This paper explores the problems of robust information fusion for wireless sensor networks with state delay, parameter uncertainty, and communication constraints. Based on a data-driven transmission strategy, the robust fusion estimator proposed in this paper can greatly reduce the possibility of network congestion, while ensuring the accuracy of the estimation fusion. The uncertainty of random parameters in the model is not limited to special forms, which means that this estimator is applicable to a wide range of situations. The pseudo cross covariance matrix used for estimation fusion is derived by local robust state estimation algorithm, which is based on state augmentation and expectation minimization of estimation errors. Furthermore, we prove that the error variance of this fusion estimator is uniformly bounded, and the corresponding condition is given. According to this condition, the selection of key matrices and vectors in the transmission strategy is determined. Finally, some numerical simulations are utilized to verify the performance of this algorithm.