Analysis of the Ensemble Kalman--Bucy Filter for correlated observation noise

Understand

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.