Innovative And Additive Outlier Robust Kalman Filtering With A Robust Particle Filter

Anomaly detection is an area of considerable importance and has been subject to increasing attention in recent years. Comprehensive reviews of the area can be found in [1, 2]. The field's growing importance arises from the increasing range of applications to which anomaly detection lends itself: from fraud prevention [1, 2], to fault detection [1, 2], and even the detection of exoplanets [3]. More recently, the emergence of internet of things and the ubiquity of sensors has led to emergence of the online detection of anomalies as an important statistical challenge. Kalman filters [4] provide a convenient framework to detect anomalies within a streaming data context. In particular, they can be updated in a fully online fashion at a fixed computational cost. At each time point, Kalman filters also provide an estimate both for the expectation and variance of the next observation. These can be used to determine whether that observation is anomalous or not. However, the major drawback of Kalman filters is their lack of robustness to outliers: once the filter has encountered an outlier, it will often produce inaccurate predictions for many future time points.