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The basic structure of the Maximum Likelihood Ensemble Filter (MLEF) is an iterative minimization algorithm. The nonlinear analysis solution is obtained by an iterative minimization of the cost function. This is one of the main differences between the MLEF and other ensemble data assimilation algorithms. It also provides a link with variational data assimilation methods.
We typically use the nonlinear conjugate gradient and the quasi-Newton unconstrained minimization algorithms, but we are also exploring other algorithms. Development of non-differentiable iterative minimization algorithms is also in focus of our research.
The MLEF includes an implicit Hessian preconditioning. We are interested in further development of Hessian preconditioning which allows better assimilation of highly nonlinear cost functions that may arise in a non-Gaussian PDF framework.
