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This article presents anomaly detection algorithms for marine robots based on their trajectories under the influence of unknown ocean flow. A learning algorithm identifies the flow field and estimates the through-water speed of a marine robot. By comparing the through-water speed with a nominal speed range, the algorithm is able to detect anomalies causing unusual speed changes. The identified ocean flow field is used to eliminate false alarms, where an abnormal trajectory may be caused by unexpected flow. The convergence of the algorithms is justified through the theory of adaptive control. The proposed strategy is robust to speed constraints and inaccurate flow modeling. Experimental results are collected on an indoor testbed formed by the Georgia Tech Miniature Autonomous Blimp and Georgia Tech Wind Measuring Robot, while simulation study is performed for ocean flow field. Data collected in both studies confirm the effectiveness of the algorithms in identifying the through-water speed and the detection of speed anomalies while avoiding false alarms.