Department of Applied Mathematics, University of Colorado, Boulder, CO, United States of America.
PLoS One. 2021 Mar 11;16(3):e0248266. doi: 10.1371/journal.pone.0248266. eCollection 2021.
A hybrid particle ensemble Kalman filter is developed for problems with medium non-Gaussianity, i.e. problems where the prior is very non-Gaussian but the posterior is approximately Gaussian. Such situations arise, e.g., when nonlinear dynamics produce a non-Gaussian forecast but a tight Gaussian likelihood leads to a nearly-Gaussian posterior. The hybrid filter starts by factoring the likelihood. First the particle filter assimilates the observations with one factor of the likelihood to produce an intermediate prior that is close to Gaussian, and then the ensemble Kalman filter completes the assimilation with the remaining factor. How the likelihood gets split between the two stages is determined in such a way to ensure that the particle filter avoids collapse, and particle degeneracy is broken by a mean-preserving random orthogonal transformation. The hybrid is tested in a simple two-dimensional (2D) problem and a multiscale system of ODEs motivated by the Lorenz-'96 model. In the 2D problem it outperforms both a pure particle filter and a pure ensemble Kalman filter, and in the multiscale Lorenz-'96 model it is shown to outperform a pure ensemble Kalman filter, provided that the ensemble size is large enough.
一种混合粒子集合卡尔曼滤波器被开发出来用于解决中等非高斯性问题，即先验非常非高斯但后验近似高斯的问题。这种情况会出现在，例如，当非线性动力学产生非高斯预测，但紧密的高斯似然导致几乎高斯的后验时。混合滤波器首先对似然函数进行因式分解。首先，粒子滤波器使用似然函数的一个因子同化观测值，以产生接近高斯的中间先验，然后集合卡尔曼滤波器使用剩余的因子完成同化。似然函数在这两个阶段之间如何分割是根据确保粒子滤波器避免崩溃的方式确定的，并且通过保持均值的随机正交变换打破粒子退化。该混合滤波器在一个简单的二维（2D）问题和一个由洛伦兹-96 模型启发的多尺度常微分方程组（ODEs）系统中进行了测试。在 2D 问题中，它优于纯粒子滤波器和纯集合卡尔曼滤波器，在多尺度洛伦兹-96 模型中，只要集合大小足够大，它就优于纯集合卡尔曼滤波器。
