Optimal Linear Stealthy Attacks on Remote State Estimation: A Colored Noise-Based Approach

This article focuses on the design of optimal linear stealthy (OLS) attacks with colored noises for linear cyber-physical systems (CPSs). Unlike existing linear attacks that neglect the autocorrelation of attack signals, OLS attacks with colored noises are more destructive while eliminating their impact on the residuals. By leveraging eigendecomposition and matrix splitting methods, explicit solutions for optimal attacks are derived by solving two distinct optimization problems. To illustrate the superiority of such attack behaviors, we further investigate OLS attacks with colored noises and historical innovations, where the leverage of historical data is maximized to enhance attack performances. Finally, we provide an illustration of the effectiveness of these attacks through an example of an uncrewed aerial vehicle (UAV).