This survey provides an extensive overview of the state-of-the-art model-based online semi-supervised and unsupervised anomaly detection algorithms used on multivariate time series. It also outlines the most popular benchmark datasets used in literature, as well as a novel taxonomy where a distinction between online and offline, and training and inference is made. To achieve this, almost 50 peer-reviewed publications are surveyed and categorised into different model families to paint a clear picture of the anomaly detection landscape for the reader. Then, where possible, a comparison of the anomaly detection performance of the surveyed approaches is provided and the key research gaps are highlighted. It is concluded that few approaches propose any enhancements that involve the user feedback. In addition to that, transformer-based models seem to have found little application in anomaly detection so far, though this is most likely due to the novelty of the model type, not necessarily due to the lack of potential. Moreover, there is no standard benchmark procedure to assess anomaly detection performance. A variety of different datasets and evaluation metrics used for evaluation are used hence it is difficult to draw conclusions from comparisons between papers. Lastly, the rarity of approaches trained and inferred in an online manner is also pointed out, possibly explained by the lower performance compared to offline trained approaches.
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