A geometric perspective on the Schur algorithm

A time-varying version of the Schur algorithm is developed. The development based on the autoregressive (AR) lattice structure and an orthogonalization procedure different from the one usually associated with the AR lattice. The development lends physical identity to all internal variables of the algorithm, thereby providing insight into some of the properties of the algorithm. It is concluded that the orthogonal decomposition (the key step in the algorithm development) can just as easily be formulated for the autoregressive moving average (ARMA) lattice structure, enabling the development of an ARMA Schur-type algorithm with numerical properties similar to those of the standard AR Schur algorithm