Particle Filters for nonlinear data assimilation in high-dimensional systems
Particle Filters for nonlinear data assimilation in high-dimensional systems
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DOI：
10.5802/afst.1560
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
van Leeuwen;P. Jan
中科院分区：
文献类型：
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作者：
van Leeuwen;P. Jan
粒子滤波是一种用于贝叶斯推理的蒙特卡罗方法。贝叶斯推理基于贝叶斯定理，该定理规定了当系统的观测形式的新信息变得可用时，如何更新以概率密度函数编码的关于该系统的先验信息。这个过程在地球科学中被称为数据同化。这篇文章讨论了什么是粒子过滤器，以及当试图在地球科学中使用粒子过滤器时的主要问题是什么，在地球科学中，数据同化问题通常是非常高维的。一个例子是数值天气预报，其状态空间大小为10亿或更多。然后讨论了在试图克服所谓的“维度诅咒”方面取得的最新进展，例如本地化和巧妙地略微改变模型方程以通过所谓的建议密度获得更好的后验概率密度的近似。这最终导致了一类新的粒子过滤器，它确实能够提供后验概率密度的估计。重点不是数学上的严谨性，而是在这个快速发展的领域传达主要的新思想。
Particle Filters are Monte-Carlo methods used for Bayesian Inference. Bayesian Inference is based on Bayes Theorem that states how prior information about a system, encoded in a probability density function, is updated when new information in the form of observations of that system become available. This process is called data assimilation in the geosciences. This contribution discusses what particle filters are and what the main issue is when trying to use them in the geosciences, in which the data-assimilation problem is typically very high dimensional. An example is numerical weather forecasting, with a state-space size of a billion or more. Then it discusses recent progress made in trying to beat the so-called 'curse of dimensionality', such as localisation and clever ways to slightly change the model equations to obtain better approximations to the posterior probability density via so-called proposal densities. This culminates in a new class of particle filters that is indeed able to provide estimates of the posterior probability density. The emphasis is not on mathematical rigour but on conveying the main new ideas in this rapidly growing field.