论文标题
一种基于PDE的自适应核法，用于解决最佳过滤问题
A PDE-based Adaptive Kernel Method for Solving Optimal Filtering Problems
论文作者
论文摘要
在本文中，我们引入了一种自适应内核方法来解决最佳过滤问题。我们采用的计算框架是贝叶斯过滤器，在该过滤器中，我们基于部分噪声观察数据对目标随机动力学系统的状态进行递归生成的最佳估计。我们用来制定状态动力学传播的数学模型是Fokker-Planck方程，我们引入了一种操作员分解方法来有效地求解Fokker-Planck方程。引入了一种自适应核法以自适应构建高斯内核，以近似目标状态的概率分布。应用贝叶斯推断将观测数据纳入状态模型仿真中。已经进行了数值实验来验证我们的内核方法的性能。
In this paper, we introduce an adaptive kernel method for solving the optimal filtering problem. The computational framework that we adopt is the Bayesian filter, in which we recursively generate an optimal estimate for the state of a target stochastic dynamical system based on partial noisy observational data. The mathematical model that we use to formulate the propagation of the state dynamics is the Fokker-Planck equation, and we introduce an operator decomposition method to efficiently solve the Fokker-Planck equation. An adaptive kernel method is introduced to adaptively construct Gaussian kernels to approximate the probability distribution of the target state. Bayesian inference is applied to incorporate the observational data into the state model simulation. Numerical experiments have been carried out to validate the performance of our kernel method.
