Robust Fusion Kalman Estimator of the Multi-Sensor Descriptor System with Multiple Types of Noises and Packet Loss
Under the influence of multiple types of noises, missing measurement, one-step measurement delay and packet loss, the robust Kalman estimation problem is studied for the multi-sensor descriptor system (MSDS) in this paper. Moreover, the established MSDS model describes uncertain-variance noises, mul...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/23/15/6968 |
| _version_ | 1827730773688451072 |
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| author | Jie Zheng Wenxia Cui Sian Sun |
| author_facet | Jie Zheng Wenxia Cui Sian Sun |
| author_sort | Jie Zheng |
| collection | DOAJ |
| description | Under the influence of multiple types of noises, missing measurement, one-step measurement delay and packet loss, the robust Kalman estimation problem is studied for the multi-sensor descriptor system (MSDS) in this paper. Moreover, the established MSDS model describes uncertain-variance noises, multiplicative noises, time delay and packet loss phenomena. Different types of noises and packet loss make it more difficult to build the estimators of MSDS. Firstly, MSDS is transformed to the new system model by applying the singular value decomposition (SVD) method, augmented state and fictitious noise approach. Furthermore, the robust Kalman estimator is constructed for the newly deduced augmented system based on the min-max robust estimation principle and Kalman filter theory. In addition, the given estimator consists of four parts, which are the usual Kalman filter, predictor, smoother and white noise deconvolution estimator. Then, the robust fusion Kalman estimator is obtained for MSDS according to the relation of augmented state and the original system state. Simultaneously, the robustness is demonstrated for the actual Kalman estimator of MSDS by using the mathematical induction method and Lyapunov’s equation. Furthermore, the error variance of the obtained Kalman estimator is guaranteed to the upper bound for all admissible uncertain noise variance. Finally, the simulation example of a circuit system is examined to illustrate the performance and effectiveness of the robust estimators. |
| first_indexed | 2024-03-11T00:16:24Z |
| format | Article |
| id | doaj.art-545087f42359437eb7c22517e1e58e75 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-11T00:16:24Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-545087f42359437eb7c22517e1e58e752023-11-18T23:36:54ZengMDPI AGSensors1424-82202023-08-012315696810.3390/s23156968Robust Fusion Kalman Estimator of the Multi-Sensor Descriptor System with Multiple Types of Noises and Packet LossJie Zheng0Wenxia Cui1Sian Sun2School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, ChinaSchool of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, ChinaSchool of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, ChinaUnder the influence of multiple types of noises, missing measurement, one-step measurement delay and packet loss, the robust Kalman estimation problem is studied for the multi-sensor descriptor system (MSDS) in this paper. Moreover, the established MSDS model describes uncertain-variance noises, multiplicative noises, time delay and packet loss phenomena. Different types of noises and packet loss make it more difficult to build the estimators of MSDS. Firstly, MSDS is transformed to the new system model by applying the singular value decomposition (SVD) method, augmented state and fictitious noise approach. Furthermore, the robust Kalman estimator is constructed for the newly deduced augmented system based on the min-max robust estimation principle and Kalman filter theory. In addition, the given estimator consists of four parts, which are the usual Kalman filter, predictor, smoother and white noise deconvolution estimator. Then, the robust fusion Kalman estimator is obtained for MSDS according to the relation of augmented state and the original system state. Simultaneously, the robustness is demonstrated for the actual Kalman estimator of MSDS by using the mathematical induction method and Lyapunov’s equation. Furthermore, the error variance of the obtained Kalman estimator is guaranteed to the upper bound for all admissible uncertain noise variance. Finally, the simulation example of a circuit system is examined to illustrate the performance and effectiveness of the robust estimators.https://www.mdpi.com/1424-8220/23/15/6968descriptor systemKalman estimatorunified measurement modelmulti-sensormultiplicative noisesuncertain-variance noises |
| spellingShingle | Jie Zheng Wenxia Cui Sian Sun Robust Fusion Kalman Estimator of the Multi-Sensor Descriptor System with Multiple Types of Noises and Packet Loss Sensors descriptor system Kalman estimator unified measurement model multi-sensor multiplicative noises uncertain-variance noises |
| title | Robust Fusion Kalman Estimator of the Multi-Sensor Descriptor System with Multiple Types of Noises and Packet Loss |
| title_full | Robust Fusion Kalman Estimator of the Multi-Sensor Descriptor System with Multiple Types of Noises and Packet Loss |
| title_fullStr | Robust Fusion Kalman Estimator of the Multi-Sensor Descriptor System with Multiple Types of Noises and Packet Loss |
| title_full_unstemmed | Robust Fusion Kalman Estimator of the Multi-Sensor Descriptor System with Multiple Types of Noises and Packet Loss |
| title_short | Robust Fusion Kalman Estimator of the Multi-Sensor Descriptor System with Multiple Types of Noises and Packet Loss |
| title_sort | robust fusion kalman estimator of the multi sensor descriptor system with multiple types of noises and packet loss |
| topic | descriptor system Kalman estimator unified measurement model multi-sensor multiplicative noises uncertain-variance noises |
| url | https://www.mdpi.com/1424-8220/23/15/6968 |
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