测量噪声大小相关的低复杂度顺序搜索算法
Low Complexity Sequential Search with Size-Dependent Measurement Noise
摘要：
本文考虑了一个目标定位问题，在任何给定的时间代理可以选择一个区域来查询该区域中的目标的存在。假设测量噪声随着代理选择的查询区域的大小而增加。出于实际应用，如阵列处理中的初始波束对准，网络中的重击检测，机器人中的视觉搜索，我们考虑实际上重要的复杂性约束/指标：\textit{time complexity}，\textit{computational and memory complexity}，和可能的查询集的复杂性的几何形状和基数。提出了两种新的搜索策略：$dyaPM$和$hiePM$。与解决方案的实用性有关，$dyaPM$和$hiePM$是以低计算和存储复杂度实现的连通查询几何（即查询集总是连通集）。此外，$hiePM$具有分层结构，因此进一步减少了可能查询集的基数，使得$hiePM$实际上适合于诸如阵列处理中的波束成形的应用，其中存储器限制有利于较小的码本大小。通过与Extrinsic Jensen Shannon（EJS）Divergence的统一分析，证明了$dyaPM$在搜索时间复杂度上是渐近最优的（在分辨率（速率）和错误（可靠性）上都是渐近的）.另一方面，$hiePM$被证明是接近最佳的速率。此外，这两个$hiePM$和$dyaPM$被证明优于以前的工作在非渐近制度。
英文摘要：
This paper considers a target localization problem where at any given time an agent can choose a region to query for the presence of the target in that region. The measurement noise is assumed to be increasing with the size of the query region the agent chooses. Motivated by practical applications such as initial beam alignment in array processing, heavy hitter detection in networking, and visual search in robotics, we consider practically important complexity constraints/metrics: \textit{time complexity}, \textit{computational and memory complexity}, and the complexity of possible query sets in terms of geometry and cardinality. Two novel search strategy, $dyaPM$ and $hiePM$, are proposed. Pertinent to the practicality of out solutions, $dyaPM$ and $hiePM$ are of a connected query geometry (i.e. query set is always a connected set) implemented with low computational and memory complexity. Additionally, $hiePM$ has a hierarchical structure and, hence, a further reduction in the cardinality of possible query sets, making $hiePM$ practically suitable for applications such as beamforming in array processing where memory limitations favors a smaller codebook size. Through a unified analysis with Extrinsic Jensen Shannon (EJS) Divergence, $dyaPM$ is shown to be asymptotically optimal in search time complexity (asymptotic in both resolution (rate) and error (reliability)). On the other hand, $hiePM$ is shown to be near-optimal in rate. In addition, both $hiePM$ and $dyaPM$ are shown to outperform prior work in the non-asymptotic regime.
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