Optimality of the auxiliary particle filter
Optimality of the auxiliary particle filter
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发表时间：
2009
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通讯作者：
R. Douc;É. Moulines;J. Olsson
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作者：
R. Douc;É. Moulines;J. Olsson
本文研究了Pitt和Shephard [17]提出的辅助粒子滤波器（APF）产生的加权样本的渐近性质。除了建立一个中心极限定理（CLT）的光滑粒子估计，我们也得到了有限的粒子样本大小的Lp误差和偏差的界限。通过检查CLT的渐近方差的递归公式，我们确定了第一阶段的重要性权重，其中在算法的单次迭代中渐近方差的增加是最小的。根据这些发现，我们讨论并演示了几个例子如何APF算法可以改进。
In this article we study asymptotic properties of weighted samples produced by the auxiliary particle filter (APF) proposed by Pitt and Shephard [17]. 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.