Dynamic state estimation in the presence of compromised sensory data

In this article, we consider the state estimation problem of a linear time invariant system in adversarial environment. We assume that the process noise and measurement noise of the system are l∞ functions. The adversary compromises at most γ sensors, the set of which is unknown to the estimation algorithm, and can change their measurements arbitrarily. We first prove that if after removing a set of 2γ sensors, the system is undetectable, then there exists a destabilizing noise process and attacker's input to render the estimation error unbounded. For the case that the system remains detectable after removing an arbitrary set of 2γ sensors, we construct a resilient estimator and provide an upper bound on the l∞ norm of the estimation error. Finally, a numerical example is provided to illustrate the effectiveness of the proposed estimator design.