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...