Separable nonlinear least-squares methods for efficient adaptation of Kautz filters in identifying dynamic systems

Kautz (1954) filters are effective filters that can describe accurately an unknown dynamic system with fewer parameters than that required by FIR filters. When the estimation of Kautz filters is based on a minimization of the least-squares error criterion, the minimization problem becomes separable with respect to their linear coefficients. Therefore, the original nonlinear problem can be reduced to a problem only in the nonlinear poles. The proposed recursive algorithms are derived using such separable nonlinear least-squares method. In an echo cancellation example, the proposed algorithms are shown to have similar computational loads, but better convergence properties than those that result from the original unseparated problem.