R. A. Anthes, Data Assimilation and Initialization of Hurricane Prediction Models, Journal of the Atmospheric Sciences, vol.31, issue.3, pp.702-719, 1974.
DOI : 10.1175/1520-0469(1974)031<0702:DAAIOH>2.0.CO;2

H. Banks, K. Ito, and C. Wang, Exponentially stable approximations of weakly damped wave equations, Estimation and control of distributed parameter systems, pp.1-33, 1990.
DOI : 10.1007/978-3-0348-6418-3_1

C. Bardos, G. Lebeau, and J. Rauch, Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary, SIAM Journal on Control and Optimization, vol.30, issue.5, pp.1024-1065, 1992.
DOI : 10.1137/0330055

A. Bensoussan, Filtrage optimal des systèmes linéaires. Dunod, 1971.

J. Blum, F. X. Ledimet, and I. N. Navon, Data assimilation for geophysical fluids. Handbook of Numerical Analysis: Computational Methods for the Atmosphere and the Oceans, pp.377-434, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00391892

R. Chabiniok, P. Moireau, P. Lesault, A. Rahmouni, J. Deux et al., Trials on Tissue Contractility Estimation from Cardiac Cine??MRI Using a Biomechanical Heart Model, Proceedings of FIMH'11, pp.304-313, 2011.
DOI : 10.1016/j.media.2006.04.002
URL : https://hal.archives-ouvertes.fr/hal-00654547

D. Chapelle, N. C??ndeac??ndea, M. De-buhan, and P. Moireau, Exponential Convergence of an Observer Based on Partial Field Measurements for the Wave Equation, Mathematical Problems in Engineering, vol.2012, p.12, 2012.
DOI : 10.1016/j.matpur.2008.09.002
URL : https://hal.archives-ouvertes.fr/inria-00619504

D. Chapelle, N. C??ndeac??ndea, and P. Moireau, IMPROVING CONVERGENCE IN NUMERICAL ANALYSIS USING OBSERVERS ??? THE WAVE-LIKE EQUATION CASE, Mathematical Models and Methods in Applied Sciences, vol.22, issue.12, 2012.
DOI : 10.1142/S0218202512500406
URL : https://hal.archives-ouvertes.fr/inria-00621052

D. Chapelle, M. Fragu, V. Mallet, and P. Moireau, Fundamental principles of data assimilation underlying the Verdandi library: applications to biophysical model personalization within euHeart, Medical & Biological Engineering & Computing, vol.4, issue.7, pp.1221-1233, 2013.
DOI : 10.1007/s11517-012-0969-6
URL : https://hal.archives-ouvertes.fr/hal-00760887

S. Cox and E. Zuazua, The rate at which energy decays in a damped String, Communications in Partial Differential Equations, vol.67, issue.1-2, pp.213-243, 1994.
DOI : 10.1080/03605309408821015

M. Daoulatli, B. Dehman, and M. Khenissi, Local Energy Decay for the Elastic System with Nonlinear Damping in an Exterior Domain, SIAM Journal on Control and Optimization, vol.48, issue.8, pp.5254-5275, 2010.
DOI : 10.1137/090757332

S. Ervedoza, C. Zheng, and E. Zuazua, On the observability of time-discrete conservative linear systems, Journal of Functional Analysis, vol.254, issue.12, pp.3037-3078, 2008.
DOI : 10.1016/j.jfa.2008.03.005
URL : https://hal.archives-ouvertes.fr/hal-00681702

S. Ervedoza and E. Zuazua, Uniformly exponentially stable approximations for a class of damped systems, Journal de Math??matiques Pures et Appliqu??es, vol.91, issue.1, pp.20-48, 2009.
DOI : 10.1016/j.matpur.2008.09.002
URL : https://hal.archives-ouvertes.fr/hal-00681693

S. Ervedoza, Spectral conditions for admissibility and observability of wave systems: applications to finite element schemes, Numerische Mathematik, vol.47, issue.2, pp.377-415, 2009.
DOI : 10.1007/s00211-009-0235-5
URL : https://hal.archives-ouvertes.fr/hal-00681689

G. Evensen, Data Assimilation ? The Ensemble Kalman Filter, 2007.

G. Haine and K. Ramdani, Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations, Numerische Mathematik, vol.47, issue.2, pp.307-343, 2012.
DOI : 10.1007/s00211-011-0408-x
URL : https://hal.archives-ouvertes.fr/hal-00730512

F. M. Hante, M. Sigalotti, and M. Tucsnak, On conditions for asymptotic stability of dissipative infinite-dimensional systems with intermittent damping, Journal of Differential Equations, vol.252, issue.10, pp.5569-5593, 2012.
DOI : 10.1016/j.jde.2012.01.037
URL : https://hal.archives-ouvertes.fr/inria-00616474

A. Haraux and E. Zuazua, Decay estimates for some semilinear damped hyperbolic problems, Archive for Rational Mechanics and Analysis, vol.193, issue.4, pp.191-206, 1988.
DOI : 10.1007/BF00282203

J. E. Hoke and R. A. Anthes, The Initialization of Numerical Models by a Dynamic-Initialization Technique, Monthly Weather Review, vol.104, issue.12, pp.1551-1556, 1976.
DOI : 10.1175/1520-0493(1976)104<1551:TIONMB>2.0.CO;2

R. E. Kalman and R. S. Bucy, New Results in Linear Filtering and Prediction Theory, Journal of Basic Engineering, vol.83, issue.1, pp.95-108, 1961.
DOI : 10.1115/1.3658902

S. Lakshmivarahan and J. M. Lewis, Nudging Methods: A Critical Overview, Data Assimilation for Atmospheric, Oceanic, and Hydrologic Applications, 2008.
DOI : 10.1007/978-3-642-35088-7_2

F. Dimet and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects, Tellus A, vol.109, issue.2, pp.97-110, 2010.
DOI : 10.1111/j.1600-0870.1986.tb00459.x

X. Li and C. Xu, Infinite-dimensional Luenberger-like observers for a rotating body-beam system, Systems & Control Letters, vol.60, issue.2, pp.138-145, 2011.
DOI : 10.1016/j.sysconle.2010.11.005
URL : https://hal.archives-ouvertes.fr/hal-00647239

K. Liu, Locally Distributed Control and Damping for the Conservative Systems, SIAM Journal on Control and Optimization, vol.35, issue.5, pp.1574-1590, 1997.
DOI : 10.1137/S0363012995284928

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

P. Moireau, D. Chapelle, and P. Letallec, Joint state and parameter estimation for distributed mechanical systems, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.6-8, pp.659-677, 2007.
DOI : 10.1016/j.cma.2007.08.021
URL : https://hal.archives-ouvertes.fr/hal-00175623

P. Moireau, D. Chapelle, and P. Letallec, Filtering for distributed mechanical systems using position measurements: perspectives in medical imaging, Inverse Problems, vol.25, issue.3, p.35010, 2009.
DOI : 10.1088/0266-5611/25/3/035010
URL : https://hal.archives-ouvertes.fr/hal-00358914

I. M. Navon, Data Assimilation for Numerical Weather Prediction: A Review, Data Assimilation for Atmospheric, Oceanic, and Hydrologic Applications, 2009.
DOI : 10.1007/978-3-540-71056-1_2

N. K. Nichols, Mathematical Concepts of Data Assimilation, Data Assimilation, pp.13-39, 2010.
DOI : 10.1007/978-3-540-74703-1_2

K. Ramdani, T. Takahashi, and M. Tucsnak, Uniformly exponentially stable approximations for a class of second order evolution equations, ESAIM: Control, Optimisation and Calculus of Variations, vol.13, issue.3, pp.503-527, 2007.
DOI : 10.1051/cocv:2007020
URL : https://hal.archives-ouvertes.fr/hal-00140476

K. Ramdani, M. Tucsnak, and G. Weiss, Recovering the initial state of an infinite-dimensional system using observers, Automatica, vol.46, issue.10, pp.1616-1625, 2012.
DOI : 10.1016/j.automatica.2010.06.032
URL : https://hal.archives-ouvertes.fr/hal-00529834

D. Simon, Optimal state estimation: Kalman, H? and nonlinear approaches, 2006.
DOI : 10.1002/0470045345

T. Louis, E. Tebou, and . Zuazua, Uniform boundary stabilization of the finite difference space discretization of the 1-d wave equation, Adv Comput Math, vol.26, issue.1-3, pp.337-365, 2007.

D. , T. Pham, J. Verron, and L. Gourdeau, Singular evolutive kalman filters for data assimilation in oceanography, C. R. Acad. Sci. Paris, pp.255-260, 1997.

M. Tucsnak and G. Weiss, Observation and control for operator semigroups, 2009.
DOI : 10.1007/978-3-7643-8994-9
URL : https://hal.archives-ouvertes.fr/hal-00590673

X. Zhang, C. Zheng, and E. Zuazua, Exact Controllability of the Time Discrete Wave Equation: A Multiplier Approach, Discret. Contin. Dyn. S, pp.229-245, 2007.
DOI : 10.1007/978-90-481-3239-3_17

E. Zuazua, Propagation, Observation, and Control of Waves Approximated by Finite Difference Methods, SIAM Review, vol.47, issue.2, pp.197-243, 2005.
DOI : 10.1137/S0036144503432862