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This paper addresses a distributed event-based filtering problem for wireless sensor networks. In order to reduce the data transmission rate of the sensor nodes, we consider an event-driven transmission scheme based on the Kullback-Leibler divergence. In this scheme, each sensor node makes transmission decision only by using local data from its neighbors, and transmission occurs only if the Kullback-Leibler divergence exceeds a prescribed threshold. With this transmission scheme, we derive the optimal distributed consensus Kalman filter based on event-driven transmission. In order to get a scalable form of the filter, a suboptimal version of distributed consensus filter is then developed based on event-driven transmission. Finally, simulation studies are presented to validate the performance of the proposed algorithm.