发表机构
University of Manchester; Massachusetts Institute of Technology; École Polytechnique Fédérale de Lausanne（曼彻斯特大学; 麻省理工学院; 洛桑联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对基于随机微分方程的数据同化问题，提出动态低秩型滤波器，推导DLRA滤波器并扩展至Kalman-Bucy型及集合方法，还提出粒子型DLRA滤波器，数值模拟验证了其在非线性场景的有效性。
AI 中文摘要
针对基于随机微分方程（SDEs）的数据同化问题，我们提出了动态低秩（DLR）型滤波器。具体而言，我们首先推导了DLRA滤波器，用于联合最小化均值和协方差误差，同时提出了一种有效纳入相关正交方向的策略，该策略允许主子空间也根据观测算子演化。这些过程在处理线性漂移时自然扩展为Kalman-Bucy型滤波器，也适用于集合方法，因此也适用于由非线性漂移和可能的非高斯分布描述的问题。此外，我们进一步提出了一种初步的粒子型DLRA滤波器，其在非线性场景中展现出潜力。数值模拟表明，这些方法在相关应用中具有有效性，为这些滤波方向的进一步研究开辟了道路。
英文摘要
We propose dynamical low-rank (DLR) type filters for data-assimilation problems based on stochastic differential equations (SDEs). In detail, first we derive a DLRA filter for minimizing jointly the mean and covariance error, as well as a strategy to efficiently include the relevant orthogonal directions. This last approach allows the main subspace to evolve also according to the observation operator. Those procedures naturally extend to a Kalman-Bucy type filter when dealing with linear drift, and to ensemble methods, too, resulting also suitable for problems described by nonlinear drift and possible non-Gaussian distribution. Moreover, we further propose a preliminary particle-type DLRA filter that shows potentiality in nonlinear settings. Numerical simulations show the efficacy of these procedures in relevant applications, opening up to further studies in these filtering directions.
Comments37 pages, 26 figures
