Title: Particle filters for large-dimensional problems

Author: Melanie Ades (University of Reading) Peter Jan van Leeuwen(University of Reading)

With ever increasing model resolution and more complicated observations the data-assimilation problem becomes more and more nonlinear. This calls for fully nonlinear data-assimilation methods, such as particle filters. In particle filters the importance of each particle in estimating the posterior density is dominated by the likelihood of that particle. In high-dimensional systems with a large number of independent observations the likelihood can differ substantially between particles resulting in only a few having statistical significance.

The idea of using the proposal density within the particle filter to provide a continuous guidance towards a future observation has already been discussed in the literature. Using the proposal density the aim is to increase the likelihood of all particles by ensuring they end up significantly close to the observation. However the proposal density is not restricted to continuous guidance but offers a much greater freedom in how we treat the particles. In particular it can be used to ensure that the majority of particles have an approximately equal significance in estimating the posterior density. With the majority of particles being both close to the observations and having statistical significance, the ability to represent a multi-modal posterior density with only a few particles starts to be realised.

We will show how such a particle filter is derived and discuss its application to the barotropic vorticity equations, both in the regime with periodic trajectories and in the chaotic regime, with state dimensions of a few thousands and more.

GMAO Head: Michele Rienecker Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: March 1 2011