On the asymptotic variance in the central limit theorem for particle filters
On the asymptotic variance in the central limit theorem for particle filters
复制标题
关于粒子滤波器中心极限定理的渐近方差
DOI：
10.1051/ps/2010019
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Benjamin Favetto
中科院分区：
文献类型：
--
作者：
Benjamin Favetto
粒子滤波算法通过由模拟粒子群产生的一系列经验测量来近似一系列分布。在隐马尔可夫模型（HMM）中，它们提供了与这些模型相关的最优滤波器分布的近似值。给定一组观测值，研究了粒子滤波器在粒子数量趋于无穷时的渐近行为：一个中心极限定理成立，其渐近方差取决于一组固定的观测值。本文在隐马尔可夫模型的一般假设下，建立了当观测值的数目趋于无穷时，将渐近方差序列作为随机观测值的函数考虑时的紧密性。我们通过实例讨论了我们的假设，并提供了数值模拟。卡尔曼滤波的情况是单独处理的。
Particle filters algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. Given a set of observations, the asymptotic behaviour of particle filters, as the number of particles tends to infinity, has been studied: a central limit theorem holds with an asymptotic variance depending on the fixed set of observations. In this paper we establish, under general assumptions on the hidden Markov model, the tightness of the sequence of asymptotic variances when considered as functions of the random observations as the number of observations tends to infinity. We discuss our assumptions on examples and provide numerical simulations. The case of the Kalman filter is treated separately.