@TechReport{ it:2007-015,
author = {Torbj{\"o}rn Wigren},
title = {{MATLAB} Software for Recursive Identification of Systems
With Output Quantization ~ Revision 1},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Systems and Control},
year = {2007},
number = {2007-015},
month = apr,
note = {The software package can be downloaded from
\url{http://www.it.uu.se/research/publications/reports/2007-015/QRISRev1.zip}}
,
abstract = {This reports is intended as a users manual for a package
of MATLAB scripts and functions, developed for recursive
identification of discrete time nonlinear Wiener systems,
where the static output nonlinearity is a known arbitrary
quantization function, not necessarily monotone. Wiener
systems consist of linear dynamics in cascade with a static
nonlinearity. Hence the systems treated by the software
package can also be described as discrete time linear
systems, where the output is measured after a known
quantization function. The identification algorithms thus
identify the linear dynamics of the Wiener system. The core
of the package is an implementation of 5 recursive SISO
output error identification algorithms. The measurement
noise is assumed to affect the system after quantization.
The identified linear dynamic part of the system is allowed
to be of FIR or IIR type. A key feature of the
identification algorithms is the use of a smooth
approximation of the quantizer, for derivation of an
approximation of the gradient of the algorithm. This is
necessary since the derivative of the quantizer consists of
a set of pulses, in the quantization steps. Using such an
approximation 2 recursive stochastic gradient algorithms
and 3 recursive Gauss-Newton algorithms are obtained. The
algorithms differ by the choice of gradient approximation.
It should be noted that the stochastic gradient algorithms
are primarily suited for (high order) FIR systems ~ they
converge very slowly for IIR systems due to the large
eigenvalue spread of the Hessian that typically results for
IIR 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 with mean residual analysis.}
}