IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v119y2016icp128-141.html
   My bibliography  Save this article

A unified square-root approach for the score and Fisher information matrix computation in linear dynamic systems

Author

Listed:
  • Kulikova, M.V.
  • Tsyganova, J.V.

Abstract

One of the most frequently encountered problems in practice is to combine a priori knowledge about a physical system with experimental data to provide on-line estimation of an unknown dynamic state and system parameters. The classical way for solving this problem is to use adaptive filtering techniques. The adaptive schemes for the maximum likelihood estimation based on gradient-based optimization methods are, in general, preferable. They require the likelihood function and its gradient evaluation (score), and might demand the Fisher information matrix (FIM) computation. All techniques for the score and the FIM calculation in linear dynamic systems yield the implementation of the Kalman filter (KF) and its derivatives (with respect to unknown system parameters), which is known to be numerically unstable. An alternative solution can be found among algorithms developed in the KF community for solving ill conditioned problems: the square-root algorithms, the UD-based factorization methods and the fast SR Chandrasekhar–Kailath–Morf–Sidhu techniques. Recently, these advanced KF implementations have been extended on the filter derivatives computation. However there is no systematic way of designing the robust “differentiated” methods. In this paper, we develop a unified square-root methodology of generating the computational techniques for the filter/smoother derivatives evaluation required in gradient-based adaptive schemes for the score and the FIM computation.

Suggested Citation

  • Kulikova, M.V. & Tsyganova, J.V., 2016. "A unified square-root approach for the score and Fisher information matrix computation in linear dynamic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 128-141.
  • Handle: RePEc:eee:matcom:v:119:y:2016:i:c:p:128-141
    DOI: 10.1016/j.matcom.2015.07.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475415001561
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2015.07.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kulikova, M.V., 2009. "Maximum likelihood estimation via the extended covariance and combined square-root filters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1641-1657.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Raillon, L. & Ghiaus, C., 2018. "An efficient Bayesian experimental calibration of dynamic thermal models," Energy, Elsevier, vol. 152(C), pages 818-833.

    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.

      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:eee:matcom:v:119:y:2016:i:c:p:128-141. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

      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.