Integrity Attacks on Remote Estimation Under Sequential Detection

This note investigates the worst-case performance of multi-sensor remote estimation compromised by integrity attacks. In addition to the residual-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\chi ^{2}$</tex-math></inline-formula> detector commonly deployed for unreliable sensors, the reliability of certain sensors allows for a second detector to be applied sequentially. This enhanced detection mechanism imposes stricter stealthiness constraints on integrity attacks, thereby increasing the complexity of vulnerability analysis. To characterize the maximum degradation in estimation performance, we propose a novel attack pattern that is constructed based on an efficient utilization of available information. The resulting worst-case performance and corresponding optimal attacks can be derived in closed form. The optimality of the proposed strategies among all feasible attacks is confirmed by analyzing the structure of the associated optimization problem. To improve practical applicability, we further consider attacks without access to reliable sensor data. By specifying the feasibility condition and deriving the optimal attacks, the vulnerability is more clearly revealed. Finally, numerical simulations are provided to validate the theoretical findings.