We study anomaly detection in a context that considers user trajectories as input and tries to identify anomalies for users following normal routes such as taking public transportation from the workplace to home or vice versa. Trajectories are modeled as a discrete-time series of axis-parallel constraints ("boxes") in the 2-D space. The anomaly can be estimated by considering two trajectories, where one trajectory is the current movement pattern and the other is a weighted trajectory collected from N norms. The proposed system was implemented and evaluated with eight individuals with cognitive impairments. The experimental results showed that recall was 95.0% and precision was 90.9% on average without false alarm suppression. False alarms and false negatives dropped when axis rotation was applied. The precision with axis rotation was 97.6% and the recall was 98.8%. The average time used for sending locations, running anomaly detection, and issuing warnings was in the range of 15.1-22.7 s. Our findings suggest that the ability to adapt anomaly detection devices for appropriate timing of self-alerts will be particularly important.