Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the Ensemble Kalman Filter with proper localization techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localized Ensemble Kalman Bucy Filter (l-EnKBF) for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests.

中文翻译：

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具有完整准确观测值的局部非线性系综卡尔曼布西滤波器分析

并发观测技术使得高精度实时数据大量可用。数据同化 (DA) 关注如何将这些数据与物理模型相结合以产生准确的预测。对于时空模型，具有适当定位技术的集成卡尔曼滤波器被认为是最先进的 DA 方法。本文提出并研究了一种用于具有短程相互作用的非线性模型的局部集成卡尔曼布西滤波器 (l-EnKBF)。我们推导出与维度无关和组件方式的误差界限，并显示长时间的路径方式误差仅对时间范围具有对数依赖性。通过一些简单的数值试验验证了理论结果。