Parameter Identification of the Discrete-Time Stochastic Systems with Multiplicative and Additive Noises Using the UD-Based State Sensitivity Evaluation
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/24/4964 |
| _version_ | 1797380141178945536 |
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| author | Andrey Tsyganov Yulia Tsyganova |
| author_facet | Andrey Tsyganov Yulia Tsyganova |
| author_sort | Andrey Tsyganov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T20:34:01Z |
| format | Article |
| id | doaj.art-9ad8e5c7e1b9448681ff445e48ec48e6 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T20:34:01Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9ad8e5c7e1b9448681ff445e48ec48e62023-12-22T14:23:26ZengMDPI AGMathematics2227-73902023-12-011124496410.3390/math11244964Parameter Identification of the Discrete-Time Stochastic Systems with Multiplicative and Additive Noises Using the UD-Based State Sensitivity EvaluationAndrey Tsyganov0Yulia Tsyganova1Department of Mathematics, Physics and Technology Education, Ulyanovsk State University of Education, Ulyanovsk 432071, RussiaDepartment of Mathematics, Information and Aviation Technology, Ulyanovsk State University, Ulyanovsk 432017, RussiaThe 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.https://www.mdpi.com/2227-7390/11/24/4964parameter identificationgradient-based optimizationsensitivity evaluationdiscrete-time linear stochastic systemsmultiplicative and additive noises |
| spellingShingle | Andrey Tsyganov Yulia Tsyganova Parameter Identification of the Discrete-Time Stochastic Systems with Multiplicative and Additive Noises Using the UD-Based State Sensitivity Evaluation Mathematics parameter identification gradient-based optimization sensitivity evaluation discrete-time linear stochastic systems multiplicative and additive noises |
| title | Parameter Identification of the Discrete-Time Stochastic Systems with Multiplicative and Additive Noises Using the UD-Based State Sensitivity Evaluation |
| title_full | Parameter Identification of the Discrete-Time Stochastic Systems with Multiplicative and Additive Noises Using the UD-Based State Sensitivity Evaluation |
| title_fullStr | Parameter Identification of the Discrete-Time Stochastic Systems with Multiplicative and Additive Noises Using the UD-Based State Sensitivity Evaluation |
| title_full_unstemmed | Parameter Identification of the Discrete-Time Stochastic Systems with Multiplicative and Additive Noises Using the UD-Based State Sensitivity Evaluation |
| title_short | Parameter Identification of the Discrete-Time Stochastic Systems with Multiplicative and Additive Noises Using the UD-Based State Sensitivity Evaluation |
| title_sort | parameter identification of the discrete time stochastic systems with multiplicative and additive noises using the ud based state sensitivity evaluation |
| topic | parameter identification gradient-based optimization sensitivity evaluation discrete-time linear stochastic systems multiplicative and additive noises |
| url | https://www.mdpi.com/2227-7390/11/24/4964 |
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