  This paper addresses the problem of distributed estimation of an unknown
dynamic parameter by a multi-agent 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 as
well as 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. The paper discusses the development of
the REWB algorithm using the concepts of weight balancing of directed graphs,
and the consensus+innovations approach for linear estimation. Numerical
simulations are presented to illustrate the performance of our algorithm over
directed graphs under different conditions of adversarial attacks.
