Coupling Techniques for Nonlinear Ensemble Filtering

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 ap-proach 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 com-putational 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.

Automated summary

This paper introduces a method for filtering in high-dimensional non-Gaussian state-space models, which utilizes probabilistic graphical models and convex optimization to achieve robust ensemble approximations of the filtering distribution in high dimensions. The proposed method achieves state-of-the-art tracking performance on challenging configurations of the Lorenz-96 model in the chaotic regime.