  Attack detection and mitigation strategies for cyberphysical systems (CPS)
are an active area of research, and researchers have developed a variety of
attack-detection tools such as dynamic watermarking. However, such methods
often make assumptions that are difficult to guarantee, such as exact knowledge
of the distribution of measurement noise. Here, we develop a new dynamic
watermarking method that we call covariance-robust dynamic watermarking, which
is able to handle uncertainties in the covariance of measurement noise.
Specifically, we consider two cases. In the first this covariance is fixed but
unknown, and in the second this covariance is slowly-varying. For our tests, we
only require knowledge of a set within which the covariance lies. Furthermore,
we connect this problem to that of algorithmic fairness and the nascent field
of fair hypothesis testing, and we show that our tests satisfy some notions of
fairness. Finally, we exhibit the efficacy of our tests on empirical examples
chosen to reflect values observed in a standard simulation model of autonomous
vehicles.
