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Simulation Studies

In: Stable and Efficient Cubature-based Filtering in Dynamical Systems

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  • Dominik Ballreich

    (University of Hagen)

Abstract

The efficiency and stability of the AE and Smolyak-AE cubature rules in comparison to the GK and DGKP rules will be investigated by conducting four simulation studies. In the first two studies, five- and seven-dimensional state-space models will be filtered by the nonlinear Kalman filter, which operates analogously to the unscented Kalman filter (Algorithm 3). In the third study, the conditional Kalman filter (Algorithm 5) will be applied. The algorithms of the unscented Kalman filter and the conditional unscented Kalman filter can be easily equipped with arbitrary cubature rules which are suitable for Gaussian integrals. In order to achieve this, only the sections “Definitions” and “Initialization” have to be changed using the change of variables approach for Gaussian integrals described in Sect. 3.2s.8. The modifications are here presented by the example of the unscented Kalman filter algorithm. To make clear that the algorithm is used in connection with different types of cubature rules, its name is changed to “cubature-based Kalman filter algorithm” in the following example.

Suggested Citation

  • Dominik Ballreich, 2017. "Simulation Studies," Springer Books, in: Stable and Efficient Cubature-based Filtering in Dynamical Systems, chapter 0, pages 109-134, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-62130-2_5
    DOI: 10.1007/978-3-319-62130-2_5
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