Identification of IIR Wiener systems with spline nonlinearities that have variable knots

• Published in: IEEE transactions on automatic control Vol. 50; no. 10; pp. 1617 - 1622
• Main Authors: Hughes, M.C., Westwick, D.T.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2005; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Automatic control; Block structured models; Computer simulation; Control systems; cubic spline; Levenberg-Marquardt algorithm; Multidimensional systems; nonlinear system identification; Piecewise linear techniques; Recursive estimation; separable least squares optimization; Spline; Stochastic processes; Upper bound
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2005.856660

An algorithm is developed for the identification of Wiener systems, linear dynamic elements followed by static nonlinearities. In this case, the linear element is modeled using a recursive digital filter, while the static nonlinearity is represented by a spline of arbitrary but fixed degree. The primary contribution in this note is the use of variable knot splines, which allow for the use of splines with relatively few knot points, in the context of Wiener system identification. The model output is shown to be nonlinear in the filter parameters and in the knot points, but linear in the remaining spline parameters. Thus, a separable least squares algorithm is used to estimate the model parameters. Monte-Carlo simulations are used to compare the performance of the algorithm identifying models with linear and cubic spline nonlinearities, with a similar technique using polynomial nonlinearities.