随机网络上的分布式检测：大偏差分析
Distributed Detection over Random Networks: Large Deviations Analysis
摘要：
通过大偏差理论证明了运行一致性的性能与（渐近）最优集中式检测器的性能是渐近等价的。运行一致性是最近提出的一种随机近似型传感器网络分布式检测算法。在每个时间步，每个传感器的状态通过其自身状态和其邻居状态的局部平均（共识）以及新观测（创新）来更新。我们假设高斯，空间相关的观察，我们允许底层网络随机变化。本文通过大偏差表明，贝叶斯概率的检测错误，分布式检测器，衰减在最佳可实现的速率，即，的BADFF信息率。数值例子说明了有限数量的观测分布式检测器的行为。
英文摘要：
We show by large deviations theory that the performance of running consensus is asymptotically equivalent to the performance of the (asymptotically) optimal centralized detector. Running consensus is a stochastic approximation type algorithm for distributed detection in sensor networks, recently proposed. At each time step, the state at each sensor is updated by a local averaging of its own state and the states of its neighbors (consensus) and by accounting for the new observations (innovation). We assume Gaussian, spatially correlated observations, and we allow for the underlying network to be randomly varying. This paper shows through large deviations that the Bayes probability of detection error, for the distributed detector, decays at the best achievable rate, namely, the Chernoff information rate. Numerical examples illustrate the behavior of the distributed detector for finite number of observations.
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