论文标题
计算DOOB的H转换用于在线过滤的离散观察到的扩散
Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions
论文作者
论文摘要
本文与离散观察到的非线性扩散过程的在线过滤有关。我们的方法基于完全适应的辅助粒子滤波器，该滤芯涉及DOOB的$ h $转换通常是棘手的。我们提出了一个计算框架，通过使用非线性FEYNMAN-KAC公式和神经网络求解基础的落后Kolmogorov方程来近似这些$ H $转换。该方法允许人们在数据融合过程之前训练本地最佳的粒子滤波器。数值实验表明，在高度信息观测的制度中，当观测值在模型下或状态尺寸较大时，所提出的方法可以比最新信息的最新粒子过滤器更有效的数量级。
This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob's $h$-transforms that are typically intractable. We propose a computational framework to approximate these $h$-transforms by solving the underlying backward Kolmogorov equations using nonlinear Feynman-Kac formulas and neural networks. The methodology allows one to train a locally optimal particle filter prior to the data-assimilation procedure. Numerical experiments illustrate that the proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters in the regime of highly informative observations, when the observations are extreme under the model, or if the state dimension is large.
