A. Abdallah and . Gning, Filtrage ensembliste multi-hypothèse sur des données intervalles: Application à la localisation, XXI e Colloque GRETSI: Traitement du signal et des images, 2007.

. Abellán, Upper entropy of credal sets. Applications to credal classification, International Journal of Approximate Reasoning, vol.39, issue.2-3, pp.235-255, 2005.
DOI : 10.1016/j.ijar.2004.10.001

D. Adrot, J. Maquin, and . Ragot, Diagnosis of an uncertain static system, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), pp.4150-4155, 2000.
DOI : 10.1109/CDC.2000.912366

URL : https://hal.archives-ouvertes.fr/hal-00201416

H. Adrot, D. Janati-idrissi, and . Maquin, FAULT DETECTION BASED ON INTERVAL ANALYSIS, 15th Triennial World Congress, p.106, 2002.
DOI : 10.3182/20020721-6-ES-1901.00762

URL : https://hal.archives-ouvertes.fr/hal-00278211

S. Adrot, J. Ploix, and . Ragot, Caractérisation des incertitudes dans un modèle linéaire statique, Journal Européen des Systèmes Automatisés, vol.36, issue.6, pp.799-824, 2002.

J. Adrot and . Flaus, Fault detection based on uncertain models with bounded parameters and bounded parameter variations, Proceedings of the 17th IFAC World Congress, pp.7338-7343, 2008.
DOI : 10.3182/20080706-5-KR-1001.01241

URL : https://hal.archives-ouvertes.fr/hal-00373009

J. Alamo, E. Bravo, and . Camacho, Guaranteed state estimation by zonotopes, Proceedings of the 42nd IEEE Conference of Decision and Control, pp.5831-5836, 2003.
DOI : 10.1016/j.automatica.2004.12.008

URL : https://hal.archives-ouvertes.fr/hal-00708563

A. Alhaj-dibo, D. Maquin, and J. Ragot, Data validation of uncertain dynamic systems, 15th International Workshop on Principles of Diagnosis, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00151301

. Alvarez, A Monte Carlo-based method for the estimation of lower and upper probabilities of events using infinite random sets of indexable type, Fuzzy Sets and Systems, vol.160, issue.3, pp.384-401, 2009.
DOI : 10.1016/j.fss.2008.08.006

A. Andrieu, S. Doucet, and . Singh, Particle Methods for Change Detection, System Identification, and Control, Proceedings of the IEEE, pp.423-438, 2004.
DOI : 10.1109/JPROC.2003.823142

. Ashokaraj, P. Tsourdos, B. Silson, and . White, Sensor based robot localisation and navigation: using interval analysis and unscented Kalman filter, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566), pp.1086-1093, 2005.
DOI : 10.1109/IROS.2004.1389321

]. Batarseh and Y. Wang, Reliable simulation with input uncertainties using an interval-based approach, 2008 Winter Simulation Conference, pp.344-352, 2008.
DOI : 10.1109/WSC.2008.4736087

L. Bayoudh and . Trave-massuyes, Diagnosability analysis of hybrid systems casted in a discrete-event framework. Discrete Event Dynamic Systems Theory and Applications, pp.1-27, 2011.

. Bellman, On the identification of systems and some related questions, Conference on Applications of Numerical Analysis, pp.1-8, 1971.
DOI : 10.1090/S0025-5718-1970-0275668-2

L. Benazera and . Trave-massuyes, A diagnosis driven self-reconfigurable filter, 18th International Workshop on Principles of Diagnosis, DX'07, pp.21-28, 2007.

J. Bernard and . Gouzé, Closed loop observers bundle for uncertain biotechnological models, Journal of Process Control, vol.14, issue.7, pp.765-774, 2004.
DOI : 10.1016/j.jprocont.2003.12.006

URL : https://hal.archives-ouvertes.fr/inria-00071676

A. Blanchard, C. Sandu, and . Sandu, Parameter Estimation Method using an Extended Kalman Filter, Proceedings of the Joint North America, Asia-Pacific ISTVS Conference and Annual Meeting of Japanese Society for Terramechanics, pp.1-14, 2007.

. Bloch, Incertitude, imprécision et additivité en fusion de données: point de vue historique ( Uncertainty, imprecision and additivity in data fusion: Historical point of view), pp.267-288, 1996.

J. Bourgain, V. Lindenstrauss, and . Milman, Approximation of zonoids by zonotopes, Acta Mathematica, vol.162, issue.0, pp.73-141, 1989.
DOI : 10.1007/BF02392835

D. Bourij and . Koenig, An original Petri net state estimation by a reduced Luenberger observer, Proceedings of the 1999 American Control Conference, pp.1986-1989, 1999.

]. Bravo, T. Alamo, and E. Camacho, Bounded error identification of systems with time-varying parameters, Atlantis, vol.51, issue.30, pp.1144-1150, 2004.

. Calafiore and . Ghaoui, Ellipsoidal bounds for uncertain linear equations and dynamical systems, Automatica, vol.40, issue.5, pp.773-787, 2004.
DOI : 10.1016/j.automatica.2004.01.001

J. Calderón-espinoza-2007a-]-g-calderón-espinoza, J. Armengol, and . Vehi, Dynamical diagnosis with interval analytical redundancy relations, Journal AI Communications - Model-Based Systems, vol.20, issue.1, pp.39-47, 2007.

J. Calderón-espinoza-2007b-]-g-calderón-espinoza, J. Armengol, E. Vehi, and . Gelso, Dynamic diagnosis based on interval analytical redundancy relations and signs of the symptoms, AI Communications, vol.20, issue.1, pp.39-47, 2007.

L. Canale, M. Fagiano, and . Milanese, Set Membership approximation theory for fast implementation of Model Predictive Control laws, Automatica, vol.45, issue.1, pp.45-54, 2009.
DOI : 10.1016/j.automatica.2008.06.015

L. Chabert, X. Jaulin, and . Lorca, A Constraint on the Number of Distinct Vectors with Application to Localization, 15th International Conference of Principles and Practice of Constraint Programming, pp.196-210, 2009.
DOI : 10.1109/31.34669

URL : https://hal.archives-ouvertes.fr/hal-00428967

E. Chaves and . Sontag, State-estimators for Chemical Reaction Networks of Feinberg-Horn-Jackson Zero Deficiency Type, Proceedings of European Control conference, pp.343-359, 2002.
DOI : 10.3166/ejc.8.343-359

]. Chen, J. Wang, and L. Shieh, Interval Kalman filtering, IEEE Transactions on Aerospace and Electronic Systems, vol.33, issue.1, pp.250-259, 1997.
DOI : 10.1109/7.570759

. Chisci, A. Garulli, G. Vicino, and . Zappa, Block recursive parallelotopic bounding in set membership identification, Automatica, vol.34, issue.1, pp.15-22, 1998.
DOI : 10.1016/S0005-1098(97)00160-X

A. Chow and . Willsky, Analytical redundancy and the design of robust failure detection systems, IEEE Transactions on Automatic Control, vol.29, issue.7, pp.603-614, 1984.
DOI : 10.1109/TAC.1984.1103593

]. Chui, Kalman filtering with real-time applications, 1987.
DOI : 10.1007/978-3-662-02508-6

]. Corliss, Guaranteed error bounds for ordinary differential equations, Theory of Numerics in Ordinary and Partial Differential Equations, pp.1-75, 1994.

]. Cozman, Learning convex sets of probability from data. Rapport technique CMU-RI-TR-97-25, Robotics Institute, 1997.

A. Crisan and . Doucet, A survey of convergence results on particle filtering methods for practitioners, IEEE Transactions on Signal Processing, vol.50, issue.3, pp.736-746, 2002.
DOI : 10.1109/78.984773

D. Csendes and . Ratz, Subdivision Direction Selection in Interval Methods for Global Optimization, SIAM Journal on Numerical Analysis, vol.34, issue.3, pp.922-938, 1997.
DOI : 10.1137/S0036142995281528

. Cuzzolin, Credal Semantics of Bayesian Transformations in Terms of Probability Intervals, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol.40, issue.2, pp.421-432, 2010.
DOI : 10.1109/TSMCB.2009.2025968

A. Desai and . Ray, A fault detection and isolation methodology, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes, pp.1363-1369, 1981.
DOI : 10.1109/CDC.1981.269461

M. Janssen and P. Van-hentenryck, Consistency techniques in ordinary differential equations, Constraints, vol.7, issue.3-4, pp.289-315, 2002.

S. Doucet, C. Godsill, and . Andrieu, On sequential simulation-based methods for Bayesian filtering, 1998.

N. Doucet and . Freitas, Sequential Monte Carlo methods in practice, 2001.
DOI : 10.1007/978-1-4757-3437-9

N. Doucet, V. Gordon, and . Krishnamurthy, Particle filters for state estimation of jump Markov linear systems, IEEE Transactions on Signal Processing, vol.49, issue.3, pp.613-624, 2001.
DOI : 10.1109/78.905890

]. Drakunov, Sliding-mode observers based on equivalent control method, [1992] Proceedings of the 31st IEEE Conference on Decision and Control, pp.2368-2369, 2010.
DOI : 10.1109/CDC.1992.371368

P. Durola and . Danès, Set-membership filtering of uncertain discrete-time rational systems through Recursive Algebraic Representations and LMIs, 2008 47th IEEE Conference on Decision and Control, pp.684-689, 2008.
DOI : 10.1109/CDC.2008.4739433

M. Miranda, Federated filtering for fault tolerant estimation and sensor redundancy management in coupled dynamics distributed systems, Mediterranean Conference on Control and Automation, pp.1-6, 2007.

L. Escobet and . Trave-massuyes, Parameter estimation methods for fault detection and isolation, Proceedings of the 12th International Workshop on Principles of Diagnosis, pp.1-11, 2001.

]. Fairman, Reduced order state estimators for discrete-time stochastic systems, IEEE Transactions on Automatic Control, vol.22, issue.4, pp.673-675, 1977.
DOI : 10.1109/TAC.1977.1101553

H. Faubel, J. Raja, and . Mcdonough, Particle filter based soft-mask estimation for missing feature reconstruction, Proceedings of the 11th International Workshop on Acoustic Echo and Noise Control, 2008.

L. Ferson and . Ginzburg, Whereof one cannot speak: when input distributions are unknown, Risk Analysis, 2002.

X. Frank and . Ding, Survey of robust residual generation and evaluation methods in observer-based fault detection systems, Journal of Process Control, vol.7, issue.6, pp.403-424, 1997.
DOI : 10.1016/S0959-1524(97)00016-4

. Funiak, Multi-modal particle filtering for hybrid systems with autonomous mode transitions, Workshop on Principles of Diagnosis, 2003.

. Gamerman, Markov chain Monte Carlo for dynamic generalised linear models, Biometrika, vol.85, issue.1, pp.215-227, 1998.
DOI : 10.1093/biomet/85.1.215

]. Garcia and P. Frank, Deterministic nonlinear observer-based approaches to fault diagnosis: A survey, Control Engineering Practice, vol.5, issue.5, pp.663-670, 1997.
DOI : 10.1016/S0967-0661(97)00048-8

H. Gardeñes, A. Mielgo, and . Trepat, Modal intervals : Reason and ground semantics, Interval Mathematics, vol.212, pp.27-35, 1986.
DOI : 10.1007/3-540-16437-5_4

A. Garulli, G. Vicino, and . Zappa, Optimal induced-norm and set membership state smoothing and filtering for linear systems with bounded disturbances, Automatica, vol.35, issue.5, pp.767-776, 1999.
DOI : 10.1016/S0005-1098(98)00212-X

E. Gelso, S. Biswas, J. Castillo, and . Armengol, A comparison of two methods for fault detection: a statistical decision, and an interval-based approach, 19th International Workshop on Principles of Diagnosis DX, pp.261-268, 2008.

. Gertler, Fault detection and isolation using parity relations, Control Engineering Practice, vol.5, issue.5, pp.653-661, 1997.
DOI : 10.1016/S0967-0661(97)00047-6

. Gevers, Identification for control, Annual Reviews in Control, vol.20, pp.95-106, 1996.
DOI : 10.1016/S1367-5788(97)00008-4

URL : https://hal.archives-ouvertes.fr/hal-00413370

. Goldsztejn, A Right-Preconditioning Process for the Formal???Algebraic Approach to Inner and Outer Estimation of AE-Solution Sets, Reliable Computing, vol.7, issue.2, pp.443-478, 2005.
DOI : 10.1007/s11155-005-0404-x

. Goldsztejn, A branch and prune algorithm for the approximation of nonlinear AE-solution sets, Proceedings of the ACM symposium on Applied Computing, pp.1650-1654, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00481391

G. Goldsztejn and . Chabert, A Generalized Interval LU Decomposition for the Solution of Interval Linear Systems, Numerical Methods and Applications, pp.312-319, 2007.
DOI : 10.1007/978-3-540-70942-8_37

URL : https://hal.archives-ouvertes.fr/hal-00481290

]. Gordon, D. Salmond, and A. Smith, Novel approach to nonlinear/non-Gaussian Bayesian state estimation, IEE Proceedings F on Radar and Signal Processing, pp.107-113, 1993.
DOI : 10.1049/ip-f-2.1993.0015

]. Gouzé, A. Rapaport, and M. Hadj-sadok, Interval observers for uncertain biological systems, Ecological Modelling, vol.133, issue.1-2, pp.45-56, 2000.
DOI : 10.1016/S0304-3800(00)00279-9

A. Grewal and . Andrews, Kalman filtering: theory and practice using MATLAB, 2001.
DOI : 10.1002/9781118984987

. Guitton, Démonstration de la formule +? ?? exp(?x 2 )dx = ? ?, Nouvelles annales de mathématiques, pp.237-239, 1906.

. Hable, A minimum distance estimator in an imprecise probability model ??? Computational aspects and applications, International Journal of Approximate Reasoning, vol.51, issue.9, pp.1114-1128, 2010.
DOI : 10.1016/j.ijar.2010.08.003

]. Hajiyev and F. Caliskan, Fault detection in flight control systems via innovation sequence of Kalman filter, UKACC International Conference on Control, pp.1528-1533, 1998.

]. Hall, Generation, combination and extension of random set approximations to coherent lower and upper probabilities, Reliability Engineering & System Safety, vol.85, issue.1-3, pp.89-101, 2004.
DOI : 10.1016/j.ress.2004.03.005

]. Hanebeck, Recursive nonlinear set-theoretic estimation based on pseudo ellipsoids, Conference Documentation International Conference on Multisensor Fusion and Integration for Intelligent Systems. MFI 2001 (Cat. No.01TH8590), pp.159-164, 2001.
DOI : 10.1109/MFI.2001.1013525

. Hargreaves, Interval analysis in MATLAB. Rapport technique, 2002.

B. He and . Vik, Use of extended interval Kalman filter on integrated GPS/INS system, Proceedings of the 12th International Technical Meeting of the Satellite Division of The Institute of Navigation, pp.1907-1914, 1999.

W. Zhang and . Rogers, Tomographic feature detection and classification using parallelotope bounded error estimation, IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.2849-2852, 1997.

K. Hoehmann, Laser range finder based obstacle tracking by means of a two-dimensional Kalman filter, 2007 International Workshop on Multidimensional (nD) Systems, pp.9-14, 2007.
DOI : 10.1109/NDS.2007.4509534

M. Hofbaur, Hybrid Estimation of Complex Systems, IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), vol.34, issue.5, 2004.
DOI : 10.1109/TSMCB.2004.835009

P. Hou and . Muller, Design of observers for linear systems with unknown inputs, IEEE Transactions on Automatic Control, vol.37, issue.6, pp.871-875, 1992.
DOI : 10.1109/9.256351

H. Hürzeler and . Künsch, Monte Carlo approximations for general statespace models, Journal of Computational and Graphical Statistics, vol.7, issue.2, pp.175-193, 1998.

R. Hutter and . Dearden, The gaussian particle filter for diagnosis of non-linear systems, Proceedings of the 14th International Conference on Principles of Diagnosis, pp.65-70, 2003.

J. Ingimundarson, . Bravo, T. Puig, P. Alamo, and . Guerra, Robust fault detection using zonotope-based set-membership consistency test, International Journal of Adaptive Control and Signal Processing, vol.12, issue.1, pp.311-330, 2009.
DOI : 10.1002/acs.1038

. Isermann, Process fault detection based on modeling and estimation methods???A survey, Automatica, vol.20, issue.4, pp.387-404, 1984.
DOI : 10.1016/0005-1098(84)90098-0

. Isermann, Supervision, fault-detection and fault-diagnosis methods ??? An introduction, Control Engineering Practice, vol.5, issue.5, pp.639-652, 1997.
DOI : 10.1016/S0967-0661(97)00046-4

P. Isermann and . Balle, Trends in the application of model-based fault detection and diagnosis of technical processes, Control Engineering Practice, vol.5, issue.5, pp.709-719, 1997.
DOI : 10.1016/S0967-0661(97)00053-1

. Isermann, Model-based fault-detection and diagnosis ??? status and applications, Annual Reviews in Control, vol.29, issue.1, pp.71-85, 2005.
DOI : 10.1016/j.arcontrol.2004.12.002

. Isermann, Fault-diagnosis systems: An Introduction from Fault Detection to Fault Tolerance, 2006.
DOI : 10.1007/3-540-30368-5

Y. Janssen, P. Deville, and . Hentenryck, Multistep Filtering Operators for Ordinary Differential Equations, Principles and Practice of Constraint Programming, pp.246-260, 1999.
DOI : 10.1007/978-3-540-48085-3_18

P. Janssen, Y. Van-hentenryck, and . Deville, A Constraint Satisfaction Approach for Enclosing Solutions to Parametric Ordinary Differential Equations, SIAM Journal on Numerical Analysis, vol.40, issue.5, pp.1896-1939, 2003.
DOI : 10.1137/S0036142901392316

. Jauberthie, L. Pons, P. Trave-massuyes, and . Goupil, Detection of oscillatory failures by state estimation in a bounded-error context. Rapport technique 09133, LAAS-CNRS, 2009.

E. Jaulin and . Walter, Set inversion via interval analysis for nonlinear bounded-error estimation, Automatica, vol.29, issue.4, pp.1053-1064, 1993.
DOI : 10.1016/0005-1098(93)90106-4

. Jaulin, M. Braems, E. Kieffer, and . Walter, Nonlinear state estimation using forward-backward propagation of intervals in an algorithm. Scientific computing, validated numerics, interval methods, pp.191-204, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00845047

. Jaulin, I. Kieffer, E. Braems, and . Walter, Guaranteed non-linear estimation using constraint propagation on sets, International Journal of Control, vol.32, issue.18, pp.1772-1782, 2001.
DOI : 10.1080/00207170110090642

. Jaulin, O. Kieffer, E. Didrit, and . Walter, Applied interval analysis, 2001.
DOI : 10.1007/978-1-4471-0249-6

URL : https://hal.archives-ouvertes.fr/hal-00845131

. Jaulin, O. Kieffer, E. Didrit, and . Walter, Applied interval analysis: with examples in parameter and state estimation, robust control and robotics. An emerging paradigm, pp.38-41, 2001.
DOI : 10.1007/978-1-4471-0249-6

URL : https://hal.archives-ouvertes.fr/hal-00845131

G. Jaulin and . Chabert, QUIMPER: un langage de programmation pour le calcul ensembliste; Application à l'automatique, 5ème Conférence Internationale Francophone d'Automatique, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00518591

]. Julier and J. Uhlmann, Unscented Filtering and Nonlinear Estimation, Proceedings of the IEEE, pp.401-422, 2004.
DOI : 10.1109/JPROC.2003.823141

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.136.6539

C. Kai, L. Wei, and . Liu, Robust Extended Kalman Filtering for Nonlinear Systems With Stochastic Uncertainties, Part A: Systems and Humans, pp.399-405, 2010.
DOI : 10.1109/TSMCA.2009.2034836

]. Kalman, A New Approach to Linear Filtering and Prediction Problems, Journal of Basic Engineering, vol.82, issue.1, pp.35-45, 1960.
DOI : 10.1115/1.3662552

]. Kamali, L. Longpre, and M. Koshelev, Estimating mean under interval uncertainty and variance constraint, 2011 Annual Meeting of the North American Fuzzy Information Processing Society, pp.1-6, 2011.
DOI : 10.1109/NAFIPS.2011.5752029

C. Karim, M. Jauberthie, and . Combacau, Model-based fault detection method using interval analysis: Application to an aeronautic test bench, 19th International Workshop on Principles of Diagnosis DX, pp.269-273, 2008.

]. Kearfott and V. Kreinovich, Applications of interval computations, 1996.
DOI : 10.1007/978-1-4613-3440-8

J. Kesavan and . Lee, A set based approach to detection and isolation of faults in multivariable systems, Computers & Chemical Engineering, vol.25, issue.7-8, pp.925-940, 2001.
DOI : 10.1016/S0098-1354(00)00315-X

. Kieffer, E. Jaulin, D. Walter, and . Meizel, Guaranteed mobile robot tracking using interval analysis, Proceedings of MISC'99: Workshop on Applications of Interval Analysis to Systems and Control with Special Emphasis on Recent Advances in Modal Interval Analysis, pp.347-360, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00844601

U. Klumpp and . Hanebeck, Bayesian estimation with uncertain parameters of probability density functions, 12th International Conference on Information Fusion, pp.1759-1766, 2009.

D. Kosanam and . Simon, Kalman Filtering with Uncertain Noise Covariances, 2004.

J. Koutsoukos, F. Kurien, and . Zhao, Estimation of Distributed Hybrid Systems Using Particle Filtering Methods, Hybrid Systems: Computation and Control, pp.298-313, 2003.
DOI : 10.1007/3-540-36580-X_23

J. Kreinovich, C. Beck, . Ferregut, G. Sanchez, M. Keller et al., Monte-Carlo-Type Techniques for Processing Interval Uncertainty, and Their Potential Engineering Applications, Reliable Computing, vol.54, issue.6, pp.25-69, 2007.
DOI : 10.1007/s11155-006-9021-6

. Kreinovich, . Longpre, . Starks, J. Xiang, . Beck et al., Interval versions of statistical techniques with applications to environmental analysis, bioinformatics, and privacy in statistical databases, Journal of Computational and Applied Mathematics, vol.199, issue.2, pp.418-423, 2007.
DOI : 10.1016/j.cam.2005.07.041

A. Kreinovich, G. Neumaier, and . Xiang, Towards a combination of interval and ellipsoid uncertainty, Computational Technologies, vol.13, issue.6, pp.5-16, 2009.

H. Kreinovich and . Nguyen, Interval-Valued Fuzzy Control in Space Exploration. Bulletin for Studies and Exchanges on Fuzziness and its AppLications, pp.55-64, 2011.

. Lalami, Generation of set membership tests for fault diagnosis and evaluation of their worst case sensitivit, Zhang Zhang, editeur, Fault Detection, Supervision and Safety of Technical Processes, pp.569-574, 2006.

N. Legland and . Oudjane, Stability and approximation of nonlinear filters in the Hilbert metric, and application to particle filters, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), pp.1585-1590, 2000.
DOI : 10.1109/CDC.2000.912086

A. Lesecq, K. Barraud, and . Dinh, Numerical accurate computations for ellipsoidal state bounding, 11th Mediterranean Conference on Control and Automation, 2003.

. Lhomme, Consistency techniques for numeric CSPs, International Joint Conference on Artificial Intelligence, pp.232-238, 1993.

L. Lhomme, A. Chantrerie, M. Gotlieb, and . Rueher, Boosting the interval narrowing algorithm, Proceedings of the 1996 Joint International Conference and Symposium on Logic Programming, pp.378-392, 1996.

P. Li and V. Kadirkamanathan, Particle filtering based likelihood ratio approach to fault diagnosis in nonlinear stochastic systems, IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, vol.31, issue.3, pp.337-343, 2001.

B. Li, C. C. Li, and J. Si, Interval recursive least-squares filtering with applications to video target tracking, Proceedings of the SPIE: Signal Processing, Sensor Fusion, and Target Recognition XVII, pp.69681-69681, 2008.
DOI : 10.1117/1.2993320

. Ljung, System identification: theory for the user, Upper Saddle River, N.J, 1999.

]. Lou and C. Goh, Design and real-time implementation of a control system for port AGV application, IEEE International Symposium on Computational Intelligence in Robotics and Automation, pp.527-532, 2003.

. Luenberger, Observing the State of a Linear System, IEEE Transactions on Military Electronics, vol.8, issue.2, pp.74-80, 1964.
DOI : 10.1109/TME.1964.4323124

. Luenberger, An introduction to observers, IEEE Transactions on Automatic Control, vol.16, issue.6, pp.596-602, 1971.
DOI : 10.1109/TAC.1971.1099826

. Macalak, Application of Kalman filtering to acoustic sound diagnostic measurement, MECHATRONIKA, 13th International Symposium, pp.84-86, 2010.

]. Makkuni, Residue Generation Techniques for Failure Diagnosis in Linear Systems, 1990.

Z. Maksarov and . Chalabi, Computing bounds on greenhouse energy requirements using bounded error approach, Control Engineering Practice, vol.6, issue.8, pp.947-955, 1998.
DOI : 10.1016/S0967-0661(98)00071-9

. Malti, M. Raissi, F. Thomassin, and . Khemane, Set membership parameter estimation of fractional models based on bounded frequency domain data, Communications in Nonlinear Science and Numerical Simulation, vol.15, issue.4, pp.927-938, 2010.
DOI : 10.1016/j.cnsns.2009.05.005

URL : https://hal.archives-ouvertes.fr/hal-00356886

E. Markov and . Popova, On the solution of linear algebraic equations involving interval coefficients. Iterative Methods, Linear Algebra, II, Imacs Series In Computational And Applied Mathematics, pp.216-225, 1996.

D. Marx, J. Maquin, and . Ragot, State estimation and fault detection of uncertain systems based on an interval approach, 2010 Conference on Control and Fault-Tolerant Systems (SysTol), pp.720-725, 2010.
DOI : 10.1109/SYSTOL.2010.5676036

R. Masreliez and . Martin, Robust bayesian estimation for the linear model and robustifying the Kalman filter, IEEE Transactions on Automatic Control, vol.22, issue.3, pp.361-371, 1977.
DOI : 10.1109/TAC.1977.1101538

]. Mcilraith, Diagnosing hybrid systems: A bayesian model selection approach, Proceedings of the 11th International Workshop on Principles of Diagnosis, pp.140-146, 2000.

G. Milanese and . Belforte, Estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors: Linear families of models and estimators, IEEE Transactions on Automatic Control, vol.27, issue.2, pp.408-414, 1982.
DOI : 10.1109/TAC.1982.1102926

A. Milanese and . Vicino, Optimal estimation theory for dynamic systems with set membership uncertainty, Automatica, vol.27, issue.6, pp.997-1009, 1991.
DOI : 10.1016/0005-1098(91)90134-N

M. Moore, Interval analysis, pp.38-41, 1966.

M. Moore and F. Bierbaum, Methods and Applications of Interval Analysis, SIAM Studies in Applied Mathematics, vol.2, 1979.
DOI : 10.1137/1.9781611970906

]. Morrison and P. Rayner, The application of Volterra series to signal estimation, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing, pp.1481-1484, 1991.
DOI : 10.1109/ICASSP.1991.150725

K. Mosallaei and . Salahshoor, Sensor Fault Detection using Adaptive Modified Extended Kalman Filter Based on Data Fusion Technique, 2008 4th International Conference on Information and Automation for Sustainability, pp.513-518, 2008.
DOI : 10.1109/ICIAFS.2008.4784006

M. Muenchhof, R. Beck, and . Isermann, Fault-tolerant actuators and drives???Structures, fault detection principles and applications, Annual Reviews in Control, vol.33, issue.2, pp.136-148, 2009.
DOI : 10.1016/j.arcontrol.2009.08.002

]. Nandam and P. Sen, A comparative study of a Luenberger observer and adaptive observer-based variable structure speed control system using a self-controlled synchronous motor, IEEE Transactions on Industrial Electronics, vol.37, issue.2, pp.127-132, 1990.
DOI : 10.1109/41.52961

]. Nedialkov, Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation [microform]. National Library of Canada, 1999.

]. Nedialkov, Validated solutions of initial value problems for ordinary differential equations, Applied Mathematics and Computation, vol.105, issue.1, pp.21-68, 1999.
DOI : 10.1016/S0096-3003(98)10083-8

V. Noack, D. Klumpp, and . Brunn, Nonlinear Bayesian estimation with convex sets of probability densities, 11th International Conference on Information Fusion, pp.1-8, 2008.

V. Noack, U. Klumpp, and . Hanebeck, State estimation with sets of densities considering stochastic and systematic errors, 12th International Conference on Information Fusion, pp.1751-1758, 2009.

A. Oppenheim and . Philippe, The particle filters and their applications, Chemometrics and Intelligent Laboratory Systems, vol.91, issue.1, pp.87-93, 2008.
DOI : 10.1016/j.chemolab.2007.09.010

. Pa¸scapa¸sca and . Pa¸scapa¸sca, Formally verified conditions for regularity of interval matrices, Intelligent Computer Mathematics, pp.219-233, 2010.

]. Petersen and A. Savkin, Robust Kalman Filtering For Signals and Systems with Large Uncertainties, 1999.
DOI : 10.1007/978-1-4612-1594-3

O. Ploix, J. Adrot, and . Ragot, Parameter uncertainty computation in static linear models, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), pp.1916-1921, 1999.
DOI : 10.1109/CDC.1999.830916

URL : https://hal.archives-ouvertes.fr/hal-00289534

O. Ploix, J. Adrot, and . Ragot, Bounding approach to the diagnosis of uncertain static systems, 4th Symposium on Fault Detection, Supervision and Safety for Technical Processes, pp.151-156, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00533530

O. Ploix and . Adrot, Parity relations for linear uncertain dynamic systems, Automatica, vol.42, issue.9, pp.1553-1562, 2006.
DOI : 10.1016/j.automatica.2006.04.010

N. Poignet and . Ramdani, Robust Estimation of Parallel Robot with Interval Analysis, 42nd IEEE Conference on Decision and Control, Maui, Hawaii (USA), 2003.
URL : https://hal.archives-ouvertes.fr/lirmm-00269478

N. Poignet, O. Ramdani, and . Vivas, Ellipsoidal estimation of parallel robot dynamic parameters, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453), pp.3300-3305, 2003.
DOI : 10.1109/IROS.2003.1249665

URL : https://hal.archives-ouvertes.fr/lirmm-00269729

C. Pons, L. Jauberthie, P. Trave-massuyes, and . Goupil, Interval analysis based learning for fault model identification. Application to control surfaces oscillatory failures, 19th International Workshop on Principles of Diagnosis, DX'08, 2008.

]. Popova, Algebraic Solutions to a Class of Interval Equations, Journal of Universal Computer Science, vol.4, issue.1, pp.48-67, 1998.

]. Price and G. Cook, Identification/Observation Using an Extended Luenberger Observer, IEEE Transactions on Industrial Electronics, vol.29, issue.4, pp.279-287, 1982.
DOI : 10.1109/TIE.1982.356680

J. Puig, J. Saludes, and . Quevedo, Worst-case simulation of discrete linear timeinvariant interval dynamic systems, Reliable Computing, vol.9, issue.4, pp.251-290, 2003.
DOI : 10.1023/A:1024666428387

W. Ra and I. Whang, Stochastic Robust Kalman Filtering for Linear Time-Varying Systems with a Multiplicative Measurement Noise, Proceedings of the 17th World Congress of the International Federation of Automatic Control, pp.12546-12551, 2008.
DOI : 10.3182/20080706-5-KR-1001.02123

N. Raissi, Y. Ramdani, and . Candau, Set membership state and parameter estimation for systems described by nonlinear differential equations, Automatica, vol.40, issue.10, pp.1771-1777, 2004.
DOI : 10.1016/j.automatica.2004.05.006

. Ramdani, Méthodes ensemblistes pour l'estimation. Habilitation à diriger des recherches, 2005.

P. Ramdani and . Poignet, Robust Dynamic Experimental Identification of Robots With Set Membership Uncertainty, IEEE/ASME Transactions on Mechatronics, vol.10, issue.2, pp.253-256, 2005.
DOI : 10.1109/TMECH.2005.844703

URL : https://hal.archives-ouvertes.fr/lirmm-00105331

. Ramdani, Y. Ra¯-issi, L. Candau, and . Ibos, Complex Interval Constraint Propagation for Non Linear Bounded-Error Parameter Identification, Proceedings of the 44th IEEE Conference on Decision and Control, pp.3590-3595, 2005.
DOI : 10.1109/CDC.2005.1582719

URL : https://hal.archives-ouvertes.fr/hal-00321377

. Ramdani, Computing reachable sets for uncertain nonlinear hybrid systems using interval constraint propagation techniques. Nonlinear Analysis: Hybrid Systems, pp.1-23, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00611996

]. Rami, C. Cheng, and C. Prada, Tight robust interval observers: An LP approach, 2008 47th IEEE Conference on Decision and Control, pp.2967-2972, 2008.
DOI : 10.1109/CDC.2008.4739280

]. Rao, Estimation of Parameters in a Linear Model, The Annals of Statistics, vol.4, issue.6, pp.1023-1037, 1976.
DOI : 10.1214/aos/1176343639

J. Rapaport and . Gouzé, Parallelotopic and practical observers for non-linear uncertain systems, International Journal of Control, vol.76, issue.3, pp.237-251, 2003.
DOI : 10.1109/TAC.1968.1098790

T. Ratz and . Csendes, On the selection of subdivision directions in interval branch-and-bound methods for global optimization, Journal of Global Optimization, vol.4, issue.2, pp.183-207, 1995.
DOI : 10.1007/BF01097060

J. Rauh, E. Minisini, and . Hofer, Verification Techniques for Sensitivity Analysis and Design of Controllers for Nonlinear Dynamic Systems with Uncertainties, International Journal of Applied Mathematics and Computer Science, vol.19, issue.3, pp.425-439, 2009.
DOI : 10.2478/v10006-009-0035-1

J. Reichle, R. Walker, and . Koster, Extended versus Ensemble Kalman Filtering for Land Data Assimilation, Journal of Hydrometeorology, vol.3, issue.6, pp.728-741, 2002.
DOI : 10.1175/1525-7541(2002)003<0728:EVEKFF>2.0.CO;2

C. Ribot, L. Jauberthie, and . Trave-massuyes, State estimation by interval analysis for a nonlinear differential aerospace model, Proceedings of European Control Conference, pp.4839-4844, 2007.

M. Hofbaur and L. Trave-massuyes, Mode set focused hybrid estimation, International Journal of Applied Mathematics and Computer Science, vol.23, issue.1, pp.131-144, 2013.

K. Shamma and . Tu, Set-valued observers and optimal disturbance rejection, IEEE Transactions on Automatic Control, vol.44, issue.2, pp.253-264, 1999.
DOI : 10.1109/9.746252

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.409.8880

. Shevtshenko, Decision support under uncertainties based on robust Bayesian networks in reverse logistics management, International Journal of Computer Applications in Technology, vol.36, issue.3/4, pp.247-258, 2009.
DOI : 10.1504/IJCAT.2009.028047

E. Shi, R. Boukas, and . Agarwal, Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters, IEEE Transactions on Automatic Control, vol.44, issue.8, pp.1592-1597, 1999.

K. Shi, R. Johansson, and . Murray, Kalman filtering with uncertain process and measurement noise covariances with application to state estimation in sensor networks, IEEE Conference on Control Applications, pp.1031-1036, 2007.

C. Simani, R. Fantuzzi, and . Patton, Model-based fault diagnosis in dynamic systems using identification techniques, 2003.
DOI : 10.1007/978-1-4471-3829-7

]. Souto and J. Ishihara, Enhanced robust Kalman predictor for discrete-time systems with uncertain correlated noises, 2008 47th IEEE Conference on Decision and Control, pp.1660-1665, 2008.
DOI : 10.1109/CDC.2008.4739395

. Stancu, P. Puig, J. Cugueró, and . Quevedo, Benchmarking on Approaches to Interval Observation Applied to Robust Fault Detection, Global Optimization and Constraint Satisfaction, pp.171-191, 2005.
DOI : 10.1007/11425076_13

G. Staroswiecki and . Comtet-varga, Analytical redundancy relations for fault detection and isolation in algebraic dynamic systems, Automatica, vol.37, issue.5, pp.687-699, 2001.
DOI : 10.1016/S0005-1098(01)00005-X

. Storvik, Particle filters for state-space models with the presence of unknown static parameters, IEEE Transactions on Signal Processing, vol.50, issue.2, pp.281-289, 2002.
DOI : 10.1109/78.978383

T. Trave-massuyesmassuyes, R. Escobet, S. Pons, and . Tornil, The Ca-En diagnosis system and its automatic modelling method, Computacion y Sistemas Journal, vol.5, issue.120, pp.128-143, 2001.

]. Uwamusi, On the interval hull of solution sets of parametrised nonlinear equations, Scientific Research and Essays, vol.3, issue.9, pp.383-389, 2008.

S. Verma and . Thrun, Variable resolution particle filter, Proceedings of International Joint Conference on Artificial Intelligence, 2003.

G. Verma, R. Gordon, and . Simmons, Particle filters for rover fault diagnosis, IEEE Robotics and Automation Magazine Special Issue on Human Centered Robotics and Dependability, 2004.

. Walley, Statistical reasoning with imprecise probabilities, 1991.
DOI : 10.1007/978-1-4899-3472-7

. Walley, Towards a unified theory of imprecise probability, International Journal of Approximate Reasoning, vol.24, issue.2-3, pp.125-148, 2000.
DOI : 10.1016/S0888-613X(00)00031-1

]. Walster and E. Hansen, Global Optimization Using Interval Analysis, 2004.
DOI : 10.1201/9780203026922

H. Walter and . Piet-lahanier, Estimation of parameter bounds from bounded-error data: a survey, Mathematics and Computers in Simulation, vol.32, issue.5-6, pp.449-468, 1990.
DOI : 10.1016/0378-4754(90)90002-Z

L. Walter and . Pronzato, Identification of parametric models, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00252148

Z. Wang, S. Huang, and . Daley, On the use of adaptive updating rules for actuator and sensor fault diagnosis, Automatica, vol.33, issue.2, pp.217-225, 1997.
DOI : 10.1016/S0005-1098(96)00155-0

B. Wang and . Nnaji, Solving Interval Constraints by Linearization in Computer-Aided Design, Reliable Computing, vol.39, issue.1, pp.211-244, 2007.
DOI : 10.1007/s11155-006-9023-4

. Wang, Imprecise probabilities with a generalized interval form, Third International Workshop on Reliable Engineering Computing (REC), NSF Workshop on Imprecise Probability in Engineering Analysis and Design, 2008.

. Wang, Interpretable Interval Constraint Solvers in Semantic Tolerance Analysis, Computer-Aided Design and Applications, vol.4204, issue.5, p.654, 2008.
DOI : 10.3722/cadaps.2008.654-666

G. Welch and . Bishop, An Introduction to the Kalman Filter Rapport technique TR 95-041, p.12, 2001.

. Willsky, A survey of design methods for failure detection in dynamic systems, Automatica, vol.12, issue.6, pp.601-611, 1976.
DOI : 10.1016/0005-1098(76)90041-8

]. Xie, Y. Soh, and C. Souza, Robust Kalman filtering for uncertain discretetime systems, IEEE Transactions on Automatic Control, vol.39, issue.6, pp.1310-1314, 1994.

]. Xu, D. Erdogmus, and J. Principe, Minimum error entropy Luenberger observer, Proceedings of 2005 American Control Conference, pp.1923-1928, 2005.

S. Xu and . Mannor, A Kalman Filter Design Based on the Performance/Robustness Tradeoff, IEEE Transactions on Automatic Control, vol.54, issue.5, p.1171, 2009.

Y. Xue, . Guo, and X. Zhang, A Bank of Kalman Filters and a Robust Kalman Filter Applied in Fault Diagnosis of Aircraft Engine Sensor/Actuator, Second International Conference on Innovative Computing, Informatio and Control (ICICIC 2007), pp.10-17, 2007.
DOI : 10.1109/ICICIC.2007.3

V. Yager and . Kreinovich, Decision making under interval probabilities, International Journal of Approximate Reasoning, vol.22, issue.3, 1999.
DOI : 10.1016/S0888-613X(99)00028-6

URL : http://doi.org/10.1016/s0888-613x(99)00028-6

]. Yang and Y. Li, Set-membership filtering for systems with sensor saturation, Automatica, vol.45, issue.8, pp.1896-1902, 2009.
DOI : 10.1016/j.automatica.2009.04.011

X. Zhang, A. Heemink, and J. Van-eijkeren, Performance robustness analysis of Kalman filter for linear discrete-time systems under plant and noise uncertainty, International Journal of Systems Science, vol.26, issue.2, pp.257-275, 1995.
DOI : 10.1109/TAC.1980.1102502

Y. Zhu, L. Soh, and . Xie, Robust Kalman filter design, Proceedings of the 39th IEEE Conference on Decision and Control, pp.3813-3818, 2000.

B. Zhu and . Li, Optimal interval estimation fusion based on sensor interval estimates with confidence degrees, Automatica, vol.42, issue.1, pp.101-108, 2006.
DOI : 10.1016/j.automatica.2005.07.008

. Zhuk, Recursive state estimation for noncausal discrete-time descriptor systems under uncertainties. Optimization and Control, 2007.

. Zhuk, Set-membership state estimation framework for uncertain linear differential-algebraic equations, Conference on Differential and Difference Equations and Applications: Differential equations and Topology, 2008.

]. Ziegler, Lectures on Polytopes, 1995.
DOI : 10.1007/978-1-4613-8431-1