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, sparse observations space time. propose a novel methodology that harnesses transportation of measures, convex optimization, ideas from probabilistic graphical to yield robust ensemble approximations the distribution high dimensions. Our approach can be understood as natural generalization Kalman filter (EnKF) updates, using stochastic or deterministic couplings. The use updates reduce intrinsic bias EnKF at marginal increase computational cost. avoid any form importance sampling introduce localization approaches for dimension scalability. framework achieves state-of-the-art tracking performance on challenging configurations Lorenz-96 model regime.