SYSTEM IDENTIFICATION TOOL

Version 1.6.1 (R9.3b), last mod. 25-Feb-2008 12:34:15

General Notes

The system identification tool (SIT) for MATLAB^® contains the nonlinear extension of the Kalman filter (unscented Kalman filter). It is a collection of M-files implementing several numerical schemes (state estimation, simultaneous state and parameter estimation) within the framework of state space filtering. Furthermore, a graphical user interface is provided. It includes a comfortable editing environment for the design of the models to be fitted.

Requires Matlab 5.3 or higher.

Usage and Notation

State space models considered here are restricted to the continuous-discrete form:

	d — dt	x	(t)	=	f(x, p, ε),
	y(kΔt)			=	h(x(kΔt)) + η(kΔt),

where

y	- observation vector (i.e. multivariate data point),
x	- state vector,
p	- parameter vector,
η	- observational noise (vector),
ε	- dynamical noise (vector),
kΔt	- discrete sampling time (k=0,1,...),
Δt	- sampling rate.

(Currently, the case of dynamical noise is not implemented yet.)

sit calls the main programme for the system identification. First a data set has to be imported from a file or generated by using a predefined model. Afterwards a model can be fitted. Model quations can be applied within a comfortable euqation editor. Calling the sitdemo gives an imagination of the procedure of system identification.

The input notation for the equation editor corresponds to the Matlab syntax

y(1), y(2), ...	- components of the observation vector,
x(1), x(2), ...	- components of the state vector,
p(1), p(2), ...	- components of the parameter vector,
\eta(1), \eta(2), ...	- components of the observational noise,
\epsilon(1), \epsilon(2), ...	- components of the dynamical noise.

This tool stores the applied data in a native format which is based on a structure array and stored in the Matlab format (MAT). For more information call help sit.

Data stored in another format as MAT or plain ASCII can also be imported.

Estimation results are stored as a MAT-file in the results folder with a sub-prefix _filter or _filter_state and the current time of estimation. It contains a structure L, whose fields contain the data and the parameters of the model system and the estimation. The estimated states and the estimated parameters are in the field XEST.

Sessions and models can be saved and loaded. The extension of these files is EQU. Furthermore, the model equations can be exported to an M-file in order to use the model with standard Matlab ODE solvers. Models given by ODE M-files can be imported into the SIT equation editor, too.

Demos and Examplary Data Set

sitdemo or sitdemo lorenz calls a demo using the Lorenz system with two observations.

sitdemo circuit calls a demo where the fitting of a model to experimental data taken from a circuit in chaotic regime ist shown. As data the circuit.dat is used and for the model this that is contained in the circuit.equ session.

Screenshots

The major control window (top) and the equation editor (bottom).

The estimation progress can be followed online.

References

1. Sitz, A., Schwarz, U., Kurths, J., Voss, H. U.: Estimation of parameters and unobserved components for nonlinear systems from noisy time series, Phys. Rev. E, 66, 2002, 016210, doi:10.1103/PhysRevE.66.016210.

2. Sitz, A., Kurths, J., Voss, H. U.: Identification of nonlinear spatiotemporal systems via partitioned filtering, Phys. Rev. E, 68, 2003, 016202, doi:10.1103/PhysRevE.68.016202.

3. Julier, S. J., Uhlmann, J. K.: A New Extension of the Kalman Filter to Nonlinear Systems, in: The Proceedings of AeroSense: The 11th International Symposium on Aerospace/Defense Sensing, Simulation and Controls, Orlando FL, USA, 1997, SPIE, Multi Sensor Fusion, Tracking and Resource Management II.

4. Timmer, J., Rust, H., Horbelt, W., Voss, H. U.: Parametric, nonparametric and parametric modeling of a chaotic circuit time series, Phys. Lett. A, 274, 2000, 123-134, doi:10.1016/S0375-9601(00)00548-X.

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User Agreement

By downloading the SIT toolbox you agree with the following points:

1. The toolbox is provided without any warranty or conditions of any kind.

2. We assume no responsibility for errors or omissions in the results and interpretations following from application the toolbox.

3. You commit to cite the SIT toolbox in your reports or publications if used.

Copyright

Copyright (c) 2002-2003 Nonlinear Dynamics Group
Potsdam University, Germany
http://www.agnld.uni-potsdam.de
André Sitz, Norbert Marwan, Christian Hoennicke

Author

André Sitz