用数学规则生成海上异常数据，提升检测模型评估可靠性

Maritime anomaly detection is essential for ensuring maritime safety, security, and efficient traffic management at sea, with Automatic Identification System (AIS) data serving as a primary data source. Despite its importance, most publicly available AIS datasets lack predefined anomaly labels, forcing prior studies to rely on either distribution-based rarity or domain rule/expert-assisted labeling. These approaches, however, face fundamental limitations: statistical rarity often fails to reflect practically critical events, while expert-based labeling is costly, subjective, and difficult to scale. Moreover, both paradigms tend to overlook interaction-driven hazards such as near-miss approaches between vessels. To address these challenges, we propose an equation-grounded anomaly taxonomy that is implementable under a limited AIS observation schema and extensible to other AIS datasets. Specifically, the taxonomy defines three anomaly types: unexpected AIS activity (A1), route deviation (A2), and close approach (A3), covering both single-vessel and inter-vessel anomalies. Building on this taxonomy, we introduce a unified score-synthesize-label pipeline that produces LLM-guided plausibility scores, uses them to synthesize anomalies, and assigns timestamp-level labels. To rigorously assess detection performance, we further design benchmark evaluation settings that account for variations in temporal-window length and anomaly-type composition, and evaluate a broad range of time-series models and anomaly detection models. Together, these contributions provide a systematic basis for evaluating maritime anomaly detection methods across different anomaly types. Our code is available at https://github.com/snudial/open-maritime-anomaly-detection.