Distributed Estimation Over Directed Graphs Resilient to Sensor Spoofing

This article addresses the problem of distributed estimation of an unknown dynamic parameter by a multiagent system over a directed communication network in the presence of an adversarial attack on the agents' sensors. The mode of attack of the adversaries is to corrupt the sensor measurements of some of the agents, while the communication and information processing capabilities of those agents remain unaffected. To ensure that all the agents, both normal and those under attack, are able to correctly estimate the parameter value, the Resilient Estimation through Weight Balancing (REWB) algorithm is introduced. The only condition required for the REWB algorithm to guarantee resilient estimation is that at any given point in time, less than half of the total number of agents are under attack. This article discusses the development of the REWB algorithm using the concepts of weight balancing of directed graphs and the consensus+innovation approach for linear estimation. Numerical simulations are presented to illustrate the performance of our algorithm over directed graphs under different conditions of adversarial attacks.