Optimal resilient sensor placement problem for secure state estimation

Abstract

In this paper, we consider a sensor placement problem for secure state estimation in an adversarial environment. Specifically, this paper deals with a system consisting of n agents where up to l sensor measurements are potentially compromised by malicious adversaries and tackles the problem of sensor placement such that the system state can be reconstructed even if the measurements are compromised. However, since it is costly to deploy sensors for all agents, we also aim to place sensors at the lowest possible cost. We call this problem the optimal resilient sensor placement problem (ORSPP) and show that this problem is coNP-hard. Therefore, it is, in general, impossible to compute the ORSPP in polynomial time unless P=coNP. On the positive side, however, we also provide that this problem can be solved in polynomial time if the network structure of the agents satisfies certain conditions. The concrete algorithm for the ORSPP is provided, and further, in the process of providing the coNP-hardness, we also derive a new form of a necessary and sufficient condition for secure state estimation. Finally, we show the results of numerical simulations using a random graph and a diffusion process.