Unsupervised Anomaly Detection via Brownian Feature Trajectories and Stochastic Geometry
Redwane Ait-Ouammi, Ahmad Bitar, Hichem Snoussi, Alain Staron · IEEE Signal Processing Letters · 2026
Embedded sensor systems operating in heterogeneous and evolving environments face critical challenges in detecting rare or novel anomalies under strict power, communication, and supervision constraints. To address these limitations, we propose a dual-model framework that combines stochastic modeling and geometric analysis for unsupervised anomaly detection. First, we model the evolution of sensor derived feature vectors as multivariate Brownian motion trajectories, capturing both the temporal and statistical dynamics of nominal actions. This parametric representation provides interpretable descriptors, such as drift and covariance, which characterize the average direction and variability of feature evolution over time, respectively. Second, we introduce a non-parametric decision layer based on kernel density estimation and convex hulls, enabling the identification of anomalies as trajectories that traverse low-density regions or exit the geometric envelope of previously observed behaviors. This dual statistical–geometric perspective allows for real-time, unsupervised detection of anomalies without requiring labeled data or static assumptions. The proposed framework is lightweight, adaptable to multiple sensing modalities, and suitable for embedded deployment.