Analysis of a localised nonlinear Ensemble Kalman Bucy Filter with complete and accurate observations

TL;DR

This paper introduces a localized Ensemble Kalman Bucy Filter for nonlinear models with short-range interactions, providing theoretical error bounds and verifying them through numerical tests.

Contribution

It proposes a novel localized Ensemble Kalman Bucy Filter tailored for nonlinear models, with rigorous error analysis and validation.

Findings

Dimension-independent error bounds derived

Logarithmic dependence of long-term error on time range

Numerical tests confirm theoretical predictions

Abstract

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.