Coupling techniques for nonlinear ensemble filtering
This addresses the problem of robust ensemble filtering in high-dimensional, chaotic systems for applications like weather forecasting, though it appears incremental as a generalization of existing methods.
The paper tackles filtering in high-dimensional non-Gaussian state-space models with chaotic dynamics and sparse observations by proposing a novel methodology that generalizes the ensemble Kalman filter to nonlinear updates, achieving state-of-the-art tracking performance on the Lorenz-96 model.
We consider filtering in high-dimensional non-Gaussian state-space models with intractable transition kernels, nonlinear and possibly chaotic dynamics, and sparse observations in space and time. We propose a novel filtering methodology that harnesses transportation of measures, convex optimization, and ideas from probabilistic graphical models to yield robust ensemble approximations of the filtering distribution in high dimensions. Our approach can be understood as the natural generalization of the ensemble Kalman filter (EnKF) to nonlinear updates, using stochastic or deterministic couplings. The use of nonlinear updates can reduce the intrinsic bias of the EnKF at a marginal increase in computational cost. We avoid any form of importance sampling and introduce non-Gaussian localization approaches for dimension scalability. Our framework achieves state-of-the-art tracking performance on challenging configurations of the Lorenz-96 model in the chaotic regime.