  This paper studies resilient distributed estimation under measurement
attacks. A set of agents each makes successive local, linear, noisy
measurements of an unknown vector field collected in a vector parameter. The
local measurement models are heterogeneous across agents and may be locally
unobservable for the unknown parameter. An adversary compromises some of the
measurement streams and changes their values arbitrarily. The agents' goal is
to cooperate over a peer-to-peer communication network to process their
(possibly compromised) local measurements and estimate the value of the unknown
vector parameter. We present SAGE, the Saturating Adaptive Gain Estimator, a
distributed, recursive, consensus+innovations estimator that is resilient to
measurement attacks. We demonstrate that, as long as the number of compromised
measurement streams is below a particular bound, then, SAGE guarantees that all
of the agents' local estimates converge almost surely to the value of the
parameter. The resilience of the estimator -- i.e., the number of compromised
measurement streams it can tolerate -- does not depend on the topology of the
inter-agent communication network. Finally, we illustrate the performance of
SAGE through numerical examples.
