This book contains two review articles on nonlinear data assimilation that deal with closely
related topics but were written and can be read independently. Both contributions focus on
so-called particle filters. The first contribution by Jan 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
second contribution by Cheng and Reich 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 localization in particle
filters which has been lacking up to now.
