In this paper, we consider the problem of online asymptotic variance estimation for particle filtering and smoothing. Current solutions for the particle filter rely on the particle genealogy and are either unstable or hard to tune in practice. We propose to mitigate these limitations by introducing a new estimator of the asymptotic variance based on the so called backward weights. The resulting estimator is weakly consistent and trades computational cost for more stability and reduced variance. We also propose a more computationally efficient estimator inspired by the PaRIS algorithm of Olsson & Westerborn. As an application, particle smoothing is considered and an estimator of the asymptotic variance of the Forward Filtering Backward Smoothing estimator applied to additive functionals is provided.
翻译:在本文中,我们考虑了粒子过滤和平滑的在线无症状差异估计问题。 目前粒子过滤的解决方案依赖于粒子基因学, 并且要么不稳定, 要么在实践中很难调和。 我们提议根据所谓的后向重量对无症状差异进行新的估计, 从而减轻这些限制。 由此得出的估计数据不那么一致, 并且将计算成本转换为更稳定, 并减少差异。 我们还提议了一个由Olsson & Westerborn PARIS算法启发的更计算效率更高的估计数据。 作为应用程序, 粒子平滑会得到考虑, 并且提供用于添加功能的前向过滤向后滑动估计值的偏差的估算数据。