This paper considers finite-time distributed state estimation for discrete-time nonlinear systems over sensor networks. The Round-Robin protocol is introduced to overcome the channel capacity constraint among sensor nodes, and the multiplicative noise is employed to model the channel fading. In order to improve the performance of the estimator under the situation, where the transmission resources are limited, fading channels with different stochastic properties are used in each round by allocating the resources. Sufficient conditions of the average stochastic finite-time boundedness and the average stochastic finite-time stability for the estimation error system are derived on the basis of the periodic system analysis method and Lyapunov approach, respectively. According to the linear matrix inequality approach, the estimator gains are designed. Finally, the effectiveness of the developed results are illustrated by a numerical example.
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