. Dans-le-cas-statique, algorithme DiagES permet de détecter, localiser des défauts sur une des 6 mesures AM. Nous avons montré également que l'étape d'identication pouvait être résolue. Dans la table de signature, le symbole signie que la mesure fautive est prise en compte dans le sous-ensemble de mesures lors de l'estimation de l'attitude

. Dans-le-cas-dynamique, algorithme DiagED appliqué à un modèle dynamique nonlinéaire , permet de détecter et localiser des défauts sur une des 9 mesures AGM. Il a été montré que l'algorithme DiagED permet de détecter (rapidement) un défaut mais présente un retard certain

]. F. Bibliographie1, A. Abdallah, P. Gning, and . Bonnifait, Adapting particle lter on interval data for dynamic state estimation, IEEE International Conference on Acoustics, Speech and Signal Processing, 2007.

F. Abdallah, A. Gning, and P. Bonnifait, Box particle filtering for nonlinear state estimation using interval analysis, Automatica, vol.44, issue.3, pp.807-815, 2008.
DOI : 10.1016/j.automatica.2007.07.024

O. Adrot, H. Janati-idrissi, and D. Maquin, FAULT DETECTION BASED ON INTERVAL ANALYSIS, 15th IFAC World Congress on Automatic Control, 2002.
DOI : 10.3182/20020721-6-ES-1901.00762

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

A. Gning, F. Abdallah, and P. Bonnifait, Dynamic vehicle localisation using constraints propagation techniques on intervals a comparison with kalman ltering

A. Gning and P. Bonnifait, Guaranteed dynamic localizaton using constraints propagation techniques on real intervals, Proceedings of the 2004 international conference on Robotics and Automation, 2004.

J. Armengol, J. Vehi, L. Travé-massuyès, and M. A. Sainz, Interval model-based fault detection using multiple sliding time windows, 4th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes, 2000.

M. Basseville, Detecting changes in signals and systems???A survey, Automatica, vol.24, issue.3, pp.309-326, 1988.
DOI : 10.1016/0005-1098(88)90073-8

M. Basseville and I. Nikiforov, Detection of abrupt changes-Theory and applications

B. B. Salmeron-quiro, Fusion de Données multi-capteurs pour la capture de mouvement, 2007.

B. Cédric, Diagnostic des systèmes embarqués en réseau. Application à mini drone hélicoptère, 2009.

B. Bede and L. Stefanini, Numerical solution of interval dierential equations with generalized hukuhara dierentiability, Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, 2009.

F. Benhamou, F. Goualard, L. Granvilliers, and J. Puget, Revising hull and box consistency, Proceedings of the 16th International Conference on Logic Programming, 1999.

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

J. Chen and R. J. Patton, Robust Model Based Fault Diagnosis for Dynamic Systems, 1999.
DOI : 10.1007/978-1-4615-5149-2

J. C. Chou, Quaternion kinematic and dynamic differential equations, IEEE Transactions on Robotics and Automation, vol.8, issue.1, pp.53-64, 1992.
DOI : 10.1109/70.127239

J. G. Cleary, Logical arithmetic, Future Computing Systems, vol.2, pp.125-149, 1987.

E. Hansen, AN OVERVIEW OF GLOBAL OPTIMIZATION USING INTERVAL ANALYSIS, 1992.
DOI : 10.1016/B978-0-12-505630-4.50021-3

T. I. Fossen, Guidance and control of ocean vehicles, 1994.

P. M. Frank and S. X. Ding, Survey of robust residual generation and evaluation methods in observer-based faut detection systems, Journal of Process Control, vol.6, pp.403-424, 1997.

J. Gertler, Survey of model-based failure detection and isolation in complex plants, IEEE Control Systems Magazine, vol.8, issue.6, pp.3-11, 1988.
DOI : 10.1109/37.9163

J. 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

A. Gning, Localisation garantie d'automobiles. Contribution aux techniques de satisfaction de contraintes sur les intervalles, 2006.
URL : https://hal.archives-ouvertes.fr/tel-00158375

F. David, D. J. Griths, and . Higham, Numerical Methods for Ordinary Differential Equations, 2010.

J. F. Guerrero-castellanos, Estimation de l'attitude et commande bornée en attitude d'un corps rigide : Application à un mini helicoptère à quatre rotors, 2008.

D. Henry, From fault diagnosis to recovery actions for aeronautic and aerospace missions : a model-based point of view, 23rd IAR Workshop on Advanced Control and Diagnosis, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00358252

G. Heredia, A. Oilero, M. Bejar, and R. Mahtani, Sensor and actuator fault detection in small autonomous helicopters, Mechatronics, vol.18, issue.2, pp.90-99, 2008.
DOI : 10.1016/j.mechatronics.2007.09.007

. Memsense, Mag3 : Triaxial magnetometer, accelerometer & gyroscope analog inertial sensor

I. Braems, Méthodes ensemblistes garanties pour l'estimation de grandeurs physiques, 2002.

I. Braems, N. Ramdani, M. Kieer, and E. Walter, Caract??risation garantie d'un dispositif de mesure de grandeurs thermiques, Journal européen des systèmes automatisés , spécial Outils de calculs ensemblistes, pp.1129-1143, 2003.
DOI : 10.3166/jesa.37.1129-1143

R. 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

R. Isermann, Fault Diagnosis Systems : An introduction from fault detection to fault tolerance, 2006.
DOI : 10.1007/3-540-30368-5

R. Isermann and P. Ballé, 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

L. Jaulin, M. Kieer, O. Didrit, and E. Walter, Appplied Interval Annalysis, 2001.

J. L. Gouzé, A. Rapaport, and M. Z. , 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

J. L. Gouzé, M. Moisan, and O. Bernard, Simple interval observers for biotechnological processes, Proceedings of the ISCCSP 2006 conference, 2006.

R. J. Patto and J. Chen, Observer-based fault detection and isolation: Robustness and applications, Control Engineering Practice, vol.5, issue.5, pp.671-682, 1997.
DOI : 10.1016/S0967-0661(97)00049-X

A. Khosravi, J. A. Llobet, and E. R. Gelso, An Interval Intelligent-based Approach for Fault Detection and Modelling, 2007 IEEE International Fuzzy Systems Conference, 2007.
DOI : 10.1109/FUZZY.2007.4295394

J. Korbicz, J. Ko±cielny, Z. Kowalczuk, and W. Cholewa, Fault diagnosis. Models, Articial Intelligence, Applications, 2004.

K. Reinhard and W. K. Ulrich, Hardware support for interval arithmetic, Reliable Computing, vol.12, p.225237, 2006.

O. Lhomme, Consistency techniques for numeric CSPs, Proceeding of IJCAI 1993, p.232238, 1993.

L. Jaulin, M. Kieer, I. Braems, and E. 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

L. Jaulin and É. Walter, Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis, Mathematics and Computers in Simulation, vol.35, issue.2, pp.123-137, 1993.
DOI : 10.1016/0378-4754(93)90008-I

D. Maquin and J. Ragot, Diagnostic des systèmes linéaires, Hermes, 2000.

F. L. Markley, Attitude determination using vector observations : Theory, Journal of the Astronautical Sciences, vol.37, pp.41-58, 1989.

F. L. Markley, Attitude error representations for kalman ltering, Journal of Guidance , Control, and Dynamics, vol.63, pp.311-317, 2003.

F. L. Markley, J. Crassidis, and Y. Cheng, Nonlinear attitude ltering methods, AIAA Guidance, Navigation, and Control Conference, 2005.

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

M. Kieer and É. Walter, Interval analysis for guaranteed nonlinear parameter and state estimation, Mathematical and Computer Modelling of Dynamical Systems, vol.11, pp.171-181, 2005.

M. R. Napolitano, Y. An, and A. Seanor, A fault tolerant flight control system for sensor and actuator failures using neural networks, Aircraft Design, vol.3, issue.2, pp.103-128, 2000.
DOI : 10.1016/S1369-8869(00)00009-4

M. R. Napolitano, D. A. Windson, and J. L. Casanova, Kalman filters and neural-network schemes for sensor validation in flight control systems, IEEE Transactions on Control Systems Technology, vol.6, issue.5, pp.596-611, 1998.
DOI : 10.1109/87.709495

N. S. Nedialkov, K. R. Jackson, and G. F. Corliss, 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

S. Nedialko and . Nedialkov, Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Dierential Equation, 1999.

H. V. Nguyen, C. Berbra, S. Lesecq, S. Gentil, A. Barraud et al., Diagnosis of an Inertial Measurement Unit based on set membership estimation, 2009 17th Mediterranean Conference on Control and Automation, 2009.
DOI : 10.1109/MED.2009.5164541

URL : https://hal.archives-ouvertes.fr/hal-00373659

N. Meslem, Atteignabilité hybride des systèmes dynamiques continus par analyse par intervalles. Application à l'estimation ensembliste, 2008.

E. P. Oppenheimer, Application of interval analysis techniques to linear systems. II. The interval matrix exponential function, IEEE Transactions on Circuits and Systems, vol.35, issue.10, pp.1230-1242, 1988.
DOI : 10.1109/31.7598

S. A. Raka and C. Combastel, A stable interval observer for fault detection in the context of veried model-based design, Conference on Control and Fault Tolerant Systems, SysTol'10, 2010.

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

A. Rapaport and D. Docha, Interval observers for biochemical processes with uncertain kinetics and inputs, Mathematical Biosciences, vol.193, issue.2, pp.235-253, 2005.
DOI : 10.1016/j.mbs.2004.07.004

URL : https://hal.archives-ouvertes.fr/hal-01019721

A. Rapaport and J. L. 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

D. Ratz, Automatische Ergebnisverikation bei globalen Optimierungsproblemen, 1992.

V. Reppa and A. Tzes, Fault detection and diagnosis relying on set membership identication for time varying systems, Conference on Control and Fault Tolerant Systems, SysTol'10, 2010.

A. L. Satin and R. L. Gates, Evaluation of Parity Equations for Gyro Failure Detection and Isolation, Journal of Guidance, Control, and Dynamics, vol.1, issue.1, pp.14-20, 1978.
DOI : 10.2514/3.55738

J. Michael, E. E. Schulte, and J. Swartzlander, Hardware design and arithmetic algorithms for a variable-precision, interval arithmetic coprocessor, Proceedings of the 12th Symposium on Computer Arithmetic, ARITH '95, 1995.

J. Michael, E. E. Schulte, and J. Swartzlander, A family of variable-precision interval arithmetic processors, IEEE Transactions on Computers, vol.49, pp.387-397, 2000.

M. D. Shuster, A survey of attitude representations, The Journal of the Astronautical Sciences, vol.41, pp.439-517, 1993.

G. M. Siouris, G. Chen, and J. Wang, Tracking an incoming ballistic missile using an extended interval Kalman filter, IEEE Transactions on Aerospace and Electronic Systems, vol.33, issue.1, pp.232-240, 1997.
DOI : 10.1109/7.570753

A. Tanwani, J. Galdun, J. M. Thiriet, S. Lesecq, and S. Gentil, Experimental Networked Embedded Minidrone. Part I : Consideration of faults, Proceeding of ECC 2007, 2007.

T. Csendes and D. 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

V. Venkatasubramanian, R. Rengaswamy, S. N. Kavuri, and K. Yin, A review of process fault detection and diagnosis, Computers & Chemical Engineering, vol.27, issue.3, pp.293-311, 2003.
DOI : 10.1016/S0098-1354(02)00160-6

V. G. Héctor-moisés, Contribution à l'Estimation d'Etat à Horizon Glissant par Méthodes Ensemblistes : Applications à la Surveillance et Détection des Dysfonctionnements sur des Bioprocédés, 2002.

K. Vladik, H. T. Nguyen, P. D. Gracaliz, and B. Benjamin, A new dierential formalism for interval-valued functions and its potential use in detecting 1-d landscape features, The international conference on information technology Intech'03, pp.491-498, 2003.

V. Lemesle and J. L. Gouzé, Hybrid bounded error observers for uncertain bioreactor models, Bioprocess and Biosystems Engineering, vol.11, issue.3, pp.311-318, 2005.
DOI : 10.1007/s00449-005-0409-1

L. Waltz and . David, Generating semantic descriptions from drawings of scenes with shadows. The Psychology of Computer Vision, pp.19-91, 1975.

G. Whaba, A least squares estimate of spacecraft attitude Rate gyro, SIAM Review, vol.781, 1965.

A. S. 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

M. Witczak, Modelling and Estimation Strategies for Fault Diagnosis of Non-Linear Systems : From analytical to soft computing approaches, 2007.