Secure State Estimation of Cyber-Physical Systems via Gaussian Bernoulli Mixture Model

Abstract

The implementation of cyber-physical systems in real-world applications is challenged by safety requirements in the presence of sensor threats. Most cyber-physical systems, especially multi-sensor systems, struggle to detect sensor attacks when the attack model is unknown. In this paper, we tackle this issue by proposing a Gaussian-Bernoulli Secure (GBS) estimator, which transforms the detection problem into an optimal estimation problem concerning the system state and observation indicators. It encompasses two theoretical sub-problems: sequential state estimation with partial observations and estimation updates with disordered new observations. Within the framework of Kalman filter, we derive closed-form solutions for these two problems. However, due to their computational inefficiency, we propose the iterative approach employing proximal gradient descent to update the estimation in less time. Finally, we conduct experiments from three perspectives: computational efficiency, detection performance, and estimation error. Our GBS estimator demonstrates significant improvements over other methods.