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Ellipsoidal and Gaussian Kalman Filter Model for Discrete-Time Nonlinear Systems

Author

Listed:
  • Ligang Sun

    (Geodätisches Institut Hannover, Leibniz Universität Hannover, 30167 Hannover, Germany)

  • Hamza Alkhatib

    (Geodätisches Institut Hannover, Leibniz Universität Hannover, 30167 Hannover, Germany)

  • Boris Kargoll

    (Institut für Geoinformation und Vermessung Dessau, Hochschule Anhalt, 06846 Dessau, Germany)

  • Vladik Kreinovich

    (Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA)

  • Ingo Neumann

    (Geodätisches Institut Hannover, Leibniz Universität Hannover, 30167 Hannover, Germany)

Abstract

In this paper, we propose a new technique—called Ellipsoidal and Gaussian Kalman filter—for state estimation of discrete-time nonlinear systems in situations when for some parts of uncertainty, we know the probability distributions, while for other parts of uncertainty, we only know the bounds (but we do not know the corresponding probabilities). Similarly to the usual Kalman filter, our algorithm is iterative: on each iteration, we first predict the state at the next moment of time, and then we use measurement results to correct the corresponding estimates. On each correction step, we solve a convex optimization problem to find the optimal estimate for the system’s state (and the optimal ellipsoid for describing the systems’s uncertainty). Testing our algorithm on several highly nonlinear problems has shown that the new algorithm performs the extended Kalman filter technique better—the state estimation technique usually applied to such nonlinear problems.

Suggested Citation

  • Ligang Sun & Hamza Alkhatib & Boris Kargoll & Vladik Kreinovich & Ingo Neumann, 2019. "Ellipsoidal and Gaussian Kalman Filter Model for Discrete-Time Nonlinear Systems," Mathematics, MDPI, vol. 7(12), pages 1-22, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1168-:d:293465
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    References listed on IDEAS

    as
    1. Hansjorg Kutterer & Ingo Neumann, 2011. "Recursive least-squares estimation in case of interval observation data," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 5(3/4), pages 229-249.
    2. C. Durieu & É. Walter & B. Polyak, 2001. "Multi-Input Multi-Output Ellipsoidal State Bounding," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 273-303, November.
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