We study real-time detection of low-rank changes in the covariance structure of high-dimensional streaming data, motivated by robotic swarm monitoring. Building on the spiked covariance model, we propose the Multi-rank Subspace-CUSUM (MRS-C) procedure, which extends classical CUSUM by tracking projection energy onto an estimated signal subspace. We analyze performance by characterizing the expected detection delay (EDD) under a prescribed average run length (ARL), deriving closed-form asymptotically optimal choices of the window size and drift. We further prove that MRS-C is first-order asymptotically optimal relative to the oracle Exact CUSUM, with an explicit efficiency constant that depends on heterogeneity in spike strengths. When the signal rank is unknown, we use a parallel procedure. Simulations and robotic swarm-behavior data illustrate robustness and effectiveness.

翻译：本研究针对机器人集群监测需求，探讨高维流数据协方差结构中低秩变化的实时检测问题。基于尖峰协方差模型，我们提出多秩子空间累积和（MRS-C）检测方法，该方法通过追踪投影到估计信号子空间上的能量，扩展了经典CUSUM算法。我们通过刻画规定平均运行长度（ARL）下的期望检测延迟（EDD）来分析算法性能，推导出窗口尺寸与漂移参数的闭式渐近最优选择。进一步证明MRS-C相对于先知精确CUSUM具有一阶渐近最优性，其显式效率常数取决于尖峰强度的异质性。当信号秩未知时，我们采用并行检测流程。仿真实验与机器人集群行为数据验证了该方法的鲁棒性与有效性。