M. Asch, M. Bocquet, and M. Nodet, Data assimilation: methods, algorithms, and applications, Fundamentals of Algorithms, Society for Industrial and Applied Mathematics, p.306, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01402885

C. Bishop, Pattern Recognition and Machine Learning, Information Science and Statistics, vol.738, 2006.

Å. Björck and M. Bocquet, Ensemble Kalman filtering without the intrinsic need for inflation, Society for Industrial and Applied Mathematics, vol.408, pp.735-750, 1996.

M. Bocquet, Localization and the iterative ensemble Kalman smoother, Q. J. Roy. Meteor. Soc, vol.142, pp.1075-1089, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01592378

M. Bocquet and A. Carrassi, Four-dimensional ensemble variational data assimilation and the unstable subspace, Tellus A, 69, 1304504, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01592362

M. Bocquet and P. Sakov, Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems, Nonlin. Processes Geophys, vol.19, pp.383-399, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00714384

M. Bocquet and P. Sakov, Joint state and parameter estimation with an iterative ensemble Kalman smoother, Nonlin. Processes Geophys, vol.20, pp.803-818, 2013.

M. Bocquet and P. Sakov, An iterative ensemble Kalman smoother, Q. J. Roy. Meteor. Soc, vol.140, pp.1521-1535, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00947740

M. Bocquet, P. N. Raanes, and A. Hannart, Expanding the validity of the ensemble Kalman filter without the intrinsic need for inflation, Nonlin. Processes Geophys, vol.22, pp.645-662, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01238318

A. Carrassi, M. Bocquet, A. Hannart, and M. Ghil, Estimating model evidence using data assimilation, Q. J. Roy. Meteor. Soc, vol.143, pp.866-880, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01592369

E. Cosme, J. Verron, P. Brasseur, J. Blum, A. et al., Smoothing Problems in a Bayesian Framework and Their Linear Gaussian Solutions, Mon. Weather Rev, vol.140, pp.683-695, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00905009

M. Goodliff, J. Amezcua, and P. J. Van-leeuwen, Comparing hybrid data assimilation methods on the Lorenz 1963 model with increasing non-linearity, Tellus A, 67, 26928, 2015.

K. Judd, L. Smith, and A. Weisheimer, Gradient free descent: shadowing, and state estimation using limited derivative information, Physica D, vol.190, pp.153-166, 2004.

A. Lorenc and E. Lorenz, Deterministic Nonperiodic Flow, Four-dimensional variational data assimilation, vol.20, pp.130-141, 1963.

E. Lorenz and K. Emanuel, Optimal Sites for Supplementary Weather Observations: Simulation with a Small Model, J. Atmos. Sci, vol.55, pp.399-414, 1998.

R. N. Miller, M. Ghil, and F. Gauthiez, Advanced Data Assimilation in Strongly Nonlinear Dynamical Systems, J. Atmos. Sci, vol.51, pp.1037-1056, 1994.

C. Pires, R. Vautard, and O. Talagrand, On extending the limits of variational assimilation in nonlinear chaotic systems, Tellus A, vol.48, pp.96-121, 1996.

P. Sakov and M. Bocquet, Asynchronous data assimilation with the EnKF in presence of additive model error, Tellus A, vol.70, 2018.

P. Sakov, J. Haussaire, and M. Bocquet, An iterative ensemble Kalman filter in presence of additive model error, Q. J. Roy. Meteor. Soc, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01632670

K. Swanson, R. Vautard, and C. Pires, Four-dimensional variational assimilation and predictability in a quasi-geostrophic model, Tellus A, vol.50, pp.369-390, 1998.

Y. Trémolet, Accounting for an imperfect model in 4D-Var, Q. J. Roy. Meteor. Soc, vol.132, pp.2483-2504, 2006.

A. Trevisan, M. D'isidoro, and O. Talagrand, Four-dimensional variational assimilation in the unstable subspace and the optimal subspace dimension, Q. J. Roy. Meteor. Soc, vol.136, pp.487-496, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01136782

P. Walters, An Introduction to Ergodic Theory, Graduate texts in mathematics, p.250, 1982.

J. Ye, D. Rey, N. Kadakia, M. Eldridge, U. Morone et al., Systematic variational method for statistical nonlinear state and parameter estimation, Phys. Rev. E, vol.92, p.52901, 2015.

. Nonlin, Processes Geophys, vol.25, pp.315-334, 2018.