Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice. These algorithms rely on an ensemble of interacting particles to sequentially estimate the state as new observations become available. Despite the practical success of ensemble Kalman filters, theoretical understanding is hindered by the intricate dependence structure of the interacting particles. This paper investigates ensemble Kalman filters that incorporate an additional resampling step to break the dependency between particles. The new algorithm is amenable to a theoretical analysis that extends and improves upon those available for filters without resampling, while also performing well in numerical examples.

翻译：滤波关注的是根据部分且含噪声的观测值对动态系统的状态进行在线估计。在系统状态为高维度的应用中，集合卡尔曼滤波器通常是首选方法。这些算法依赖于一组相互作用的粒子，在获得新观测值时依次估计状态。尽管集合卡尔曼滤波器在实际应用中取得了成功，但理论理解受到相互作用粒子复杂依赖结构的阻碍。本文研究了一种额外引入重采样步骤以打破粒子间依赖关系的集合卡尔曼滤波器。该新算法在理论分析上可扩展并改进现有针对无重采样滤波器的分析结果，同时在数值示例中表现良好。