ANALYSIS OF THE ENSEMBLE KALMAN-BUCY FILTER FOR CORRELATED OBSERVATION NOISE

• 成果类型: Article
• 署名作者: Ertel, Sebastian W.; Stannat, Wilhelm
• 署名单位: Technical University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1985
• 发表日期: 2024
• 页码: 1072-1107
• 关键词: mckean-vlasov sdes; uniform propagation; Data assimilation; STABILITY; accuracy; chaos

摘要

Ensemble Kalman-Bucy filters (EnKBFs) are an important tool in data assimilation that aim to approximate the posterior distribution for continuous time filtering problems using an ensemble of interacting particles. In this work we extend a previously derived unifying framework for consistent representations of the posterior distribution to correlated observation noise and use these representations to derive an EnKBF suitable for this setting as a constant gain approximation of these optimal filters. Existence and uniqueness results for both the EnKBF and its mean field limit are provided. The existence and uniqueness of solutions to its limiting McKean-Vlasov equation does not seem to be covered by the existing literature. In the correlated noise case the evolution of the ensemble depends also on the pseudoinverse of its empirical covariance matrix, which has to be controlled for global well-posedness. These bounds may also be of independent interest. Finally the convergence to the mean field limit is proven. The results can also be extended to other versions of EnKBFs.