  This work considers resilient, cooperative state estimation in unreliable
multi-agent networks. A network of agents aims to collaboratively estimate the
value of an unknown vector parameter, while an {\em unknown} subset of agents
suffer Byzantine faults. Faulty agents malfunction arbitrarily and may send out
{\em highly unstructured} messages to other agents in the network. As opposed
to fault-free networks, reaching agreement in the presence of Byzantine faults
is far from trivial. In this paper, we propose a computationally-efficient
algorithm that is provably robust to Byzantine faults. At each iteration of the
algorithm, a good agent (1) performs a gradient descent update based on noisy
local measurements, (2) exchanges its update with other agents in its
neighborhood, and (3) robustly aggregates the received messages using
coordinate-wise trimmed means. Under mild technical assumptions, we establish
that good agents learn the true parameter asymptotically in almost sure sense.
We further complement our analysis by proving (high probability) {\em
finite-time} convergence rate, encapsulating network characteristics.
