Particle filters hold the promise of fully nonlinear data assimilation. They used to have a bad reputation in the geosciences because of the weight-collapse in high-dimensional applications. Classical statistical methods to avoid weight collapse by changing the transition proposal density, such as the optimal proposal density, are not sufficient to solve the problem. The main problem is that most of these particle filters are based on importance sampling. However, a solution is appearing in the form of transporting equal-weight samples from the prior to equal-weight particles of the posterior, in which importance sampling does not play a role. I will discuss one and two step methods, but also transportation methods that iteratively minimize the KL-divergence between prior and posterior. Specifically, I will focus on kernel embedding of the transport map, leading to efficient and very promising filter that is unbiased and applicable to high-dimensional geoscience applications.
Invited by Wilhelm Stannat and Jana de Wiljes