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A Survey of Observers for Nonlinear Dynamical Systems

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Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. II)

Abstract

The Kalman filter, invented initially for control systems, has been widely used in science and engineering including data assimilation. For the last several decades, the estimation theory for dynamical systems has been actively developed in control theory. In this paper, we survey several observers, including Kalman filters, for nonlinear systems. We also review some fundamental concepts on the observability of systems defined by either differential equations or a numerical model. The hope is that some of these ideas will inspire research that can benefit the area of data assimilation.

This work was supported in part by NRL and AFOSR

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Authors and Affiliations

  1. Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, USA

    Wei Kang & Arthur J. Krener

  2. Department of Mathematics, Southern Illinois University, Carbondale, IL, USA

    Mingqing Xiao

  3. Naval Research Laboratory, Monterey, CA, USA

    Liang Xu

Authors
  1. Wei Kang
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  2. Arthur J. Krener
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  3. Mingqing Xiao
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  4. Liang Xu
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Corresponding author

Correspondence to Wei Kang .

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Editors and Affiliations

  1. , Environmental Science and Engineering, Ewha Womans University, Ewhayeodae-gil, Seodaemun-gu 52, Seoul, 120-750, Korea, Republic of (South Korea)

    Seon Ki Park

  2. Naval Research Laboratory, Grace Hopper Ave. 7, Monterey, 93943-5502, California, USA

    Liang Xu

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Kang, W., Krener, A.J., Xiao, M., Xu, L. (2013). A Survey of Observers for Nonlinear Dynamical Systems. In: Park, S., Xu, L. (eds) Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. II). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35088-7_1

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