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Parameter Identification of the Discrete-Time Stochastic Systems with Multiplicative and Additive Noises Using the UD-Based State Sensitivity Evaluation

Author

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  • Andrey Tsyganov

    (Department of Mathematics, Physics and Technology Education, Ulyanovsk State University of Education, Ulyanovsk 432071, Russia
    These authors contributed equally to this work.)

  • Yulia Tsyganova

    (Department of Mathematics, Information and Aviation Technology, Ulyanovsk State University, Ulyanovsk 432017, Russia
    These authors contributed equally to this work.)

Abstract

The paper proposes a new method for solving the parameter identification problem for a class of discrete-time linear stochastic systems with multiplicative and additive noises using a numerical gradient-based optimization. The constructed method is based on the application of a covariance UD filter for the above systems and an original method for evaluating state sensitivities within the numerically stable, matrix-orthogonal MWGS transformation. In addition to the numerical stability of the proposed algorithm to machine roundoff errors due to the application of the MWGS-UD orthogonalization procedure at each step, the main advantage of the obtained results is the possibility of analytical calculation of derivatives at a given value of the identified parameter without the need to use finite-difference methods. Numerical experiments demonstrate how the obtained results can be applied to solve the parameter identification problem for the considered stochastic system model.

Suggested Citation

  • Andrey Tsyganov & Yulia Tsyganova, 2023. "Parameter Identification of the Discrete-Time Stochastic Systems with Multiplicative and Additive Noises Using the UD-Based State Sensitivity Evaluation," Mathematics, MDPI, vol. 11(24), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4964-:d:1300573
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    References listed on IDEAS

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    1. Andrey Tsyganov & Yulia Tsyganova, 2023. "SVD-Based Identification of Parameters of the Discrete-Time Stochastic Systems Models with Multiplicative and Additive Noises Using Metaheuristic Optimization," Mathematics, MDPI, vol. 11(20), pages 1-13, October.
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