Optimal parameter estimation of the Laguerre filter via the complex performance function

The adaptation of the optimal Laguerre filter parameters to model the impulse response of an unknown ARMA system is a parametric least squares problem. Unfortunately the squared error (SE) performance function is nonlinear with respect to the feedback parameter and is difficult to solve. We offer a new approach to determine the optimal feedback parameter, also called the time scale. The methodology used here is one of extending the SE performance function to the complex domain. This is done by defining a new complex performance function. We show how this performance function is derived, how it relates to the conventional function, and the additional information it offers. In particular, we observe (experimentally) that for ARMA systems the imaginary component of the new function can be used to obtain a set of values that contains the optimal (in the minimum SE sense) time scale parameter of the Laguerre model.