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

Andrey Tsyganov () and Yulia Tsyganova
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Andrey Tsyganov: Department of Mathematics, Physics and Technology Education, Ulyanovsk State University of Education, Ulyanovsk 432071, Russia
Yulia Tsyganova: Department of Mathematics, Information and Aviation Technology, Ulyanovsk State University, Ulyanovsk 432017, Russia

Mathematics, 2023, vol. 11, issue 24, 1-11

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.

Keywords: parameter identification; gradient-based optimization; sensitivity evaluation; discrete-time linear stochastic systems; multiplicative and additive noises (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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