Have a personal or library account? Click to login

An interval Kalman filter enhanced by lowering the covariance matrix upper bound

Open Access
|Jul 2021

References

  1. Cayero, J., Rotondo, D., Morcego, B. and Puig, V. (2019). Optimal state observation using quadratic boundedness: Application to UAV disturbance estimation, International Journal of Applied Mathematics and Computer Science 29(1): 99–109, DOI: 10.2478/amcs-2019-0008.10.2478/amcs-2019-0008
  2. Chabir, K., Rhouma, T., Keller, J.Y. and Sauter, D. (2018). State filtering for networked control systems subject to switching disturbances, International Journal of Applied Mathematics and Computer Science 28(3): 473–482, DOI: 10.2478/amcs-2018-0036.10.2478/amcs-2018-0036
  3. Chen, G., Wang, J. and Shieh, L.S. (1997). Interval Kalman filtering, IEEE Transactions on Aerospace and Electronic Systems 33(1): 250–259.10.1109/7.570759
  4. Combastel, C. (2015). Merging Kalman filtering and zonotopic state bounding for robust fault detection under noisy environment, Proceedings of the 9th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, Paris, France, pp. 289–295.
  5. Combastel, C. (2016). An Extended Zonotopic and Gaussian Kalman Filter (EZGKF) merging set-membership and stochastic paradigms: Toward non-linear filtering and fault detection, Annual Reviews in Control 42: 232–243.10.1016/j.arcontrol.2016.07.002
  6. Ingimundarson, A., Manuel Bravo, J., Puig, V., Alamo, T. and Guerra, P. (2009). Robust fault detection using zonotope-based set-membership consistency test, International Journal of Adaptive Control And Signal Processing 23(4): 311–330.10.1002/acs.1038
  7. Jaulin, L., Braems, I., Kieffer, M. and Walter, E. (2001a). Nonlinear state estimation using forward-backward propagation of intervals in an algorithm, in W. Krämer and J.W. von Gudenberg (Eds), Scientific Computing, Validated Numerics, Interval Methods, Springer US, New York, pp. 191–204..10.1007/978-1-4757-6484-0_16
  8. Jaulin, L., Kieffer, M., Didrit, O. and Walter, E. (2001b). Applied Interval Analysis with Examples in Parameter and State Estimation, Robust Control and Robotics, Springer, London.10.1007/978-1-4471-0249-6
  9. Kalman, R.E. (1960). A new approach to linear filtering and prediction problems, Journal of Basic Engineering 82(Series D): 35–45.10.1115/1.3662552
  10. Kieffer, M., Jaulin, L., Walter, E. and Meizel, D. (1999). Guaranteed mobile robot tracking using interval analysis, Proceedings of the Workshop on Application of Interval Analysis to System and Control, Girona, Spain, pp. 347–360.
  11. Lesecq, S., Barraud, A. and Dinh, K. (2003). Numerical accurate computations for ellipsoidal state bounding, Proceedings of the Mediterranean Conference on Control and Automation (MED’03), Rhodes, Greece.
  12. Masreliez, C. andMartin, R. (1977). Robust Bayesian estimation for the linear model and robustifying the Kalman filter, IEEE Transactions on Automatic Control 22(3): 361–371.10.1109/TAC.1977.1101538
  13. Moore, R.E. (1959). Automatic error analysis in digital computation, Technical report LMSD-48421, Lockheed Missiles and Space Co, Palo Alto.
  14. Moore, R.E. (1966). Interval Analysis, Prentice-Hall, Englewood Cliffs.
  15. Moore, R., Kearfott, R. and Cloud, M. (2009). Introduction to Interval Analysis, Society for Industrial and Applied Mathematics, Philadelphia.10.1137/1.9780898717716
  16. Raka, S.-A. and Combastel, C. (2013). Fault detection based on robust adaptive thresholds: A dynamic interval approach, Annual Reviews in Control 37(1): 119–128.10.1016/j.arcontrol.2013.04.001
  17. Ribot, P., Jauberthie, C. and Trave-Massuyés, L. (2007). State estimation by interval analysis for a nonlinear differential aerospace model, Proceedings of the European Control Conference, Kos, Greece, pp. 4839–4844.
  18. Rump, S.M. (1999). INTLAB—INTerval LABoratory, in T. Csendes (Ed.), Developments in Reliable Computing, Kluwer Academic Publishers, Dordrecht, pp. 77–104.10.1007/978-94-017-1247-7_7
  19. Tran, T.A. (2017). Cadre unifié pour la modélisation des incertitudes tatistiques et bornés: application à la détection et isolation de défauts dans les systémes dynamiques incertains par estimation PhD thesis, Université Toulouse 3—Paul Sabatier, Toulouse, www.theses.fr/2017TO U30292.
  20. Tran, T.A., Jauberthie, C., Le Gall, F. and Travé-Massuyès, L. (2017). Interval Kalman filter enhanced by positive definite upper bounds, Proceedings of the 20th IFACWorld Congress, Toulouse, France, pp. 1595–1600.
  21. Tran, T. A., Le Gall, F., Jauberthie, C. and Travé-Massuyès, L. (2016). Two stochastic filters and their interval extensions, Proceedings of the 4th IFAC International Conference on Intelligent Control and Automation Sciences, Reims, France, pp. 49–54.
  22. Welch, G. and Bishop, G. (2001). An introduction to the Kalman filter, SIGGRAPH, Los Angeles, USA, Course 8.
  23. Xiong, J., Jauberthie, C., Travé-Massuyés, L. and Le Gall, F. (2013). Fault detection using interval Kalman filtering enhanced by constraint propagation, Proceedings of the IEEE 52nd Annual Conference on Decision and Control (CDC), Florence, Italy, pp. 490–495.
DOI: https://doi.org/10.34768/amcs-2021-0018 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 259 - 269
Submitted on: Mar 3, 2020
Accepted on: Dec 30, 2020
Published on: Jul 8, 2021
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year

© 2021 Tuan Anh Tran, Carine Jauberthie, Louise Trave-Massuyés, Quoc Hung Lu, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.