Constant-gain filters for finite shift-rank processes

On-line identification methods for dynamic systems traditionally assume given-order rational models. The class of finite shift-rank processes includes processes with rational models of arbitrary order and, if the observed process is approximated by a finite shift-rank process, the determination of the model order becomes a natural part of the identification procedure. The Fast Cholesky and Extended Levinson algorithms exploit the finite shift-rank structure in order to compute the time-varying coefficients of the growing-order modeling/whitening filters of finite shift-rank processes. The recursions performed by the algorithms suggest that the growing-order filters may also be implemented in a modular fashion where the modules have constant coefficients, thus displaying the structural invariants. Such a modular filtering structure is presented in this paper.