This paper considers a distributed detection setup where agents in a network want to detect a time-varying signal embedded in temporally correlated noise. The signal of interest is the impulse response of an ARMA (auto-regressive moving average) filter, and the noise is the output of yet another ARMA filter which is fed white Gaussian noise. For this extended problem setup, which can prompt novel behaviour, we propose a comprehensive solution. First, we extend the well-known running consensus detector (RCD) to this correlated setup; then, we design an efficient implementation of the RCD by exploiting the underlying ARMA structures; and, finally, we derive the theoretical asymptotic performance of the RCD in this ARMA setup. It turns out that the error probability at each agent exhibits one of two regimes: either (a) the error probability decays exponentially fast to zero or (b) it converges to a strictly positive error floor. While regime (a) spans staple results in large deviation theory, regime (b) is new in distributed detection and is elicited by the ARMA setup. We fully characterize these two scenarios: we give necessary and sufficient conditions, phrased in terms of the zero and poles of the underlying ARMA models, for the emergence of each regime, and provide closed-form expressions for both the decay rates of regime (a) and the positive error floors of regime (b). Our analysis also shows that the ARMA setup leads to two novel features: (1) the threshold level used in RCD can influence the asymptotics of the error probabilities and (2) some agents might be weakly informative, in the sense that their observations do not improve the asymptotic performance of RCD and, as such, can be safely muted to save sensing resources. Numerical simulations illustrate and confirm the theoretical findings.

翻译：本文考虑分布式检测的设定，其中网络中的代理想要检测嵌入在时间相关噪声中的时变信号。感兴趣的信号是 ARMA （自回归移动平均）滤波器的脉冲响应，而噪声则是馈送白高斯噪声的另一个 ARMA 滤波器的输出。对于这个扩展的问题设置，我们提出了一个综合的方案。首先，我们将著名的运行共识检测器（RCD）扩展到这个相关设置中； 然后，我们通过利用基本的 ARMA 结构设计了一个有效的 RCD 实现； 最后，我们在这个 ARMA 设置中推导出 RCD 的理论渐近性能。结果表明，每个代理的误差概率表现出两种情况中的一种：要么（a）误差概率以指数速度快速衰减为零，要么（b）它会收敛到一个严格的正误差地板。虽然情况（a）涵盖了大偏差理论的基本结果，但情况（b）是分布式检测中的新颖现象，并且是由 ARMA 设置引起的。我们完全描述了这两种情况：我们给出了必要和充分的条件，以 ARMA 模型的零点和极点为基础，描述了每种情况的出现，并提供了两种情况的封闭表达式：情况（a）的衰减率和误差地板的积极性。 我们的分析还表明，ARMA 设置导致两个新特性：（1）RCD 中使用的阈值水平可能影响误差概率的渐近特性，并且（2）有些代理可能是信息弱的，就是说，它们的观察不会改善 RCD 的渐近性能，因此可以安全地静音以节省感知资源。数值模拟说明并验证了理论发现。