A particle flow filter for high-dimensional system applications,Quarterly Journal of the Royal Meteorological Society

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A particle flow filter for high-dimensional system applications
Quarterly Journal of the Royal Meteorological Society ( IF 3.0 ) Pub Date : 2021-03-23 , DOI: 10.1002/qj.4028
Chih-Chi Hu ₁ , Peter Jan van Leeuwen _{1,

2}

Affiliation

A novel particle filter proposed recently, the particle flow filter (PFF), avoids the long-existing weight degeneracy problem in particle filters and, therefore, has great potential to be applied in high-dimensional systems. The PFF adopts the idea of a particle flow, which sequentially pushes the particles from the prior to the posterior distribution, without changing the weight of each particle. The essence of the PFF is that it assumes the particle flow is embedded in a reproducing kernel Hilbert space, so that a practical solution for the particle flow is obtained. The particle flow is independent of the choice of kernel in the limit of an infinite number of particles. Given a finite number of particles, we have found that a scalar kernel fails in high-dimensional and sparsely observed settings. A new matrix-valued kernel is proposed that prevents the collapse of the marginal distribution of observed variables in a high-dimensional system. The performance of the PFF is tested and compared with a well-tuned local ensemble transform Kalman filter (LETKF) using the 1,000-dimensional Lorenz 96 model. It is shown that the PFF is comparable to the LETKF for linear observations, except that explicit covariance inflation is not necessary for the PFF. For nonlinear observations, the PFF outperforms LETKF and is able to capture the multimodal likelihood behavior, demonstrating that the PFF is a viable path to fully nonlinear geophysical data assimilation.

中文翻译：

适用于高维系统应用的颗粒流过滤器

最近提出的一种新型粒子滤波器——粒子流滤波器（PFF），避免了粒子滤波器中长期存在的权重简并问题，因此在高维系统中具有巨大的应用潜力。 PFF采用粒子流的思想，将粒子从先验分布依次推到后验分布，而不改变每个粒子的权重。 PFF的本质是假设粒子流嵌入到再生核希尔伯特空间中，从而得到粒子流的实用解。在无限数量粒子的限制下，粒子流与核的选择无关。给定有限数量的粒子，我们发现标量核在高维和稀疏观察的设置中会失败。提出了一种新的矩阵值核，可以防止高维系统中观测变量的边际分布崩溃。使用 1,000 维 Lorenz 96 模型测试 PFF 的性能，并与经过良好调整的局部集成变换卡尔曼滤波器 (LETKF) 进行比较。结果表明，对于线性观测，PFF 与 LETKF 相当，只是 PFF 不需要显式协方差膨胀。对于非线性观测，PFF 优于 LETKF，并且能够捕获多模态似然行为，这表明 PFF 是完全非线性地球物理数据同化的可行途径。

更新日期：2021-03-23

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