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  1. We address the problem of distributed state estimation of a linear dynamical process in an attack-prone environment. A network of sensors, some of which can be compromised by adversaries, aim to estimate the state of the process. In this context, we investigate the impact of making a small subset of the nodes immune to attacks, or “trusted”. Given a set of trusted nodes, we identify separate necessary and sufficient conditions for resilient distributed state estimation. We use such conditions to illustrate how even a small trusted set can achieve a desired degree of robustness (where the robustness metric is specific to the problem under consideration) that could otherwise only be achieved via additional measurement and communication-link augmentation. We then establish that, unfortunately, the problem of selecting trusted nodes is NP-hard. Finally, we develop an attack-resilient, provably-correct distributed state estimation algorithm that appropriately leverages the presence of the trusted nodes. 
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