Detection of anomalous trajectories is an important problem in the surveillance domain. Various algorithms based on learning of normal trajectory patterns have been proposed for this problem. Yet, these algorithms typically suffer from one or more limitations: They are not designed for sequential analysis of incomplete trajectories or online learning based on an incrementally updated training set. Moreover, they typically involve tuning of many parameters, including ad-hoc anomaly thresholds, and may therefore suffer from overfitting and poorly-calibrated alarm rates. In this article, we propose and investigate the Sequential Hausdorff Nearest-Neighbor Conformal Anomaly Detector (SHNN-CAD) for online learning and sequential anomaly detection in trajectories. This is a parameter-light algorithm that offers a well-founded approach to the calibration of the anomaly threshold. The discords algorithm, originally proposed by Keogh et al. , is another parameter-light anomaly detection algorithm that has previously been shown to have good classification performance on a wide range of time-series datasets, including trajectory data. We implement and investigate the performance of SHNN-CAD and the discords algorithm on four different labeled trajectory datasets. The results show that SHNN-CAD achieves competitive classification performance with minimum parameter tuning during unsupervised online learning and sequential anomaly detection in trajectories.