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Implicit Kalman filtering.

M Skliar1, W F Ramirez

  • 1Department of Chemical and Fuels Engineering, University of Utah, Salt Lake City 84112, USA. Mikhail.Skliar@m.cc.utah.edu

International Journal of Control
|January 1, 1997
PubMed
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A new implicit Kalman filtering algorithm is developed for discrete systems. This method efficiently handles ill-conditioned and descriptor systems, offering computational advantages for sparse systems.

Area of Science:

  • Control Systems Engineering
  • Numerical Analysis
  • Signal Processing

Background:

  • Traditional Kalman filters are designed for explicitly defined systems.
  • Ill-conditioned and descriptor systems pose challenges for standard filtering techniques.
  • Efficient numerical methods are crucial for complex system analysis.

Purpose of the Study:

  • To develop a novel Kalman filtering algorithm for implicitly defined discrete systems.
  • To propose an efficient numerical implementation for the implicit filter.
  • To demonstrate the advantages of the implicit filter over explicit methods.

Main Methods:

  • Development of a new algorithm for implicit Kalman filtering.
  • Proposal of an iterative method to solve the congruence matrix equation (A1)(Px)(AT1) = Py.
Keywords:
NASA Discipline Environmental HealthNon-NASA Center

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  • Analysis of convergence conditions for the iterative method.

    • Main Results:

    • The implicit Kalman filter is applicable to ill-conditioned and descriptor systems.
    • The iterative method provides necessary and sufficient conditions for convergence.
    • For sparse systems, the implicit filter significantly reduces computation time and storage requirements.

    Conclusions:

    • The developed implicit Kalman filter offers a robust and efficient alternative to traditional filters.
    • The proposed numerical scheme is effective for solving the underlying matrix equation.
    • The implicit filter demonstrates superior performance for sparse implicit systems.