This paper studies the problem of optimal deception attacks on remote state estimation, where an interval ${\chi }^2$ detector is deployed to reveal anomalies. The information-based attack policy that can bypass the anomaly detector and cause the maximum estimation quality degradation is derived. For both attacks with strict and relaxed stealthiness, the optimal compromised measurements can be designed with three steps: obtain the minimum mean-square error estimation of the prediction error, de-correlate the estimate with historical compromised innovations, and design the compromised innovation as an optimal linear transformation. All available information for attackers is fully utilized for performance maximization while the stealthiness constraint is satisfied precisely to deceive the anomaly detector. The attack effect depends on both the amount of online information and the duration of detection interval. Contrary to well-studied innovation-based attacks using static linear combinations, the information-based deception policy is shown to be generated by a linear time-varying system, whose coefficients can be completely determined offline. The optimality of the proposed attack is verified with numerical examples and comparative studies.

本文研究了远程状态估计的最优欺骗攻击问题，其中一个区间${\chi }^{\mathrm{2个}}$部署检测器以揭示异常。推导了可以绕过异常检测器并导致最大估计质量下降的基于信息的攻击策略。对于具有严格和宽松隐身性的两种攻击，可以通过三个步骤设计最佳折衷测量：获得预测误差的最小均方误差估计，将估计与历史折衷创新去相关，并将折衷创新设计为最佳线性变换。攻击者的所有可用信息都被充分利用以实现性能最大化，同时精确满足隐身性约束以欺骗异常检测器。攻击效果取决于在线信息量和检测间隔的持续时间。与使用静态线性组合进行充分研究的基于创新的攻击相反，基于信息的欺骗策略被证明是由线性时变系统生成的，其系数可以完全离线确定。通过数值示例和比较研究验证了所提出攻击的最优性。