Abstract
This paper investigates distributed estimation of an unknown vector parameter in adversarial environments. Individual agents make successive local measurements of the unknown parameter and aim at estimating the unknown parameter consistently by sharing these measurements with their neighbors over a time-varying directed communication graph even when some of the agents are under attacks and their measurements are manipulated arbitrarily. To this end, we design push-sum-based recursive algorithms to estimate the unknown parameter for linear and nonlinear measurement models, respectively. It is demonstrated that the presented algorithms can ensure that the local estimates at all the agents converge to the true value of the parameter under some mild assumptions, such as, B-strong-connectedness of the communication topologies and a topology-independent constraint on the number of compromised measurements. A numerical example is presented to illustrate the effectiveness of the proposed algorithms.
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