  We address the problem of distributed state estimation of a linear dynamical
process in an attack-prone environment. Recent attempts to solve this problem
impose stringent redundancy requirements on the measurement and communication
resources of the network. In this paper, we take a step towards alleviating
such strict requirements by exploring two complementary directions: (i) making
a small subset of the nodes immune to attacks, or "trusted", and (ii)
incorporating diversity into the network. We define graph-theoretic constructs
that formally capture the notions of redundancy, diversity, and trust. Based on
these constructs, we develop a resilient estimation algorithm and demonstrate
that even relatively sparse networks that either exhibit node-diversity, or
contain a small subset of trusted nodes, can be just as resilient to
adversarial attacks as more dense networks. Finally, given a finite budget for
network design, we focus on characterizing the complexity of (i) selecting a
set of trusted nodes, and (ii) allocating diversity, so as to achieve a desired
level of robustness. We establish that, unfortunately, each of these problems
is NP-complete.
