We address the problem of distributed filtering in a wireless sensor network and develop distributed approximations of three variants of the ensemble Kalman filter. We express the update equations in an alternative information form in order to formulate a distributed measurement update mechanism. The distributed filters use randomized gossip to reach consensus on the statistics needed to perform an update. Simulation results suggest that in the case of linear measurements and high-dimensional nonlinear measurements (with measurement model parameters known network-wide) with nonlinear state dynamics the proposed schemes achieve accuracy comparable to state-of-the-art distributed filters while significantly reducing the communication overhead.