标题： 带有最优重采样的推动粒子滤波器应用于杜芬振子 显示英文标题

标题： Nudged Particle Filter with Optimal Resampling Applied to the Duffing Oscillator

摘要： 高效求解连续时间信号与离散时间观测下混沌动力系统的滤波问题存在独特挑战，因为在两次观测之间被输运的分布可能会遇到导致先验分布远离观测值的分离面结构，或者分布可能分裂为多个不相连的部分。 为了感知并克服这些动力学问题，同时近似非高斯分布，引入了一种助推粒子滤波方法。 在助推粒子滤波方法中加入了一个控制项，但可能存在使粒子权重退化的潜在缺陷。 为了解决这个问题，我们引入了一种基于改进的Cramér-von Mises距离的中间重采样方法。 新方法应用于一个具有分离面结构的非混沌、无强迫的非线性Duffing振荡器的具有挑战性的场景。 我们的结果显示，它始终优于标准的带重采样的粒子滤波和原始的助推粒子滤波方法。 显示英文摘要

摘要： Efficiently solving the continuous-time signal and discrete-time observation filtering problem for chaotic dynamical systems presents unique challenges in that the advected distribution between observations may encounter a separatrix structure that results in the prior distribution being far from the observation or the distribution may become split into multiple disjoint components. In an attempt to sense and overcome these dynamical issues, as well as approximate a non-Gaussian distribution, a nudged particle filtering approach has been introduced. In the nudged particle filter method a control term is added, but has the potential drawback of degenerating the weights of the particles. To counter this issue, we introduce an intermediate resampling approach based on the modified Cram\'er-von Mises distance. The new method is applied to a challenging scenario of the non-chaotic, unforced nonlinear Duffing oscillator, which possesses a separatrix structure. Our results show that it consistently outperforms the standard particle filter with resampling and original nudged particle filter.