  Distributed estimation in the context of sensor networks is considered, where
distributed agents are given a set of sensor measurements, and are tasked with
estimating a target variable. A subset of sensors are assumed to be faulty. The
objective is to minimize i) the mean square estimation error at each node
(accuracy objective), and ii) the mean square distance between the estimates at
each pair of nodes (consensus objective). It is shown that there is an inherent
tradeoff between the former and latter objectives. Assuming a general
stochastic model, the sensor fusion algorithm optimizing this tradeoff is
characterized through a computable optimization problem, and a Cramer-Rao type
lower bound for the achievable accuracy-consensus loss is obtained. Finding the
optimal sensor fusion algorithm is computationally complex. To address this, a
general class of low-complexity Brooks-Iyengar Algorithms are introduced, and
their performance, in terms of accuracy and consensus objectives, is compared
to that of optimal linear estimators through case study simulations of various
scenarios.
