Interval Estimation and Attack Detection for CPSs Based on Unknown Input Observer and Watermarking

This paper proposes an improved proactive defense strategy for secure remote state estimation in cyber-physical systems (CPSs) subject to unknown-but-bounded (UBB) noises, disturbances and man-in-the-middle (MITM) attacks. First, an unknown input observer (UIO) is designed to estimate the system state. To improve the estimation accuracy, a decoupling approach, which can be used to decouple the UBB measurement noise and disturbances, is proposed to overcome the effect of measurement noises and process disturbances in the error system. Then, H∞ optimization is introduced to enhance the robustness of the error system. Subsequently, an unpredictable and time-varying zonotopic watermarking mechanism is introduced into the sensor-to-estimator communication channel. Furthermore, this proactive defense mechanism operates with strict transparency, eliminating false alarms and preserving nominal estimation performance under attack-free conditions, while inherently forcing stealthy data manipulations to violate predefined detection thresholds. Finally, numerical simulations on a second-order linear system demonstrate that the proposed strategy effectively amplifies malicious interceptions, guaranteeing reliable MITM attack detection against stealthy MITM attacks.