@TechReport{ it:2008-007,
author = {Torbj{\"o}rn Wigren and Linda Brus},
title = {{MATLAB} Software for Recursive Identification and Scaling
Using a Structured Nonlinear Black-box Model - Revision 4},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Systems and Control},
year = {2008},
number = {2008-007},
month = mar,
note = {Revised version of nr 2007-013. The software package can
be downloaded from
\url{http://www.it.uu.se/research/publications/reports/2008-007/NRISoftwareRev4.zip}.
\textbf{Note} that the software package was updated on
2010-03-16.},
abstract = {This reports is intended as a users manual for a package
of MATLAB scripts and functions, developed for recursive
prediction error identification of nonlinear state space
systems and nonlinear static systems. The core of the
package is an implementation of an output error
identification and scaling algorithm. The algorithm is
based on a continuous time, structured black box state
space model of a nonlinear system. An RPEM algorithm for
recursive identification of nonlinear static systems, that
re-uses the parameterization of the nonlinear ODE model, is
also included in the software package. In this version of
the software an initialization algorithm based on Kalman
filter theory has been added to the package. The purpose of
the initialization algorithm is to find initial parameters
for the prediction error algorithm, and thus reduce the
risk of convergence to local minima for the nonlinear
identification problem. 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 loop. 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
scripts and functions for the setup and execution of the
identification algorithms are somewhat more general than
what is described in the references. There is e.g. support
for automatic re-initiation of the algorithms using the
parameters obtained at the end of a previous identification
run. This allows for multiple runs through a set of data,
something that is useful for data sets that are too short
to allow convergence in a single run. The re-initiation
step also allows the user to modify the degrees of the
polynomial model structure and to specify terms that are to
be excluded from the model. This makes it possible to
iteratively re-fine the estimated model using multiple
runs. The functionality for display of results include
scripts for plotting of data, parameters, prediction
errors, eigenvalues and the condition number of the
Hessian. The estimated model obtained at the end of a run
can be simulated and the model output plotted, alone or
together with the data used for identification. Model
validation is supported by two methods apart from the
display functionality. First, a calculation of the RPEM
loss function can be performed, using parameters obtained
at the end of an identification run. Secondly, the accuracy
as a function of the output signal amplitude can be
assessed.}
}