  This paper presents a new approach to distributed linear filtering and
prediction. The problem under consideration consists of a random dynamical
system observed by a multi-agent network of sensors where the network is
sparse. Inspired by the consensus+innovations type of distributed estimation
approaches, this paper proposes a novel algorithm that fuses the concepts of
consensus and innovations. The paper introduces a definition of distributed
observability, required by the proposed algorithm, which is a weaker assumption
than that of global observability and connected network assumptions combined
together. Following first principles, the optimal gain matrices are designed
such that the mean-squared error of estimation is minimized at each agent and
the distributed version of the algebraic Riccati equation is derived for
computing the gains.
