Abstract
We describe a novel approach, called data driven local coordinates (DDLC), for parametrizing linear systems in state space form, and we analyze some of its properties which are relevant for e.g. maximum likelihood estimation. In addition we describe how this idea can be used for a concentrated likelihood function, obtained by a least squares type concentration step, which gives the so called sls (separable least squares) DDLC approach. Both approaches give favourable results in numerically optimizing the likelihood function in simulation studies.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Deistler M. (2000). System identification — general aspects and structure. In G. Goodwin (ed.), System Identification and Adaptive Control, Springer, London, 3–26. (Festschrift for B.D.O. Anderson).
Hannan E.J., Deistler M. (1988). The statistical theory of linear systems. John Wiley & Sons, New York, 1988.
McKelvey T., Helmersson A. (1997). System identification using an over-parametrized model class — improving the optimization algorithm. In Proc.36th IEEE Conference on Decision and Control, San Diego, California, USA 3, 2984–2989.
McKelvey T., Helmersson A., Ribarits T. (2004). Data driven local coordinates for multivariable linear systems and their application to system identification. Forthcoming in Automatica.
Ribarits T. The role of parametrizations in identification of linear dynamic systems. PhD thesis, TU Wien.
Ribarits T., Deistler M. (2003). A new parametrization method for the estimation of state-space models.
Ribarits T., Deistler M., Hanzon B. (2004). An analysis of separable least squares data driven local coordinates for maximum likelihood estimation of linear systems. Submitted to Automatica.
Ribarits T., Deistler M., Hanzon B. (2004). On new parametrization methods for the estimation of state-space models. Forthcoming in Intern. Journal of Adaptive Control and Signal Processing.
Ribarits T., Deistler M., McKelvey T. (2004). An analysis of the parametrization by data driven local coordinates for multivariable linear systems. Automatica 40(5), 789–803.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Deistler, M., Ribarits, T., Hanzon, B. (2004). A Novel Approach to Parametrization and Parameter Estimation in Linear Dynamic Systems. In: Antoch, J. (eds) COMPSTAT 2004 — Proceedings in Computational Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-2656-2_10
Download citation
DOI: https://doi.org/10.1007/978-3-7908-2656-2_10
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1554-2
Online ISBN: 978-3-7908-2656-2
eBook Packages: Springer Book Archive