Neyman-Pearson准则下的低复杂度一位存储分布式检测
Low-complexity Distributed Detection with One-bit Memory Under Neyman-Pearson Criterion
摘要：
我们考虑一个多阶段的分布式检测方案，其中部署$n$传感器和融合中心（FC）来完成一个二元假设检验。在每个时间阶段，本地传感器生成二进制消息，假设在给定的假设下是空间和时间独立的，然后将它们上传到FC进行全局检测决策。我们假设一个一位的内存是可用的FC存储其决策历史，并专注于开发迭代融合方案。首先研究了在各个阶段进行Neyman-Pearson（N-P）检验的检测问题，给出了求解该问题的最优算法--预言算法，并分析了预言算法的结构特性和渐近融合性能的局限性。我们注意到的计算效率低下的预言融合，并提出了一个低复杂度的替代方案，其中似然比（LR）测试阈值调整连接到融合决策的历史压缩在一位内存。低复杂度算法大大降低了从$O(4^n)$到$O(n)$每一阶段的计算复杂度。我们表明，该算法是能够指数收敛到相同的检测概率的预言之一。此外，收敛速度被证明是渐近相同的预言机算法。最后，数值模拟和真实世界的实验证明了我们的分布式算法的有效性和效率。
英文摘要：
We consider a multi-stage distributed detection scenario, where $n$ sensors and a fusion center (FC) are deployed to accomplish a binary hypothesis test. At each time stage, local sensors generate binary messages, assumed to be spatially and temporally independent given the hypothesis, and then upload them to the FC for global detection decision making. We suppose a one-bit memory is available at the FC to store its decision history and focus on developing iterative fusion schemes. We first visit the detection problem of performing the Neyman-Pearson (N-P) test at each stage and give an optimal algorithm, called the oracle algorithm, to solve it. Structural properties and limitation of the fusion performance in the asymptotic regime are explored for the oracle algorithm. We notice the computational inefficiency of the oracle fusion and propose a low-complexity alternative, for which the likelihood ratio (LR) test threshold is tuned in connection to the fusion decision history compressed in the one-bit memory. The low-complexity algorithm greatly brings down the computational complexity at each stage from $O(4^n)$ to $O(n)$. We show that the proposed algorithm is capable of converging exponentially to the same detection probability as that of the oracle one. Moreover, the rate of convergence is shown to be asymptotically identical to that of the oracle algorithm. Finally, numerical simulations and real-world experiments demonstrate the effectiveness and efficiency of our distributed algorithm.
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