Partile filter code with an example of weight collapse in importance sampling methods

We propose an implementation of the particle filter in a quasi-static case in the example of Gaussian prior with independent and identically distributed prior states and observation errors. Weight collapse occurs in the particle filter when the number of model states and observations increases for a given ensemble size. In this example, we use a synthetic experiment to illustrate how weight collapse varies in the posterior distribution.This code provides a basis for the implementation of importance sampling methods and can be easily adapted to other problems.本研究提出了一种准静态场景下粒子滤波器 (particle filter) 的实现方案，该方案以带有独立同分布 (independent and identically distributed) 先验状态与观测误差的高斯先验 (Gaussian prior) 为示例场景。当给定集合规模时，随着模型状态与观测数量的增加，粒子滤波器会出现权值坍缩问题。本示例通过合成实验，展示了权值坍缩在后验分布 (posterior distribution) 中的变化规律。本代码为重要性采样 (importance sampling) 方法的实现提供了基础框架，且可便捷适配至其他相关问题。