Sequential Monte Carlo methods, also known as particle filtering, have seen an explosion of development both in theory and applications. The publication of [1] sparked huge interest in the area of sequential signal processing, particularly in sequential filtering. Ever since, the number of publications in which particle filtering plays a prominent role has continued to grow. An early reference of development is [2] and later tutorials include [3]-[9]. With particle filtering, we estimate probability density functions (pdfs) of interest by probability mass functions, whose masses are placed at randomly chosen locations (particles) and whose weights are assigned to the particles. The particle filter (PF) proposed in [1] is often called the bootstrap PF (BPF), and although it is not optimal, it is the most often used filter by practitioners. A filter that became also popular is known as the auxiliary PF (APF) and was proposed in [10]. With the APF, the objective is to generate better particles at each time step compared to those generated with the BPF, thereby improving filtering accuracy. In this article, we derive the APF from a new perspective, one based on interpreting the APF from the multiple importance sampling (MIS) paradigm. The derivation also shows its relationship with the BPF.

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通过多重重要采样阐明辅助粒子过滤器 [讲义]

顺序蒙特卡洛方法，也称为粒子滤波，在理论和应用上都得到了爆炸式的发展。[1] 的发表引起了对序列信号处理领域的极大兴趣，尤其是在序列滤波方面。从那以后，粒子过滤发挥重要作用的出版物数量持续增长。早期的开发参考是 [2]，后来的教程包括 [3]-[9]。通过粒子滤波，我们通过概率质量函数来估计感兴趣的概率密度函数 (pdf)，其质量被放置在随机选择的位置（粒子）并且其权重被分配给粒子。[1]中提出的粒子滤波器（PF）通常被称为自举PF（BPF），虽然它不是最优的，但它是从业者最常用的滤波器。一种也变得流行的过滤器被称为辅助 PF (APF)，并在 [10] 中提出。与使用 BPF 生成的粒子相比，使用 APF 的目标是在每个时间步生成更好的粒子，从而提高过滤精度。在本文中，我们从一个新的角度推导出 APF，一个基于从多重重要性采样 (MIS) 范式解释 APF 的角度。推导还显示了它与 BPF 的关系。