The Kalman filter as an effective tool to solve the state estimation problem for linear dynamic systems can be derived from a generalized perspective by applying the sum-product message passing over a factor graph. This viewpoint encourages us to visualize the state estimation problem over a network where all the nodes aspire to obtain consensus-based state estimates of a dynamic system by collecting sequential measurements over time. In this work, nodes process in a distributed and cooperative fashion and exchange Gaussian messages among neighbors resulting in a Gaussian belief propagation algorithm. We discuss and illustrate the performance of our proposed method under acyclic and cyclic network typologies.