论文标题
对香草和确定性集合Kalman-bucy过滤器的无偏估计
Unbiased Estimation of the Vanilla and Deterministic Ensemble Kalman-Bucy Filters
论文作者
论文摘要
在本文中，我们考虑了集合卡尔曼（ENKBF）的无偏估计器的开发。 ENKBF是一种连续的时间过滤方法，可以看作是著名的离散时间集合卡尔曼滤波器的连续时间类似物。我们的公正估计器将从最近的工作[Rhee \＆Glynn 2010，[31]]中引起动机，该工作将随机化作为产生无偏见和有限的方差估计器的一种手段。随机化通过离散水平和每个级别的样品数量进入。我们的估计器将特定于线性和高斯设置，在那里我们知道ENKBF是一致的，在粒子限制$ n \ rightarrow \ infty \ Infty $中，kbf和kbf。我们为ENKBF的两个特定变体（即确定性和香草变体）强调了这一点，并在线性ornstein-uhlenbeck过程中证明了这一点。我们将其与ENKBF和多级（MLENKBF）进行比较，以进行不同的尺寸大小的实验。我们还提供了多级确定性ENKBF的证明，该确定性ENKBF为某些无偏见的方法提供了指南。
In this article we consider the development of an unbiased estimator for the ensemble Kalman--Bucy filter (EnKBF). The EnKBF is a continuous-time filtering methodology which can be viewed as a continuous-time analogue of the famous discrete-time ensemble Kalman filter. Our unbiased estimators will be motivated from recent work [Rhee \& Glynn 2010, [31]] which introduces randomization as a means to produce unbiased and finite variance estimators. The randomization enters through both the level of discretization, and through the number of samples at each level. Our estimator will be specific to linear and Gaussian settings, where we know that the EnKBF is consistent, in the particle limit $N \rightarrow \infty$, with the KBF. We highlight this for two particular variants of the EnKBF, i.e. the deterministic and vanilla variants, and demonstrate this on a linear Ornstein--Uhlenbeck process. We compare this with the EnKBF and the multilevel (MLEnKBF), for experiments with varying dimension size. We also provide a proof of the multilevel deterministic EnKBF, which provides a guideline for some of the unbiased methods.
