D. Auroux and J. Blum, A nudging-based data assimilation method: the Back and Forth Nudging (BFN) algorithm. Nonlinear Processes In Geophysics, pp.305-319, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00327422

A. Bensoussan, Filtrage Optimal des Systèmes Linéaires, 1971.

C. Bertoglio, P. Moireau, and J. Gerbeau, Sequential parameter estimation for fluidstructure problems. application to hemodynamics, Int. J. Num. Meth. Biomedical Engng., published online, 2012.
URL : https://hal.archives-ouvertes.fr/inria-00603399

R. Chabiniok, P. Moireau, P. Lesault, A. Rahmouni, J. Deux et al., Estimation of tissue contractility from cardiac cine-mri using a biomechanical heart model, Biomechanics and Modeling in Mechanobiology, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00654541

G. Chavent, Nonlinear Least Squares for Inverse Problems, 2010.
DOI : 10.1007/978-90-481-2785-6

D. Elia, M. Perego, M. Veneziani, and A. , A variational data assimilation procedure for the incompressible Navier-Stokes equations in hemodynamics, Journal of Scientific Computing, pp.1-20, 2011.

H. Delingette, F. Billet, K. Wong, M. Sermesant, K. Rhode et al., Personalization of Cardiac Motion and Contractility From Images Using Variational Data Assimilation, IEEE Transactions on Biomedical Engineering, vol.59, issue.1, pp.20-24, 2012.
DOI : 10.1109/TBME.2011.2160347
URL : https://hal.archives-ouvertes.fr/inria-00616183

G. Evensen, Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, Journal of Geophysical Research, vol.109, issue.Part 4, pp.10143-10162, 1994.
DOI : 10.1029/94JC00572

D. Chapelle, A. Gariah, P. Moireau, and J. Sainte-marie, A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems ??? Analysis, assessments and applications to parameter estimation, ESAIM: Mathematical Modelling and Numerical Analysis, vol.47, issue.6, 2012.
DOI : 10.1051/m2an/2013090
URL : https://hal.archives-ouvertes.fr/hal-00834397

I. Hoteit, D. Pham, and J. Blum, A simplified reduced order Kalman filtering and application to altimetric data assimilation in Tropical Pacific, Journal of Marine Systems, vol.36, issue.1-2, pp.101-127, 2002.
DOI : 10.1016/S0924-7963(02)00129-X

A. Imperiale, R. Chabiniok, P. Moireau, and D. Chapelle, Constitutive Parameter Estimation Methodology Using Tagged-MRI Data, Proceedings of FIMH'11, 2011.
DOI : 10.1109/42.414605

S. Julier, J. Uhlmann, and H. Durrant-whyte, A new method for the nonlinear transformation of means and covariances in filters and estimators, IEEE Transactions on Automatic Control, vol.45, issue.3, pp.447-482, 2000.
DOI : 10.1109/9.847726

E. Konukoglu, J. Relan, U. Cilingir, B. Menze, P. Chinchapatnam et al., Efficient probabilistic model personalization integrating uncertainty on data and parameters: Application to Eikonal-Diffusion models in cardiac electrophysiology, Progress in Biophysics and Molecular Biology, vol.107, issue.1, pp.134-146, 2011.
DOI : 10.1016/j.pbiomolbio.2011.07.002
URL : https://hal.archives-ouvertes.fr/inria-00616198

D. Luenberger, Determining the State of a Linear with Observers of Low Dynamic Order, 1963.

P. Moireau, Filtering-based Data Assimilation for Second-Order Hyperbolic PDEs. Applications in Cardiac Mechanics, 2008.
URL : https://hal.archives-ouvertes.fr/tel-00358582

P. Moireau and D. Chapelle, Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems, COCV, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00550104

P. Moireau and D. Chapelle, Erratum of article ???Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems???, ESAIM: Control, Optimisation and Calculus of Variations, vol.17, issue.2, pp.406-409, 2011.
DOI : 10.1051/cocv/2011001

P. Moireau, D. Chapelle, L. Tallec, and P. , Joint state and parameter estimation for distributed mechanical systems, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.6-8, pp.659-677, 2008.
DOI : 10.1016/j.cma.2007.08.021
URL : https://hal.archives-ouvertes.fr/hal-00175623

P. Moireau, D. Chapelle, and L. Tallec, 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

V. Moreau-villeger, H. Delingette, M. Sermesant, H. Ashikaga, E. Mcveigh et al., Building maps of local apparent conductivity of the epicardium with a 2-D electrophysiological model of the heart, IEEE Transactions on Biomedical Engineering, vol.53, issue.8, pp.531457-1466, 2006.
DOI : 10.1109/TBME.2006.877794
URL : https://hal.archives-ouvertes.fr/inria-00614992

D. Pham, Stochastic Methods for Sequential Data Assimilation in Strongly Nonlinear Systems, Monthly Weather Review, vol.129, issue.5, pp.194-195, 2001.
DOI : 10.1175/1520-0493(2001)129<1194:SMFSDA>2.0.CO;2
URL : https://hal.archives-ouvertes.fr/inria-00073082

D. Pham, J. Verron, and M. Roubaud, A singular evolutive extended Kalman filter for data assimilation in oceanography, Journal of Marine systems, vol.16, pp.3-4323, 1998.

J. Relan, P. Chinchapatnam, M. Sermesant, K. Rhode, M. Ginks et al., Coupled personalization of cardiac electrophysiology models for prediction of ischaemic ventricular tachycardia, Interface Focus, vol.48, issue.12, pp.396-407, 2011.
DOI : 10.1016/j.jacc.2006.07.062
URL : https://hal.archives-ouvertes.fr/inria-00616188

N. Smith, A. De-vecchi, M. Mccormick, D. Nordsletten, O. Camara et al., euHeart: personalized and integrated cardiac care using patient-specific cardiovascular modelling, Interface Focus, vol.41, issue.10, pp.349-364, 2011.
DOI : 10.1016/j.jbiomech.2008.04.035
URL : https://hal.archives-ouvertes.fr/inria-00616189

L. Wang, H. Zhang, K. Wong, and P. Shi, A reduced-rank square root filtering framework for noninvasive functional imaging of volumetric cardiac electrical activity, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.533-536, 2009.
DOI : 10.1109/ICASSP.2009.4959638

J. Xi, L. Lamata, J. Lee, P. Moireau, D. Chapelle et al., Myocardial transversely isotropic material parameter estimation from in-silico measurements based on a reduced-order unscented Kalman filter, Journal of the Mechanical Behavior of Biomedical Materials, vol.4, issue.7, pp.1090-1102, 2011.
DOI : 10.1016/j.jmbbm.2011.03.018

J. Xi, P. Lamata, W. Shi, S. Niederer, S. Land et al., An automatic data assimilation framework for patient-specific myocardial mechanical parameter estimation. Functional Imaging and Modeling of the Heart, pp.392-400, 2011.