Improved state estimator for linear-Gaussian systems subject to initialization errors
This paper proposes an improved state estimator for linear-Gaussian systems subject to initialization errors. A one-step prediction function depicted by the Student-t is reconstructed artificially by inserting an auxiliary variable into the original Gaussian distribution. The variational Bayesian (V...
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| Published in: | Chemometrics and intelligent laboratory systems Vol. 227; p. 104608 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
15.08.2022
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| ISSN: | 0169-7439, 1873-3239 |
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| Abstract | This paper proposes an improved state estimator for linear-Gaussian systems subject to initialization errors. A one-step prediction function depicted by the Student-t is reconstructed artificially by inserting an auxiliary variable into the original Gaussian distribution. The variational Bayesian (VB) technique is then employed to obtain the approximated posterior joint distribution of the additional variable and the state. A fixed-point iteration is used for recursions to calculate the necessary moments of state with the updated distribution of the auxiliary variable. Simulation and experiment verify the performance of the proposed algorithm. It shows that the proposed method yields significant improvements over the existing initialization approaches, such as the practical Kalman filter (KF) and the recently-developed Bayesian initialization algorithm.
•We propose to model one-step predicted function as the Student-t distribution to reduce the negative effects of the uncertain initializers.•By constructing the extended state-space model, we make use of the batch form of Kalman filter to analyze how the initial state affects the current state estimate and how the proposed scheme compensates for the initialization errors.•We reveal the essence of the compensating factor on the current state estimate. |
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| AbstractList | This paper proposes an improved state estimator for linear-Gaussian systems subject to initialization errors. A one-step prediction function depicted by the Student-t is reconstructed artificially by inserting an auxiliary variable into the original Gaussian distribution. The variational Bayesian (VB) technique is then employed to obtain the approximated posterior joint distribution of the additional variable and the state. A fixed-point iteration is used for recursions to calculate the necessary moments of state with the updated distribution of the auxiliary variable. Simulation and experiment verify the performance of the proposed algorithm. It shows that the proposed method yields significant improvements over the existing initialization approaches, such as the practical Kalman filter (KF) and the recently-developed Bayesian initialization algorithm.
•We propose to model one-step predicted function as the Student-t distribution to reduce the negative effects of the uncertain initializers.•By constructing the extended state-space model, we make use of the batch form of Kalman filter to analyze how the initial state affects the current state estimate and how the proposed scheme compensates for the initialization errors.•We reveal the essence of the compensating factor on the current state estimate. |
| ArticleNumber | 104608 |
| Author | Zhao, Shunyi Liu, Fei Zhang, Tianyu Luan, Xiaoli |
| Author_xml | – sequence: 1 givenname: Tianyu surname: Zhang fullname: Zhang, Tianyu – sequence: 2 givenname: Shunyi surname: Zhao fullname: Zhao, Shunyi email: shunyi.s.y@gmail.com – sequence: 3 givenname: Xiaoli surname: Luan fullname: Luan, Xiaoli – sequence: 4 givenname: Fei surname: Liu fullname: Liu, Fei |
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| Cites_doi | 10.1021/ie5023282 10.1109/7.106121 10.1016/j.automatica.2020.109184 10.1109/TAC.2016.2557999 10.1016/0009-2509(92)80270-M 10.1109/TAC.2020.2995674 10.1109/TII.2021.3057421 10.1016/j.chemolab.2021.104403 10.1109/TIT.2014.2320500 10.1109/TAC.2008.2008348 10.1109/9.989082 10.1109/TAES.2017.2651684 10.1002/rnc.1366 10.1016/j.jprocont.2009.03.006 10.1109/TII.2019.2924421 10.1109/TSP.2008.928969 10.1016/0005-1098(87)90026-4 10.1016/j.jprocont.2021.07.005 10.1016/S0005-1098(97)00188-X 10.1109/TASE.2019.2915286 |
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| Keywords | Variational Bayesian approximation Student-t distribution Linear Gaussian systems State estimation Initialization strategy |
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