We study distributed filtering for a class of uncertain systems over corrupted communication channels. We propose a distributed robust Kalman filter with stochastic gains, through which upper bounds of the conditional mean square estimation errors are calculated online. We present a robust collective observability condition, under which the mean square error of the distributed filter is proved to be uniformly upper bounded if the network is strongly connected. For better performance, we modify the filer by introducing a switching fusion scheme based on a sliding window. It provides a smaller upper bound of the conditional mean square error. Numerical simulations are provided to validate the theoretical results and show that the filter scales to large networks.

中文翻译：

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损坏通道上的鲁棒卡尔曼滤波器的分布式设计

我们研究了在通信通道受损的情况下针对一类不确定系统的分布式过滤。我们提出了一种具有随机增益的分布式鲁棒卡尔曼滤波器，通过它可以在线计算条件均方估计误差的上限。我们提出了一个鲁棒的集体可观察性条件，在该条件下，如果网络连接牢固，则分布式滤波器的均方误差被证明是一致的上限。为了获得更好的性能，我们通过引入基于滑动窗口的切换融合方案来修改文件管理器。它提供了条件均方误差的较小上限。提供了数值模拟，以验证理论结果，并表明该滤波器可扩展到大型网络。