Remote State Estimation under Stochastic Stealthy Attacks: Short-Term Optimization and Long-Term Convergence Analysis

Abstract

This paper investigates the problem of remote state estimation in cyber-physical systems subject to stochastic stealthy attacks. Unlike existing studies that assume persistent intrusion, the attack success is modeled as a stochastic process, thereby providing a more realistic characterization of adversarial capabilities. A comprehensive analysis is conducted from both short-term and long-term perspectives. In the short-term analysis, the evolution of the estimation error covariance is examined, and optimal attack strategies are derived under explicit stealthiness constraints, which limit the detection probability of the attacker. In the long-term analysis, the conditions under which the expected estimation error covariance diverges or converges are explored as a function of the attack success rate and strategy. Rigorous necessary, sufficient, and equivalent conditions for error covariance divergence are established. Moreover, the convergence behavior of the estimation process is characterized under various attack designs, revealing critical thresholds and trade-offs between attack frequency and intensity. Simulation results are provided to validate the theoretical findings and to illustrate the quantitative impact of attack parameters on estimation performance degradation.