Brownian Feature Trajectories with Geometric Decision Boundaries for Edge Anomaly Detection

Embedded sensor systems deployed in heterogeneous and evolving environments face strong constraints in power, supervision, and connectivity, which limit the applicability of classical anomaly detection methods. This paper introduces a lightweight framework for unsupervised anomaly detection based on Brownian feature trajectories. Each sensor event is modeled as a stochastic trajectory whose drift and covariance parameters summarize the nominal temporal evolution of features. To overcome the limitations of purely parametric models, the framework integrates a geometric decision layer that combines kernel density estimation with convex envelopes, enabling robust detection of trajectories that traverse low-density or out-ofbound regions. The selection of the kernel bandwidth and decision thresholds is guided by data-driven statistical rules to ensure interpretability and consistent sensitivity across devices. A statistical consistency test, based on Gaussianity and covariance conformity of increments, provides additional validation of deviations from the Brownian hypothesis. The proposed approach achieves interpretable, adaptive, and computationally efficient anomaly detection suitable for real-time edge deployment in isolated infrastructure monitoring and surveillance scenarios, where data remain specific to each use case.