IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i12p1168-d293465.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/12/1168/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/12/1168/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Amirreza Fahim Golestaneh, 2022. "A Closed-Form Parametrization and an Alternative Computational Algorithm for Approximating Slices of Minkowski Sums of Ellipsoids in R 3," Mathematics, MDPI, vol. 11(1), pages 1-21, December.
    2. Liao, Wei & Liang, Taotao & Wei, Xiaohui & Yin, Qiaozhi, 2022. "Probabilistic reach-Avoid problems in nondeterministic systems with time-Varying targets and obstacles," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    3. Zhang, Liang & Feng, Zhiguang & Jiang, Zhengyi & Zhao, Ning & Yang, Yang, 2020. "Improved results on reachable set estimation of singular systems," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    4. Yongchun Jiang & Hongli Yang & Ivan Ganchev Ivanov, 2024. "Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances," Mathematics, MDPI, vol. 12(2), pages 1-10, January.
    5. Nguyen D. That & Phan T. Nam & Q. P. Ha, 2013. "Reachable Set Bounding for Linear Discrete-Time Systems with Delays and Bounded Disturbances," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 96-107, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1168-:d:293465. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.