simulations show the expected numerical advantages of the delta-based algorithms for fast-sampled data in real time, over the q-domain ones under finite precision implementation