非高斯观测下一致+新息分布式检测的大偏差性能
Large Deviations Performance of Consensus+Innovations Distributed Detection with Non-Gaussian Observations
摘要：
我们建立了随机网络上具有一般（非高斯）传感器观测的共识+创新分布式检测的大偏差渐近性能（误差指数）。在每个时刻，传感器1）将其与其邻居的决策变量相结合（共识），2）吸收其新的观察结果（创新）。本文表明，对于一般的非高斯分布，共识+创新分布式检测表现出相对于网络连通度的相变行为。在阈值以上，分布式与集中式一样好，具有相同的最佳渐近检测性能，但是，在阈值以下，分布式检测相对于集中式检测是次优的。我们确定这个阈值，并量化低于阈值的性能损失。最后，我们展示了阈值和性能对观测分布的依赖性：在同一随机网络上的分布式检测器，但具有不同的观测分布，例如高斯，拉普拉斯或量化，可能具有不同的渐近性能，即使相应的集中式检测器具有相同的渐近性能。
英文摘要：
We establish the large deviations asymptotic performance (error exponent) of consensus+innovations distributed detection over random networks with generic (non-Gaussian) sensor observations. At each time instant, sensors 1) combine theirs with the decision variables of their neighbors (consensus) and 2) assimilate their new observations (innovations). This paper shows for general non-Gaussian distributions that consensus+innovations distributed detection exhibits a phase transition behavior with respect to the network degree of connectivity. Above a threshold, distributed is as good as centralized, with the same optimal asymptotic detection performance, but, below the threshold, distributed detection is suboptimal with respect to centralized detection. We determine this threshold and quantify the performance loss below threshold. Finally, we show the dependence of the threshold and performance on the distribution of the observations: distributed detectors over the same random network, but with different observations' distributions, for example, Gaussian, Laplace, or quantized, may have different asymptotic performance, even when the corresponding centralized detectors have the same asymptotic performance.
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