Locally Robust Identification of Linear Systems Containing Unknown Gain Elements with Application to Adapted IIR Lattice Models

We consider the identification of stable linear systems whose unknown parameters may be interpreted as feedback gains. By using the output error between the true system and a model of it containing adjustable parameters, we develop a recursive algorithm for estimating the unknown parameters. We describe a persistency of excitation condition on the system input which guarantees a robust, local convergence property for the algorithm. We then apply our results to the identification of the parameters of a tapped lattice model of a linear, infinite-impulse response (IIR) plant. Considering the identification of 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 properties of the lattice structure. Reproducible simulation evidence is presented that supports our results.