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Estimation of Continuous-time Stochastic System Parameters

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Identification of Continuous-time Models from Sampled Data

Part of the book series: Advances in Industrial Control ((AIC))

Abstract

Identification of continuous-time (CT) systems is a fundamental problem that has applications in virtually all disciplines of science. Examples of mathematical models of CT phenomena appear in such diverse areas as biology, economics, physics, and signal processing. A small selection of references are cited below. Models in the economics of renewable resources, e.g., in biology, is discussed in [9]. Sunspot data modelling by means of CT ARMA models is carried out in [39]. Aspects of economic growth models is the topic of [59]. Models for stock-price fluctuations are discussed in [48] and stochastic volatility models of the short-term interest rate can be found in [2]. The use of Ito’s calculus in modern financial theory with applications in financial decision making is presented in [36]. Continuous-time models for the heat dynamics of a building is described in [35]. Modelling of random fatigue crack growth in materials can be found in [50], and models of human head movements appear in [20]. Identification of ship-steering dynamics by means of linear CT models and the maximum likelihood (ML) method is considered in [6]. Numerous other examples of applications of stochastic differential equations (SDEs) can be found in the literature. See, for example, [25, Chapter 7] where various modelling examples, including population dynamics, investment finance, radio-astronomy, biological waste treatment, etc. can be found.

This work was performed during Erik Larsson’s PhD studies at Uppsala University.

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Author information

Authors and Affiliations

  1. Ericsson Research, Stockholm, Sweden

    Erik K. Larsson

  2. Karlstad University, Sweden

    Magnus Mossberg

  3. Uppsala University, Sweden

    Torsten Söderström

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  1. Erik K. Larsson
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  2. Magnus Mossberg
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  1. Faculté des Sciences et Techniques, Centre de Recherche en Automatique de Nancy (CRAN), Nancy-Université CNRS, 54506, Vandoeuvre-les-Nancy, France

    Hugues Garnier PhD

  2. School of Electrical and Computing Engineering, RMIT University, Swanston Street, Melbourne, 3000, Victoria, Australia

    Liuping Wang PhD

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Larsson, E.K., Mossberg, M., Söderström, T. (2008). Estimation of Continuous-time Stochastic System Parameters. In: Garnier, H., Wang, L. (eds) Identification of Continuous-time Models from Sampled Data. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-84800-161-9_2

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  • DOI: https://doi.org/10.1007/978-1-84800-161-9_2

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