Given trajectories with gaps (i.e., missing data), we investigate algorithms to identify abnormal gaps in trajectories which occur when a given moving object did not report its location, but other moving objects in the same geographic region periodically did. The problem is important due to its societal applications, such as improving maritime safety and regulatory enforcement for global security concerns such as illegal fishing, illegal oil transfers, and trans-shipments. The problem is challenging due to the difficulty of bounding the possible locations of the moving object during a trajectory gap, and the very high computational cost of detecting gaps in such a large volume of location data. The current literature on anomalous trajectory detection assumes linear interpolation within gaps, which may not be able to detect abnormal gaps since objects within a given region may have traveled away from their shortest path. In preliminary work, we introduced an abnormal gap measure that uses a classical space-time prism model to bound an object's possible movement during the trajectory gap and provided a scalable memoized gap detection algorithm (Memo-AGD). In this paper, we propose a Space Time-Aware Gap Detection (STAGD) approach to leverage space-time indexing and merging of trajectory gaps. We also incorporate a Dynamic Region Merge-based (DRM) approach to efficiently compute gap abnormality scores. We provide theoretical proofs that both algorithms are correct and complete and also provide analysis of asymptotic time complexity. Experimental results on synthetic and real-world maritime trajectory data show that the proposed approach substantially improves computation time over the baseline technique.

翻译：针对带有缺失数据的轨迹中的间隙（即缺失数据）问题，本文研究了一种识别异常间隙的算法：当给定移动对象未报告其位置，而同一地理区域内的其他移动对象却定期报告时，该算法可检测此类异常现象。该问题因具有重要社会应用价值（例如提升海事安全、强化针对非法捕捞、非法石油转运及过驳等全球安全问题的监管执法）而备受关注。问题的挑战在于：轨迹间隙期间移动对象可能位置的边界难以界定，且从海量位置数据中检测间隙的计算成本极高。现有异常轨迹检测文献通常假设间隙内位置呈线性插值，但该方法可能无法检测异常间隙——因为特定区域内的对象可能偏离最短路径移动。在前期工作中，我们提出了一种基于经典时空棱镜模型的异常间隙度量方法，用于约束轨迹间隙期间对象的可能移动范围，并设计了可扩展的备忘录式间隙检测算法（Memo-AGD）。本文提出了一种时空感知间隙检测方法（STAGD），通过结合轨迹间隙的时空索引与合并技术，同时引入动态区域合并（DRM）策略高效计算间隙异常分数。我们给出了两个算法的正确性与完备性的理论证明，并分析了其渐近时间复杂度。在合成数据与真实世界海上轨迹数据上的实验结果表明，所提方法相较于基线技术显著提升了计算效率。