An Iterative EnKF for Strongly Nonlinear Systems

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A Second-Order Exact Ensemble Square Root Filter for Nonlinear Data Assimilation (2015, methodology): “This prevents computational instabilities caused by considerably small singular values, which are sometimes neglected in ETKF implementations for that reason (Sakov et al. 2012).”
An iterative ensemble Kalman smoother (2014, methodology): “The iterative ensemble Kalman filter (IEnKF: Sakov et al., 2012) is an illustration of this strategy, with a clear demonstration of its success for strongly nonlinear low-order models and a circumstantial answer to the last question.”
Levenberg–Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification (2013, methodology): “[17], in which the Levenberg–Marquardt method was used for regularization, and also evaluated the combined used of the finite-size EnKF and the iterative schemes.”
Ensemble Randomized Maximum Likelihood Method as an Iterative Ensemble Smoother (2011, methodology): “Iterative ensemble Kalman filters (Gu and Oliver 2007; Li and Reynolds 2009; Sakov et al. 2011), like the EnKF, have been used to sequentially assimilate data for problems in which the relationship between data and model parameters is highly nonlinear.”