标题： 关于辅助粒子滤波 显示英文标题

标题： On the auxiliary particle filter

摘要： 在本文中，我们研究了由Pitt和Shephard（1999）提出的辅助粒子滤波器（APF）所产生的加权样本的渐近性质。除了建立平滑粒子估计的中心极限定理（CLT）外，我们还推导了有限粒子样本大小下相同估计的Lp误差和偏差的界限。通过检查CLT渐近方差的递归公式，我们确定了第一阶段重要性权重，使得算法单次迭代中渐近方差的增加最小。基于这些发现，我们讨论并通过几个例子展示了如何改进APF算法。 显示英文摘要

摘要： In this article we study asymptotic properties of weighted samples produced by the auxiliary particle filter (APF) proposed by pitt and shephard (1999). Besides establishing a central limit theorem (CLT) for smoothed particle estimates, we also derive bounds on the Lp error and bias of the same for a finite particle sample size. By examining the recursive formula for the asymptotic variance of the CLT we identify first-stage importance weights for which the increase of asymptotic variance at a single iteration of the algorithm is minimal. In the light of these findings, we discuss and demonstrate on several examples how the APF algorithm can be improved.