During decades, estimation and detection tasks in many Signal Processing and Communications applications have been significantly improved by using subspace and component-based techniques. More recently, subspace methods have been adopted in many hot topics such as Machine Learning, Data Analytics or smart MIMO communications, in order to have a geometric interpretation of the problem. In that way, the Subspace-based algorithms often arise new approaches for already-explored problems, while offering the valuable advantage of giving interpretability to the procedures and solutions. On the other hand, in those recent hot topics, one may also find applications where the detection of unwanted or out-of-the-model artifacts and outliers is crucial. To this extend, we were previously working in the domain of GNSS PPP, detecting phase ambiguities, where we found motivation into the development of novel solutions for this application. After considering the applications and advantages of subspace-based approaches, this work will be focused on the exploration and extension of the ideas of subspace learning in the context of anomaly detection, where we show promising and original results in the areas of anomaly detection and subspace-based anomaly detection, in the form of two new algorithms: the Dual Ascent for Sparse Anomaly Detection and the Subspace-based Dual Ascent for Anomaly Detection and Tracking
