We introduce a new online approach for constructing proposal distributions in particle filters using a forward scheme. Our method progressively incorporates future observations to refine proposals. This is in contrast to backward-scheme algorithms that require access to the entire dataset, such as the iterated auxiliary particle filters (Guarniero et al., 2017, arXiv:1511.06286) and controlled sequential Monte Carlo (Heng et al., 2020, arXiv:1708.08396) which leverage all future observations through backward recursion. In comparison, our forward scheme achieves a gradual improvement of proposals that converges toward the proposal targeted by these backward methods. We show that backward approaches can be numerically unstable even in simple settings. Our forward method, however, offers significantly greater robustness with only a minor trade-off in performance, measured by the variance of the marginal likelihood estimator. Numerical experiments on both simulated and real data illustrate the enhanced stability of our forward approach.

翻译：本文提出了一种新的在线方法，用于在粒子滤波中通过前向方案构建提议分布。我们的方法逐步融合未来观测以优化提议分布。这与需要访问完整数据集的后向方案算法形成对比，例如迭代辅助粒子滤波（Guarniero等人，2017，arXiv:1511.06286）和控制序贯蒙特卡洛方法（Heng等人，2020，arXiv:1708.08396），这些方法通过后向递归利用所有未来观测。相比之下，我们的前向方案实现了提议分布的渐进式改进，并收敛于这些后向方法所针对的提议分布。我们证明，即使在简单场景下，后向方法也可能出现数值不稳定性。然而，我们的前向方法在仅以边际似然估计量方差衡量的性能上作出微小妥协的同时，提供了显著更强的鲁棒性。基于模拟数据和真实数据的数值实验均验证了我们前向方法增强的稳定性。