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The iterative ensemble Kalman filter (IEnKF) is widely used in inverseproblems to estimate system parameters from limited observations. However, theIEnKF, when applied to nonlinear systems, can be plagued by poor convergence.Here we provide a comprehensive convergence analysis of the IEnKF and propose anew method to improve its convergence. A theoretical analysis of the standardIEnKF is presented and we demonstrate that the interaction between thenonlinearity of the forward model and the diminishing effect of the Kalmanupdates results in "early stopping" of the IEnKF, i.e. the Kalman operatorconverges to zero before the innovation is minimized. The steady state behaviorof the early stopping phenomenon and its relation to observation uncertainty isdemonstrate. We then propose an approach to prevent the early stopping byperturbing the covariance with hidden parameter ensemble resampling. Theensemble mean and covariance are kept unchanged during the resampling process,which ensures the Kalman operator at each iteration maintains a correct updatedirection. We briefly discuss the influence higher moments, such as kurtosis,of the resampling distribution on algorithm convergence. Parallel to the abovedevelopments, an example problem is presented to demonstrate the early stoppingeffect, and the application and merit of the proposed resampling scheme.

Improving the Convergence of the Iterative Ensemble Kalman Filter by Resampling