@TechReport{ it:2004-004,
author = {Torbj{\"o}rn Wigren},
title = {Recursive Prediction Error Identification of Nonlinear
State Space Models},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Systems and Control},
year = {2004},
number = {2004-004},
month = jan,
abstract = {A recursive prediction error algorithm for identification
of systems described by nonlinear ordinary differential
equation (ODE) models is presented. The model is a MIMO ODE
model, parameterized with coefficients of a multi-variable
polynomial that describes one component of the right hand
side function of the ODE. It is explained why such a
parameterization is a key to obtain a well defined
algorithm, that does not suffer from singularities and
over-parameterization problems. Furthermore, it is proved
that the selected model can also handle systems with more
complicated right hand side structure, by identification of
an input-output equivalent system in the coordinate system
of the selected states. The linear output measurements can
be corrupted by zero mean disturbances that are correlated
between measurements and over time. The disturbance
correlation matrix is estimated on-line and need not be
known beforehand. The algorithm is applied to live data
from a system consisting of two cascaded tanks with free
outlets. It is illustrated that the identification
algorithm is capable of producing a highly accurate
nonlinear model of the system, despite the fact that the
right hand structure of the system has two nontrivial
nonlinear components. A novel technique based on scaling of
the sampling period that significantly improves the
numerical properties of the algorithm is also disclosed.}
}