@TechReport{	  it:2010-022,
  author	= {Torbj{\"o}rn Wigren and Linda Brus and Soma Tayamon},
  title		= {{MATLAB} Software for Recursive Identification and Scaling
		  Using a Structured Nonlinear Black-box Model - Revision 6},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Systems and Control},
  year		= {2010},
  number	= {2010-022},
  month		= sep,
  note		= {Revised version of nr 2010-002. The software package can
		  be downloaded from
		  \url{http://www.it.uu.se/research/publications/reports/2010-022/NRISSoftwareRev6.zip}.}
		  ,
  abstract	= {This report 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 related output error
		  identification and scaling algorithms. The algorithms are
		  based on a continuous time, structured black box state
		  space model of a nonlinear system. Furthermore, to
		  initialize the algorithm an initiation scheme based on
		  Kalman filter theory is included. The purpose of the
		  initialization algorithm is to find initial parameters for
		  the prediction error algorithm, and thus reducing the risk
		  of convergence to local false minima. 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 a new discretization of the continuous time
		  model based on the midpoint integration algorithm is added.
		  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.}
}