Technical Report 2007-010

MATLAB software for Recursive Identification of Wiener Systems - Revision 2

Torbjörn Wigren

March 2007

This reports is intended as a users manual for a package of MATLAB scripts and functions, developed for recursive prediction error identification of discrete time nonlinear Wiener systems and nonlinear static systems. Wiener systems consist of linear dynamics in cascade with a static nonlinearity. The core of the package is an implementation of 9 recursive SISO output error identification algorithms. Three main cases are treated. The first set of 5 algorithms identify the IIR linear dynamics in cases where the static nonlinearity is known. It is stressed that the nonlinearity is allowed to be non-invertible. The second set of 2 algorithms simultaneously identifies the linear dynamics and the static non-linearity. The nonlinearity is parameterized as a piecewise linear or a piecewise quadratic nonlinear function. The last set of two algorithms exploits the above parameterization of the static nonlinearity for estimation of static nonlinear systems. Arbitrarily colored additive measurement noise is handled by all algorithms. The software can only be run off-line, i.e. no true real time operation is possible. The algorithms are however implemented so that true on-line operation can be obtained by extraction of the main algorithmic loops. The user must then provide the real time environment. The software package contains scripts and functions that allow the user to either input live measurements or to generate test data by simulation. The functionality for display of results include scripts for plotting of data, parameters and prediction errors. Model validation is supported by several methods apart from the display functionality. First, calculation of the RPEM loss function can be performed, using parameters obtained at the end of an identification run. Pole-zero plots can be used to investigate possible overparameterization in the linear dynamic part of the Wiener model. Finally, the static accuracy as a function of the output signal amplitude can be assessed.

Note: The software package was updated to handle FIR systems, revision 3, April 2007. The updated software package and manual can be downloaded from

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