This paper studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that the gain parameter optimization in a networked Kalman filter requires a centralized framework. Then, a sub-optimal distributed Kalman filter (DKF) is proposed by employing the covariance intersection (CI) fusion strategy. It is proven that the proposed DKF is of consistency, that is, an upper bound of error covariance matrix can be provided by the filter in real time. The consistency also enables the design of adaptive CI weights for better filter precision. Furthermore, the boundedness of covariance matrix and the convergence of the proposed filter are proven based on the strong connectivity of directed network topology and the global observability which permits the subsystem with local sensor's measurements to be unobservable. Meanwhile, to keep the covariance of the estimation error bounded, the proposed DKF does not require the system matrix to be nonsingular at each moment, which seems to be a necessary condition in the main DKF designs under global observability. Finally, simulation results of two examples show the effectiveness of the algorithm in the considered scenarios. (C) 2018 Elsevier Ltd. All rights reserved.