<p>Abnormal trajectory detection is pivotal for ensuring safety and optimizing operations in urban traffic management. Despite the progress in this field, current anomaly detection methods, such as the Spatial-Temporal Relationship (STR) algorithm, face limitations including high computational complexity due to simultaneous model calculations, delayed anomaly detection, and an inability to estimate anomalies in the remaining route during online detection. These limitations can lead to inefficiencies and reduced safety in real-world applications. In this paper, we address these limitations by introducing two novel algorithms: Anomaly Trajectory Detection based on Temporal model (ATTD) and Abnormal Trajectory Detection based on Dual Standards (ATDS). The ATTD algorithm simplifies the detection process by integrating a unified spatio-temporal model, which reduces computational complexity and accelerates the detection of anomalies. Furthermore, the ATDS algorithm introduces a proactive approach to anomaly detection that not only identifies anomalies in real-time but also predicts potential deviations in the remaining trajectory, thus providing a more comprehensive and timely detection mechanism. Through extensive experiments on real taxi trajectory datasets, we demonstrate that our algorithms significantly outperform the STR algorithm and other existing methods in terms of detection accuracy and computational efficiency. Our work contributes to the field by providing a more robust and efficient approach to anomaly trajectory detection.</p>