The main challenge in ensemble-based filtering methods is the updating of a prior ensemble to a posterior ensemble. In the ensemble Kalman filter (EnKF), a linear-Gaussian model is introduced to overcome this issue, and the prior ensemble is updated with a linear shift. In the current article, we consider how the underlying ideas of the EnKF can be applied when the state vector consists of binary variables. While the EnKF relies on Gaussian approximations, we instead introduce a first-order Markov chain approximation. To update the prior ensemble we simulate samples from a distribution which maximizes the expected number of equal components in a prior and posterior state vector. The proposed approach is demonstrated in a simulation experiment where, compared with a more naive updating procedure, we find that it leads to an almost 50% reduction in the difference between true and estimated marginal filtering probabilities with respect to the Frobenius norm.

中文翻译：

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通过最大化未更改组件的预期数量来集成更新二进制状态向量

基于集成的过滤方法的主要挑战是将先验集成更新为后验集成。在集成卡尔曼滤波器 (EnKF) 中，引入了线性高斯模型来克服这个问题，并通过线性移位更新先验集成。在当前的文章中，我们考虑在状态向量由二进制变量组成时如何应用 EnKF 的基本思想。虽然 EnKF 依赖于高斯近似，但我们改为引入一阶马尔可夫链近似。为了更新先验集合，我们模拟分布中的样本，该分布最大化先验和后验状态向量中相等分量的预期数量。所提出的方法在模拟实验中得到证明，与更天真的更新过程相比，