  We study resilient distributed field estimation under measurement attacks. A
network of agents or devices measures a large, spatially distributed physical
field parameter. An adversary arbitrarily manipulates the measurements of some
of the agents. Each agent's goal is to process its measurements and information
received from its neighbors to estimate only a few specific components of the
field. We present $\mathbf{SAFE}$, the Saturating Adaptive Field Estimator, a
consensus+innovations distributed field estimator that is resilient to
measurement attacks. Under sufficient conditions on the compromised measurement
streams, the physical coupling between the field and the agents' measurements,
and the connectivity of the cyber communication network, $\mathbf{SAFE}$
guarantees that each agent's estimate converges almost surely to the true value
of the components of the parameter in which the agent is interested. Finally,
we illustrate the performance of $\mathbf{SAFE}$ through numerical examples.
