We propose the ensemble Kalman smoother multiple distribution estimation filter (EnKS-MDEF) for nonlinear state estimation problems. The EnKS-MDEF is an example of the multiple distribution estimation filter (MDEF), which is a particle filter (PF) that estimates the filtered state probability density function (pdf) using multiple conditional state pdfs. The one step behind (OSB) smoothed state pdf used for calculating the filtered state pdf of the MDEF is approximated by the ensemble Kalman smoother (EnKS). Then, the particle weights for the EnKS-MDEF remain equal during the filter execution, which indicates that the EnKS-MDEF is a degeneracy-free PF. Since, the MDEF and the EnKS-MDEF, both estimate the OSB smoothed state pdf prior to calculating the filtered state pdf, these filters provide a simultaneous estimation of filtered and OSB smoothed states. The examples of the EnKS-MDEF are the EnKS-extended and unscented Kalman multiple distribution estimation filters, and their filtering and OSB smoothing performances are evaluated and compared with those for the representative filters and smoothers using a benchmark simulation problems.

中文翻译：

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无退化粒子滤波器：集成卡尔曼平滑多重分布估计滤波器

我们针对非线性状态估计问题提出了集成卡尔曼平滑多重分布估计滤波器 (EnKS-MDEF)。EnKS-MDEF 是多重分布估计滤波器 (MDEF) 的示例，它是一种粒子滤波器 (PF)，使用多个条件状态 pdf 来估计滤波后的状态概率密度函数 (pdf)。用于计算 MDEF 的滤波状态 pdf 的落后一步 (OSB) 平滑状态 pdf 由集合卡尔曼平滑器 (EnKS) 近似。然后，EnKS-MDEF 的粒子权重在滤波器执行期间保持相等，这表明 EnKS-MDEF 是无退化的 PF。因为，MDEF 和 EnKS-MDEF，都在计算过滤状态 pdf 之前估计 OSB 平滑状态 pdf，这些过滤器提供了过滤和 OSB 平滑状态的同步估计。EnKS-MDEF 的例子是 EnKS 扩展和无迹卡尔曼多重分布估计滤波器，它们的滤波和 OSB 平滑性能被评估并与使用基准模拟问题的代表性滤波器和平滑器的性能进行比较。