The ensemble Kalman filter (EnKF) is a popular technique for performing inference in state-space models (SSMs), particularly when the dynamic process is high-dimensional. Unlike reweighting methods such as sequential Monte Carlo (SMC, i.e. particle filters), the EnKF leverages either the linear Gaussian structure of the SSM or an approximation thereof, to maintain diversity of the sampled latent states (the so-called ensemble members) via shifting-based updates. Joint parameter and state inference using an EnKF is typically achieved by augmenting the state vector with the static parameter. In this case, it is assumed that both parameters and states follow a linear Gaussian state-space model, which may be unreasonable in practice. In this paper, we combine the reweighting and shifting methods by replacing the particle filter used in the SMC^2 algorithm of Chopin et al. (2013), with the ensemble Kalman filter. Hence, parameter particles are weighted according to the estimated observed-data likelihood from the latest observation computed by the EnKF, and particle diversity is maintained via a resample-move step that targets the marginal parameter posterior under the EnKF. Extensions to the resulting algorithm are proposed, such as the use of a delayed acceptance kernel in the rejuvenation step and incorporation of nonlinear observation models. We illustrate the resulting methodology via several applications.

翻译：集成卡尔曼滤波器（EnKF）是一种流行的状态空间模型（SSM）推断技术，尤其适用于动态过程高维的情形。与序列蒙特卡洛（SMC，即粒子滤波器）等重加权方法不同，EnKF利用SSM的线性高斯结构或其近似形式，通过基于平移的更新来维持采样潜状态（即所谓的集成成员）的多样性。使用EnKF进行参数与状态联合推断通常通过将静态参数增广至状态向量来实现。此时假定参数与状态均服从线性高斯状态空间模型，这在实践中可能不合理。本文通过用集成卡尔曼滤波器替代Chopin等人（2013）SMC^2算法中使用的粒子滤波器，将重加权与平移方法相结合。据此，参数粒子根据EnKF从最新观测计算出的估计观测数据似然进行加权，并通过目标为EnKF下边际参数后验的再抽样-移动步骤维持粒子多样性。我们提出了该算法的扩展，例如在焕新步骤中使用延迟接受核及融合非线性观测模型。通过多个应用实例演示了所提方法的有效性。