Locally robust identification of linear systems containing unknown gain elements with application to adapted IIR lattice models,

A h d W e consider the identification of stable linear systems whose unknom parameters may be interpreted as feedback gains. By using the output e m r between the true system and a model of it containing adjustable parameters. we develop a recursive algorithm for estimating the unknown parameten. We describe a persistency of excitation wndition on the system input which guarantees a robust, local convergence propeny for the algorithm. We then apply our results to the identification of the pa rmeten of a tapped lattice model of a linear, infinite-impuise response (IIR) plant. Considering the identification o i a lattice. rather than a direct form. model of a linear system is attractive due to (i) the simplicity of its crucial stability check and maintenance procedure for the adapted IIR parametrization and (ii) the numerical insensitivity propemes of the lattice structure. Reproducible simulation evidence is presented that suppons our results.