A distributed Kalman filter with global covariance

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 Alter 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 state-fusion, 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.