Anomaly Detection Under Multiplicative Noise Model Uncertainty

Venkatraman Renganathan, Benjamin J. Gravell, Justin Ruths, Tyler H. Summers

State estimators are crucial components of anomaly detectors that are used to monitor cyber-physical systems. Many frequently used state estimators are susceptible to model risk as they rely critically on the availability of an accurate state-space model. Modeling errors make it more difficult to distinguish whether deviations from expected behavior are due to anomalies or simply a lack of knowledge about the system dynamics. In this research, we account for model uncertainty through a multiplicative noise framework. Specifically, we propose two different state estimators in this setting to hedge against the model uncertainty risk namely, 1) multiplicative noise LQG, and 2) Wasserstein distributionally robust Kalman filter. The size of the residual from either estimator can then be compared against a threshold to detect anomalies. Finally, the proposed detectors are validated using numerical simulations. Extension of state-of-the-art anomaly detection in cyber-physical systems to handle model uncertainty represents the main novel contribution of the present work.

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