Interval Kalman filter enhanced by positive definite upper bounds
A method based on the interval Kalman filter for discrete uncertain linear systems is presented. The system under consideration is subject to bounded parameter uncertainties not only in the state and observation matrices, but also in the covariance matrices of Gaussian noises. The gain matrix provid...
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| Published in | IFAC-PapersOnLine Vol. 50; no. 1; pp. 1595 - 1600 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.07.2017
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| Subjects | |
| Online Access | Get full text |
| ISSN | 2405-8963 2405-8963 |
| DOI | 10.1016/j.ifacol.2017.08.315 |
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| Abstract | A method based on the interval Kalman filter for discrete uncertain linear systems is presented. The system under consideration is subject to bounded parameter uncertainties not only in the state and observation matrices, but also in the covariance matrices of Gaussian noises. The gain matrix provided by the filter is optimized to give a minimal upper bound on the state estimation error covariance for all admissible uncertainties. The state estimation is then determined by using interval analysis in order to enclose the set of all possible solutions with respect to the classical Kalman filtering structure. |
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| AbstractList | A method based on the interval Kalman filter for discrete uncertain linear systems is presented. The system under consideration is subject to bounded parameter uncertainties not only in the state and observation matrices, but also in the covariance matrices of Gaussian noises. The gain matrix provided by the filter is optimized to give a minimal upper bound on the state estimation error covariance for all admissible uncertainties. The state estimation is then determined by using interval analysis in order to enclose the set of all possible solutions with respect to the classical Kalman filtering structure. |
| Author | Tran, Tuan Anh Gall, Françoise Le Jauberthie, Carine Travé-Massuyès, Louise |
| Author_xml | – sequence: 1 givenname: Tuan Anh surname: Tran fullname: Tran, Tuan Anh – sequence: 2 givenname: Carine surname: Jauberthie fullname: Jauberthie, Carine – sequence: 3 givenname: Françoise Le surname: Gall fullname: Gall, Françoise Le – sequence: 4 givenname: Louise surname: Travé-Massuyès fullname: Travé-Massuyès, Louise |
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| CitedBy_id | crossref_primary_10_1109_TAC_2023_3268307 crossref_primary_10_1016_j_sigpro_2021_108175 |
| Cites_doi | 10.1115/1.3662552 10.1109/7.570759 10.1109/LSP.2006.873148 10.1115/1.1648308 10.1109/TAC.2011.2174697 10.1016/j.ijhydene.2015.12.071 |
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| Keywords | Interval analysis Uncertain linear systems Gaussian noise Covariance matrices Kalman filter |
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| References | Pukrushpan, Peng, Stefanopoulou (bib0008) 2004; 126 Chen, Wang, Shieh (bib0001) 1997; 33 Moore (bib0006) 1966 Rotondo, Fernandez-Canti, Tornil-Sin, Blesa, Puig (bib0009) 2016; 41 Xiong, Jauberthie, Travé-Massuyès, Le Gall (bib00011) 2013 Kalman (bib0004) 1960 Moore, Kearfott, Cloud (bib0007) 2009 Jaulin, Kieffer, Didrit, Walter (bib0003) 2001 Combastel (bib0002) 2015 Tran, Le Gall, Jauberthie, Travé-Massuyès (bib00010) 2016 Zhe, Zheng (bib00012) 2006; 13 Mohamed, Nahavandi (bib0005) 2012; 57 Moore (10.1016/j.ifacol.2017.08.315_bib0007) 2009 Jaulin (10.1016/j.ifacol.2017.08.315_bib0003) 2001 Chen (10.1016/j.ifacol.2017.08.315_bib0001) 1997; 33 Mohamed (10.1016/j.ifacol.2017.08.315_bib0005) 2012; 57 Combastel (10.1016/j.ifacol.2017.08.315_bib0002) 2015 Rotondo (10.1016/j.ifacol.2017.08.315_bib0009) 2016; 41 Tran (10.1016/j.ifacol.2017.08.315_bib00010) 2016 Pukrushpan (10.1016/j.ifacol.2017.08.315_bib0008) 2004; 126 Kalman (10.1016/j.ifacol.2017.08.315_bib0004) 1960 Xiong (10.1016/j.ifacol.2017.08.315_bib00011) 2013 Zhe (10.1016/j.ifacol.2017.08.315_bib00012) 2006; 13 Moore (10.1016/j.ifacol.2017.08.315_bib0006) 1966 |
| References_xml | – year: 2001 ident: bib0003 publication-title: Applied Interval Analysis, with Examples in Parameter and State Estimation, Robust Control and Robotics – year: 1966 ident: bib0006 publication-title: Interval analysis – volume: 126 start-page: 14 year: 2004 ident: bib0008 article-title: Control-Oriented Modeling and Analysis for Automotive Fuel Cell Systems publication-title: Journal of Dynamic Systems, Measurement, and Control – year: 2015 ident: bib0002 publication-title: Merging Kalman filtering and zonotopic state bounding for robust fault detection under noisy environment. In Proceedings of the 9th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes – year: 2009 ident: bib0007 publication-title: Introduction to Interval Analysis – volume: 57 start-page: 1548 year: 2012 end-page: 1552 ident: bib0005 article-title: Robust finite-horizon Kalman filtering for uncertain discrete-time systems publication-title: IEEE Transactions on Automatic Control – year: 2016 ident: bib00010 publication-title: Two stochastic filters and their interval extensions. In Proceedings of the 4th IFAC International Conference on Intelligent Control and Automation Sciences – start-page: 35 year: 1960 end-page: 45 ident: bib0004 article-title: A new approach to linear filtering and prediction problems publication-title: Transactions of the ASME–Journal of Basic Engineering, 82(Series D) – volume: 13 start-page: 493 year: 2006 end-page: 496 ident: bib00012 article-title: Finite-horizon robust Kalman filtering for uncertain discrete time-varying systems with uncertain-covariance white noises publication-title: IEEE Signal Processing Letters – volume: 41 start-page: 2875 year: 2016 end-page: 2886 ident: bib0009 article-title: Robust fault diagnosis of proton exchange membrane fuel cells using a takagi-sugeno interval observer approach publication-title: International Journal of Hydrogen Energy – year: 2013 ident: bib00011 publication-title: Fault detection using interval Kalman filtering enhanced by constraint propagation. In Proceedings of the 52nd IEEE Annual Conference on Decision and Control (CDC), 490–495 – volume: 33 start-page: 250 year: 1997 end-page: 259 ident: bib0001 article-title: Interval Kalman filtering publication-title: IEEE Transactions on Aerospace and Electronic Systems – start-page: 35 year: 1960 ident: 10.1016/j.ifacol.2017.08.315_bib0004 article-title: A new approach to linear filtering and prediction problems publication-title: Transactions of the ASME–Journal of Basic Engineering, 82(Series D) doi: 10.1115/1.3662552 – year: 1966 ident: 10.1016/j.ifacol.2017.08.315_bib0006 – volume: 33 start-page: 250 issue: 1 year: 1997 ident: 10.1016/j.ifacol.2017.08.315_bib0001 article-title: Interval Kalman filtering publication-title: IEEE Transactions on Aerospace and Electronic Systems doi: 10.1109/7.570759 – year: 2013 ident: 10.1016/j.ifacol.2017.08.315_bib00011 – volume: 13 start-page: 493 issue: 8 year: 2006 ident: 10.1016/j.ifacol.2017.08.315_bib00012 article-title: Finite-horizon robust Kalman filtering for uncertain discrete time-varying systems with uncertain-covariance white noises publication-title: IEEE Signal Processing Letters doi: 10.1109/LSP.2006.873148 – year: 2015 ident: 10.1016/j.ifacol.2017.08.315_bib0002 – year: 2001 ident: 10.1016/j.ifacol.2017.08.315_bib0003 – volume: 126 start-page: 14 issue: 1 year: 2004 ident: 10.1016/j.ifacol.2017.08.315_bib0008 article-title: Control-Oriented Modeling and Analysis for Automotive Fuel Cell Systems publication-title: Journal of Dynamic Systems, Measurement, and Control doi: 10.1115/1.1648308 – year: 2016 ident: 10.1016/j.ifacol.2017.08.315_bib00010 – volume: 57 start-page: 1548 issue: 6 year: 2012 ident: 10.1016/j.ifacol.2017.08.315_bib0005 article-title: Robust finite-horizon Kalman filtering for uncertain discrete-time systems publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2011.2174697 – year: 2009 ident: 10.1016/j.ifacol.2017.08.315_bib0007 – volume: 41 start-page: 2875 issue: 4 year: 2016 ident: 10.1016/j.ifacol.2017.08.315_bib0009 article-title: Robust fault diagnosis of proton exchange membrane fuel cells using a takagi-sugeno interval observer approach publication-title: International Journal of Hydrogen Energy doi: 10.1016/j.ijhydene.2015.12.071 |
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| SubjectTerms | Covariance matrices Gaussian noise Interval analysis Kalman filter Uncertain linear systems |
| Title | Interval Kalman filter enhanced by positive definite upper bounds |
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