To ensure the safety of a spacecraft, operators collect thousands of telemetry signals and monitor them for anomalies, which is both expensive and time-consuming. Space agencies have been researching Machine Learning (ML)-based Time Series Anomaly Detection (TSAD) methods to improve automation, but this is hindered by a lack of high-quality benchmarks. This thesis explores the application of ML-based TSAD on instrument telemetry data for the XMM-Newton space telescope. The data was explored to find several unique challenges, such as recurring eclipses and a high volume of missing data. A methodology was then developed to pre-process the raw data into an ML-compatible format, detect anomalies using a semi-supervised forecasting approach and post-process the detections into a benchmark-suitable format. The method yielded over 40 detections, which were partially validated in discussion with instrument engineers. A refined methodology, incorporating areas for improvement, is presented to proceed with an eventual XMM-Newton anomaly benchmark.