The vulnerability of distributed state estimator under stealthy attacks

This paper focuses on a spatially large linear system with a distributed array of sensors, each of which offers partial state measurements. Suppose that each sensor runs a distributed state estimator and they may be suffering either partially or fully manipulated stealthy attacks. A partially manipulated attack can inject data to replace the measurements from an infected sensor. While, a fully manipulated attack can totally control the infected sensor including its computation and transmission. Moreover, an attack on sensor is called stealthy if it produces bounded changes in the detection residue. We will study both the impacts of partially and fully manipulated stealthy attacks on the distributed state estimator. Correspondingly, a distributed state estimation system is called vulnerable if one of its local estimate can be destabilized by a stealthy attack. Considering both static and dynamic systems, we will provide four necessary and sufficient conditions for the vulnerability of static/dynamic system under partially/fully manipulated stealthy attacks. Numerical examples are given to illustrate the theoretical results.