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Adaptive and robust experimental design for linear dynamical models using Kalman filter

Author

Listed:
  • Arno Strouwen

    (KU Leuven)

  • Bart M. Nicolaï

    (KU Leuven)

  • Peter Goos

    (KU Leuven
    University of Antwerp)

Abstract

Current experimental design techniques for dynamical systems often only incorporate measurement noise, while dynamical systems also involve process noise. To construct experimental designs we need to quantify their information content. The Fisher information matrix is a popular tool to do so. Calculating the Fisher information matrix for linear dynamical systems with both process and measurement noise involves estimating the uncertain dynamical states using a Kalman filter. The Fisher information matrix, however, depends on the true but unknown model parameters. In this paper we combine two methods to solve this issue and develop a robust experimental design methodology. First, Bayesian experimental design averages the Fisher information matrix over a prior distribution of possible model parameter values. Second, adaptive experimental design allows for this information to be updated as measurements are being gathered. This updated information is then used to adapt the remainder of the design.

Suggested Citation

  • Arno Strouwen & Bart M. Nicolaï & Peter Goos, 2023. "Adaptive and robust experimental design for linear dynamical models using Kalman filter," Statistical Papers, Springer, vol. 64(4), pages 1209-1231, August.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:4:d:10.1007_s00362-023-01438-9
    DOI: 10.1007/s00362-023-01438-9
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    References listed on IDEAS

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    1. Elizabeth G. Ryan & Christopher C. Drovandi & James M. McGree & Anthony N. Pettitt, 2016. "A Review of Modern Computational Algorithms for Bayesian Optimal Design," International Statistical Review, International Statistical Institute, vol. 84(1), pages 128-154, April.
    2. Jian He & Asma Khedher & Peter Spreij, 2021. "A Kalman particle filter for online parameter estimation with applications to affine models," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 353-403, July.
    3. Cavanaugh, Joseph E. & Shumway, Robert H., 1996. "On computing the expected Fisher information matrix for state-space model parameters," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 347-355, March.
    4. Rong Chen & Jun S. Liu, 2000. "Mixture Kalman filters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 493-508.
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    Cited by:

    1. Andrea Beccarini, 2024. "Testing omitted variables in VARs," Statistical Papers, Springer, vol. 65(5), pages 3093-3109, July.

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