Optimal space-time attacks on system state estimation under a sparsity constraint

System state estimation in the presence of an adversary that injects false information into sensor readings has attracted much attention in wide application areas, such as target tracking with compromised sensors, secure monitoring of dynamic electric power systems, secure driverless cars, and radar tracking and detection in the presence of jammers. From a malicious adversary’s perspective, the optimal strategy for attacking a multi-sensor dynamic system over sensors and over time is investigated. It is assumed that the system defender can perfectly detect the attacks and identify and remove sensor data once they are corrupted by false information injected by the adversary. With this in mind, the adversary’s goal is to maximize the covariance matrix of the system state estimate by the end of attack period under a sparse attack constraint such that the adversary can only attack the system a few times over time and over sensors. The sparsity assumption is due to the adversary’s limited resources and his/her intention to reduce the chance of being detected by the system defender. This becomes an integer programming problem and its optimal solution, the exhaustive search, is intractable with a prohibitive complexity, especially for a system with a large number of sensors and over a large number of time steps. Several suboptimal solutions, such as those based on greedy search and dynamic programming are proposed to find the attack strategies. Examples and numerical results are provided in order to illustrate the effectiveness and the reduced computational complexities of the proposed attack strategies.