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This paper addresses a distributed estimator design problem for linear systems deployed over sensor networks within a multiple communication channels (MCCs) framework. A practical scenario is taken into account such that the channel used for communication can be switched and the switching is governed by a Markov chain. With the existence of communicational imperfections and external disturbances, an estimation algorithm is proposed such that the developed distributed estimators are able to give accurate state estimates against the channel switching phenomenon. The distributed estimation framework is applied to a chemical process to illustrate the effectiveness of the proposed methodology and the superiority of the MCCs framework featured by channel switching.