Secure State Estimation for Multi-Sensor Cyber–Physical Systems Using Virtual Sensor and Deep Reinforcement Learning Under Multiple Attacks on Major Sensor

In multi-sensor Cyber-Physical Systems (CPSs), an indispensable and highly accurate sensor, referred to as the major sensor, such as GPS in the Global Navigation Satellite System (GNSS), plays a crucial role. However, despite their reliability, these sensors are susceptible to various attacks, such as false data injection and denial of service, potentially undermining state estimation accuracy. To counteract this challenge, our study presents the innovative Virtual Sensor Based Secure State Estimator (VSBSSE) framework. This system utilizes Virtual SensorNet to generate preliminary estimations when a major sensor is compromised and integrates deep reinforcement learning to refine these estimations online. We have meticulously derived and validated the upper bounds of state estimation errors within the VSBSSE framework. Comparing it to another method that employs reinforcement learning for secure state estimation and using open-source GNSS datasets, including Kitti and Multi-Spectral Stereo (MS2), our findings demonstrate that VSBSSE's average state estimation error remains below the theoretical upper limit of 10%, even amidst multiple attacks on the major sensor of CPSs.