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 the bootstrap particle filter in the regime of highly informative observations, when the observations are extreme under the model, and if the state dimension is large.
翻译:本文涉及对离散观测的非线性扩散过程的在线过滤。 我们的方法基于完全调整的辅助粒子过滤器, 其中包括Doob通常难以处理的$h$的变异器。 我们提出了一个计算框架,通过使用非线性Feynman-Kac公式和神经网络解决后向的Kolmogorov方程式和神经网络来接近这些变异。 该方法允许在数据模拟程序之前对本地最佳的粒子过滤器进行培训。 数字实验表明,在高度信息化的观察体系中,当观测是极端的时,如果国家层面是巨大的,那么拟议的方法可以比靴状粒子过滤器的效率更高。