Peter Jan van Leeuwen, University of Reading

Non-degenerate particle filters for high-dimensional systems

Mengbin Zhu and Javier Amezcua


With ever increasing model resolution and ever more complex observation operators the data-assimilation problem is becoming highly nonlinear. Particle Filters are fully nonlinear data assimilation methods, but until recently were not efficient in high-dimensional systems. However, the so-called proposal density allows enormous freedom in particle filters, and does provide the potential for efficient particle filters in high dimensional systems.

Recent advances have been made exploring localisation, a standard technique from Ensemble Kalman Filtering, in which the high-dimensional problem is broken up in small dimensional filtering problems in subdomains, allowing for efficiency again. Unfortunately, stitching these subdomains together again can lead to unphysical behaviour in systems that exhibit complex nonlinear spatial balances between model variables, such as geophysical systems.

In this talk a new class of proposal densities is studied in which the proposal of each particle is dependent on not only the past of that particle but on the past of all particles. This strongly enhances the proposal freedom, and indeed new schemes can be generated that are non-degenerate for very high dimensional systems. We present one example of this class, in which the number of particles is independent of the dimension of the system, curing the curse of dimensionality. The new scheme is also of interest for high-dimensional parameter estimation problems. Results on applying filters of this kind to very high-dimensional geophysical systems will be discussed.