In this paper, we address the problem of distributed state estimation, where a set of nodes are required to jointly estimate the state of a linear dynamic system based on sequential measurements. In our distributed scenario, all the nodes 1) are interested in the full state of the observed system and 2) pursue a consensus-based state estimate with high accuracy. We exploit the equivalent relation between the maximum-a-posteriori (MAP) estimation and the Kalman filter (KF) in the minimum mean square error (MMSE) sense under the Gaussian assumption. Utilizing this relation, a distributed Kalman filtering algorithm is derived, which ensures consensus-based state estimates among nodes and converges to the optimal central KF solution.