分布式粒子滤波器一致收敛性的证明
A proof of uniform convergence over time for a distributed particle filter
摘要：
分布式信号处理算法是近年来研究的热点。受到特别关注的一类算法是粒子滤波器（PF）。然而，大多数分布式PF涉及各种启发式或简化近似，因此，经典的收敛定理标准PF不适用于他们的分布式同行。在本文中，我们分析了一个分布式PF的基础上的非比例权重分配方案的Bolic { \em et al}（2005），并严格证明，在一定的稳定性假设下，它的渐近收敛是保证一致的时间，在这样一种方式，近似误差可以保持有界的一个固定的计算预算。为了说明理论研究结果，我们进行了目标跟踪问题的计算机模拟。数值结果表明，分布式PF有一个可以忽略不计的性能损失（相比集中式过滤器），这个问题，使我们能够经验验证分析的关键假设。
英文摘要：
Distributed signal processing algorithms have become a hot topic during the past years. One class of algorithms that have received special attention are particles filters (PFs). However, most distributed PFs involve various heuristic or simplifying approximations and, as a consequence, classical convergence theorems for standard PFs do not hold for their distributed counterparts. In this paper, we analyze a distributed PF based on the non-proportional weight-allocation scheme of Bolic {\em et al} (2005) and prove rigorously that, under certain stability assumptions, its asymptotic convergence is guaranteed uniformly over time, in such a way that approximation errors can be kept bounded with a fixed computational budget. To illustrate the theoretical findings, we carry out computer simulations for a target tracking problem. The numerical results show that the distributed PF has a negligible performance loss (compared to a centralized filter) for this problem and enable us to empirically validate the key assumptions of the analysis.
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