论文标题
分析合奏Kalman-相关观察噪声的滤波器
Analysis of the Ensemble Kalman--Bucy Filter for correlated observation noise
论文作者
论文摘要
集合Kalman-纤维过滤器（ENKBF）是数据同化的重要工具，旨在使用相互作用的粒子集合近似连续的时间过滤问题的后验分布。在这项工作中，我们扩展了一个先前得出的统一框架，以使后验分布的一致表示与观察噪声相关，并使用这些表示形式来得出适用于这种设置的ENKBF，作为这些最佳过滤器的恒定增益近似。提供了ENKBF及其平均场限制的存在和唯一性结果。现有文献似乎并未涵盖其限制其限制McKean-Vlasov方程的解决方案的存在和独特性。在相关的噪声情况下，整体的演变也取决于其经验协方差矩阵的伪内，该矩阵必须控制全球良好的姿势。这些界限也可能具有独立的利益。最后，证明了与平均场限制的收敛。结果也可以扩展到其他版本的ENKBF。
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.
