A Neural Network-Enhanced Kalman Filter for Time Series Anomaly Detection in Cyber-Physical Systems

Cyber-physical systems (CPSs) represent sophisticated intelligent architectures that tightly couple computational elements, communication networks, and physical processes. Their deployments now span virtually every industrial and civilian domain—from power grids and manufacturing plants to autonomous transportation networks. Ensuring the secure operation of CPSs relies fundamentally on effective time series anomaly detection, which remains a challenging task due to the complex, often unknown system dynamics and non-negligible sensor noise present in real-world environments. To address these challenges, we introduce a Neural Network-Enhanced Kalman Filter (NNEKF), a novel anomaly detection framework that combines model-based filtering with data-driven learning. The NNEKF employs a two-stage trained neural network with a specialized architecture: the first stage learns the underlying dynamics of the CPS, while the second stage optimizes the computation of the Kalman gain during the update step. At inference time, the enhanced Kalman filter recursively estimates the likelihood of observed sensor measurements to identify anomalies, supported by a batched parallel inference scheme that delivers substantial speedups. Extensive experiments on benchmark datasets demonstrate that the NNEKF attains an average F1-score of 0.935, coupled with rapid inference and minimal model footprint—surpassing all competitive baselines and facilitating dependable real-time anomaly detection for CPS environments.