  In this paper, we study resilient distributed diffusion for multi-task
estimation in the presence of adversaries where networked agents must estimate
distinct but correlated states of interest by processing streaming data. We
show that in general diffusion strategies are not resilient to malicious agents
that do not adhere to the diffusion-based information processing rules. In
particular, by exploiting the adaptive weights used for diffusing information,
we develop time-dependent attack models that drive normal agents to converge to
states selected by the attacker. We show that an attacker that has complete
knowledge of the system can always drive its targeted agents to its desired
estimates. Moreover, an attacker that does not have complete knowledge of the
system including streaming data of targeted agents or the parameters they use
in diffusion algorithms, can still be successful in deploying an attack by
approximating the needed information. The attack models can be used for both
stationary and non-stationary state estimation.In addition, we present and
analyze a resilient distributed diffusion algorithm that is resilient to any
data falsification attack in which the number of compromised agents in the
local neighborhood of a normal agent is bounded. The proposed algorithm
guarantees that all normal agents converge to their true target states if
appropriate parameters are selected. We also analyze trade-off between the
resilience of distributed diffusion and its performance in terms of
steady-state mean-square-deviation (MSD) from the correct estimates. Finally,
we evaluate the proposed attack models and resilient distributed diffusion
algorithm using stationary and non-stationary multi-target localization.
