This paper studies a distributed state estimation problem for a network of linear dynamic systems (called nodes), which evolve autonomously, but their measurements are coupled through neighborhood interactions. Power networks are typical networked systems obeying such features, with other examples including traffic networks, sensor networks and many multi-agent systems. We develop a new distributed state estimation approach, for each node to update its local state. The core of this distributed approach is a distributed maximum a posteriori (MAP) estimation technique, which delivers a globally optimal estimate under certain assumptions. We apply the distributed approach to an IEEE 118-bus system, and compare it with a centralized approach, which provides the optimal state estimate using all the measurements, and with a local state estimation approach, which uses only local measurements to estimate local states. Simulation results show that under different scenarios including normal operation, bad measurements and sudden load change, the distributed approach is clearly more accurate than the local state estimation approach and distributed static state estimation approach. Although the result is a bit less accurate than that by a centralized algorithm, the distributed algorithm enjoys low computational complexity and communication load, and is scalable to large power networks. (C) 2016 Elsevier Ltd. All rights reserved.