Separable nonlinear least-squares methods for efficient off-lineand on-line modeling of systems using Kautz and Laguerre filters

摘要

Kautz and Laguerre filters are effective linear regression modelsnthat can describe accurately an unknown linear system with a fewernparameters than finite-impulse response (FIR) filters. This is achievednby expanding the transfer functions of the Kautz and Laguerre filtersnaround some a priori knowledge, concerning the dominating time constantsnor resonant modes of the system to be identified. When the estimation ofnthese filters is based on a minimization of the least-squares errorncriterion, the minimization problem becomes separable with respect tonthe linear coefficients. Therefore, the original unseparated problem cannbe reduced to a separated problem in only the nonlinear poles, which isnnumerically better conditioned than the original unseparated one. Thisnpaper proposed batch and recursive algorithms that are derived usingnthis separable nonlinear least-squares method, for the estimation of thencoefficients and poles of Kautz and Laguerre filters. They have similarncomputational loads, but better convergence properties than theirncorresponding algorithms that solve the unseparated problem. Thenperformance of the suggested algorithms is compared to alternative batchnand recursive algorithms in some system identification examples.nGenerally, it is shown that the proposed batch and recursive algorithmsnhave better convergence properties than the alternatives