通过在线方法调整序贯蒙特卡罗方法中粒子数的收敛性
Adapting the Number of Particles in Sequential Monte Carlo Methods through an Online Scheme for Convergence Assessment
摘要：
粒子滤波器被广泛用于通过加权粒子集来近似状态空间模型中隐藏状态的后验分布。虽然当粒子数趋于无穷大时，滤波器的收敛性得到保证，但近似的质量通常是未知的，但强烈依赖于粒子数。本文提出了一种新的在线评估粒子滤波器收敛性的方法，以及一种基于收敛性评估的粒子数在线自适应的简单方案。该方法是基于实际观测值和由滤波器近似的预测概率分布之间的顺序比较。我们提供了一个严格的理论分析所提出的方法，并作为其实际应用的一个例子，我们提出了一个简单的算法的动态和在线自适应的粒子数量在操作过程中的粒子滤波器的随机版本的洛伦兹系统的模拟。
英文摘要：
Particle filters are broadly used to approximate posterior distributions of hidden states in state-space models by means of sets of weighted particles. While the convergence of the filter is guaranteed when the number of particles tends to infinity, the quality of the approximation is usually unknown but strongly dependent on the number of particles. In this paper, we propose a novel method for assessing the convergence of particle filters online manner, as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment. The method is based on a sequential comparison between the actual observations and their predictive probability distributions approximated by the filter. We provide a rigorous theoretical analysis of the proposed methodology and, as an example of its practical use, we present simulations of a simple algorithm for the dynamic and online adaption of the number of particles during the operation of a particle filter on a stochastic version of the Lorenz system.
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