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.

针对高维度的非高斯状态空间模型、非线性且可能是混沌动力学以及空间与时间稀疏的观测，我们提出了一种新的过滤方法，使用交通测度、凸优化和概率图模型的思想来产生高维度下的坚韧的集成近似过滤分布。我们的方法可被理解为集成卡尔曼滤波器（EnKF）的自然推广，使用随机或确定性耦合来进行非线性更新。使用非线性更新可以降低 EnKF 的固有偏差，只带来少量的计算成本。我们避免了任何形式的重要性采样，并引入了维度可扩展性的非高斯本地化方法。我们的框架在混沌区域的 Lorenz-96 模型的挑战配置下实现了最先进的跟踪性能。