Detection of sensor data injection attacks with multiplicative watermarking

In this paper, the problem of detecting stealthy false-data injection attacks on the measurements is considered. We propose a multiplicative watermarking scheme, where each sensor’s output is individually fed to a SISO watermark generator whose parameters are supposed to be unknown to the adversary. Under such a scenario, the detectability properties of the attack are analyzed and guidelines for designing the watermarking filters are derived. Fundamental limitations to the case of single-output systems are also uncovered, for which an alternative approach is proposed. The results are illustrated through numerical examples