Most distributed Kalman filtering (DKF) algorithms for sensor networks calculate a local estimate of the global state-vector in each node. An important challenge within distributed estimation is that all sensors in the network contribute to the local estimate in each node. In this paper, a novel DKF algorithm is proposed with the goal of attaining the above property, which is denoted as global covariance. In the considered DKF set-up each node performs two steps iteratively, i.e., it runs a standard Kalman filter using local measurements and then fuses the resulting estimates with the ones received from its neighboring nodes. The distinguishing aspect of this set-up is a novel state-fusion method, i.e., ellipsoidal intersection (EI). The main contribution consists of a proof that the proposed DKF algorithm, in combination with EI for statefusion, enjoys the desired property under similar conditions that should hold for observability of standard Kalman filters. The advantages of developed DKF with respect to alternative DKF algorithms are illustrated for a benchmark example of cooperative adaptive cruise control.