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This volume of Frontiers in Applied Dynamical Systems focuses on two potential solutions to the nonlinear data-assimilation problem in high-dimensional systems. Both contributions focus on so-called particle filters. The contribution of Van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The contribution by Reich and Cotter discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful Ensemble Kalman Filters with fully nonlinear particle filters, and allows a proper introduction of localisation in particle filters, which has been lacking up to now.§
