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In this paper, the robust information fusion Kalman filtering problem is considered for multi-sensor systems with parameter uncertainties, randomly delayed measurements and sensor failures. The stochastic parameter perturbations are included in the state space models such that the proposed fusion estimator has robustness for the varying system parameters. For each observation subsystem, multiple binary random variables with known probabilities are introduced to model sensor failures and random delays in the measurements. Without resorting to the augmentation of system states and measurements, a robust optimal recursive filter for each subsystem is derived in the linear minimum variance sense by using the innovation analysis method, and the estimation error cross-covariance matrix between any two subsystems is given recursively. Based on the optimal fusion algorithm weighted by matrices, a robust distributed state fusion Kalman filter is derived for the considered system, and the dimension of the designed filter is the same as the original system, which can reduce computation costs as compared with the augmentation method. Moreover, the performance of the designed fusion filter is dependent on the sensor failure rates. Finally, two illustrative examples are given to show the effectiveness of the proposed method.