A Survey of Observers for Nonlinear Dynamical Systems

  • Wei Kang
  • Arthur J. Krener
  • Mingqing Xiao
  • Liang Xu


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.


Observers and estimation Nonlinear systems Observability 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Wei Kang
    • 1
  • Arthur J. Krener
    • 1
  • Mingqing Xiao
    • 2
  • Liang Xu
    • 3
  1. 1.Department of Applied MathematicsNaval Postgraduate SchoolMontereyUSA
  2. 2.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA
  3. 3.Naval Research LaboratoryMontereyUSA

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