  We consider the problem of distributed state estimation of a linear
time-invariant (LTI) system by a network of sensors. We develop a distributed
observer that guarantees asymptotic reconstruction of the state for the most
general class of LTI systems, sensor network topologies and sensor measurement
structures. Our analysis builds upon the following key observation - a given
node can reconstruct a portion of the state solely by using its own
measurements and constructing appropriate Luenberger observers; hence it only
needs to exchange information with neighbors (via consensus dynamics) for
estimating the portion of the state that is not locally detectable. This
intuitive approach leads to a new class of distributed observers with several
appealing features. Furthermore, by imposing additional constraints on the
system dynamics and network topology, we show that it is possible to construct
a simpler version of the proposed distributed observer that achieves the same
objective while admitting a fully distributed design phase. Our general
framework allows extensions to time-varying networks that result from
communication losses, and scenarios including faults or attacks at the nodes.
