SVD-Based Identification of Parameters of the Discrete-Time Stochastic Systems Models with Multiplicative and Additive Noises Using Metaheuristic Optimization

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

Mathematics, 2023, vol. 11, issue 20, 1-13

Abstract: The paper addresses a parameter identification problem for discrete-time stochastic systems models with multiplicative and additive noises. Stochastic systems with additive and multiplicative noises are considered when solving many practical problems related to the processing of measurements information. The purpose of this work is to develop a numerically stable gradient-free instrumental method for solving the parameter identification problems for a class of mathematical models described by discrete-time linear stochastic systems with multiplicative and additive noises on the basis of metaheuristic optimization and singular value decomposition. We construct an identification criterion in the form of the negative log-likelihood function based on the values calculated by the newly proposed SVD-based Kalman-type filtering algorithm, taking into account the multiplicative noises in the equations of the state and measurements. Metaheuristic optimization algorithms such as the GA (genetic algorithm) and SA (simulated annealing) are used to minimize the identification criterion. Numerical experiments confirm the validity of the proposed method and its numerical stability compared with the usage of the conventional Kalman-type filtering algorithm.

Keywords: discrete-time stochastic systems with additive and multiplicative noises; parameter identification; quadratic identification criterion; metaheuristics; Kalman filter; SVD filter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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