Detection of Sensor Attacks in Uncertain Stochastic Linear Systems

A novel attack detection scheme is developed for linear discrete-time systems with unknown dynamics that are subject to the additive process and output measurements noise. A novel stochastic adaptive observer is proposed to estimate the state vector in the presence of noisy sensor measurements and uncertain dynamics, and also to generate the innovation signal to detect attacks using a modified $\chi^{2}$ detector. It has been shown that the innovation signal, which is defined as the difference between the measured and the estimated output from the observer, has a Gaussian distribution with non-zero mean. The modified $\chi^{2}$ detector uses the steady-state bound of the innovation signal. Not only this detector can detect false data injection attacks, but also sophisticated attacks like replay attacks can be detected. The learning involved in the system acts as a watermarking signal, which helps in the detection of stealthy attacks. Simulation results are presented to support the theoretical claims.