论文标题
基于能量的深层分裂方法，用于非线性过滤问题
An energy-based deep splitting method for the nonlinear filtering problem
论文作者
论文摘要
本文的目的是探索深度学习的使用来解决非线性过滤问题。这是通过通过深层分裂方法求解Zakai方程来实现的，该方法先前开发用于（随机）部分微分方程的近似解。这与深层神经网络近似功能近似的基于能量的模型结合在一起。这导致了一个计算快速过滤器，该过滤器将观测值视为输入，并且在收到新观察时不需要重新训练。该方法在四个示例上进行了测试，一个和二十个维度的两个线性和一个维度的两个非线性。当针对Kalman滤波器和引导粒子滤波器进行基准测试时，该方法显示出有希望的性能。
The purpose of this paper is to explore the use of deep learning for the solution of the nonlinear filtering problem. This is achieved by solving the Zakai equation by a deep splitting method, previously developed for approximate solution of (stochastic) partial differential equations. This is combined with an energy-based model for the approximation of functions by a deep neural network. This results in a computationally fast filter that takes observations as input and that does not require re-training when new observations are received. The method is tested on four examples, two linear in one and twenty dimensions and two nonlinear in one dimension. The method shows promising performance when benchmarked against the Kalman filter and the bootstrap particle filter.
