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This paper proposes a decentralized state-estimation approach that relies on an elaborated instance of the Lagrangian relaxation decomposition technique. The proposed algorithm does not require a central coordinator but just to moderate interchanges of information among neighboring regions, and exploits the structure of the problem to achieve a fast and accurate convergence. Additionally, a decentralized bad measurement identification procedure is developed, which is efficient and robust in terms of identifying bad measurements within regions and in border tie-lines. The accuracy and efficiency of the proposed procedures are assessed by a large number of simulations, which allows drawing statistically sound conclusions.