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We address the problem of distributed state estimation of a linear dynamicalprocess in an attack-prone environment. Recent attempts to solve this problemimpose stringent redundancy requirements on the measurement and communicationresources of the network. In this paper, we take a step towards alleviatingsuch strict requirements by exploring two complementary directions: (i) makinga small subset of the nodes immune to attacks, or "trusted", and (ii)incorporating diversity into the network. We define graph-theoretic constructsthat formally capture the notions of redundancy, diversity, and trust. Based onthese constructs, we develop a resilient estimation algorithm and demonstratethat even relatively sparse networks that either exhibit node-diversity, orcontain a small subset of trusted nodes, can be just as resilient toadversarial attacks as more dense networks. Finally, given a finite budget fornetwork design, we focus on characterizing the complexity of (i) selecting aset of trusted nodes, and (ii) allocating diversity, so as to achieve a desiredlevel of robustness. We establish that, unfortunately, each of these problemsis NP-complete.

On the Impacts of Redundancy, Diversity, and Trust in Resilient Distributed State Estimation