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This paper presents a fully distributed state estimation algorithm for wide-area monitoring in power systems. Through iterative information exchange with designated neighboring control areas, all the balancing authorities (control areas) can achieve an unbiased estimate of the entire power system's state. In comparison with existing hierarchical or distributed state estimation methods, the novelty of the proposed approach lies in that: 1) the assumption of local observability of all the control areas is no longer needed; 2) the communication topology can be different than the physical topology of the power interconnection; and 3) for DC state estimation, no coordinator is required for each local control area to achieve provable convergence of the entire power system's states to those of the centralized estimation. The performance of both DC and AC state estimation using the proposed algorithm is illustrated in the IEEE 14-bus and 118-bus systems.