Session A6 - Mathematical Foundations of Data Assimilation and Inverse Problems
July 10, 15:30 ~ 16:00
EnKF-based interacting particle filter formulations
Jana de Wiljes
University Potsdam, Germany - email@example.com
In a nonlinear setting the filtering distribution can be approximated via the empirical measure provided that an ensemble of samples is available. A computationally feasible option to generate these particles for each time instance is to define an appropriate modified evolution equation that describes the dynamics of the particles with respect to the incoming data. The most famous example of such interacting particle filter formulations is the ensemble Kalman filter (EnKF). Although it works remarkably well in practice its success is not well understood from a mathematical point of view. In a recent study we were able to derive stability and accuracy results for a specific variant of the EnKF in a continuous setting with a small number of particles. Inspired by the EnKF we explored more general interacting particle filter formulations that allow to overcome weaknesses of the EnKF as well as drawbacks of classical sequential resampling schemes. More precisely, we consider the recently proposed ensemble transform particle filter (ETPF) which is an adaption of the standard particle filter where the resampling step is replaced by a linear transformation. However, the transformation step is computationally expensive and leads to an underestimation of the ensemble spread for small and moderate ensemble sizes.
These shortcomings have recently been addressed by developing second-order accurate extensions of the ETPF. It is also demonstrated that the nonlinear ensemble transform filter (NETF) arises as a special case of our general framework. Numerical results for the Lorenz-63 and Lorenz-96 models demonstrate the effectiveness of the proposed modified particle filters.
Joint work with Wilhelm Stannat (Technical University Berlin), Sebastian Reich (University Potsdam and University of Reading) and Walter Acevedo (University Potsdam).