The result of the maximum likelihood fusion criterion under the normal density function is re-derived as an optimal information fusion criterion weighted by matrices in the linear minimum variance sense. Based on the fusion criterion, an optimal information fusion decentralized Kalman filter with fault tolerance and robustness properties is given for discrete time-varying linear stochastic control systems with multiple sensors and correlated noises. It has a two-layer fusion structure. The first fusion layer has a netted parallel structure to determine the cross covariance between every pair of faultless sensors at each time step. The second fusion layer is the fusion center that fuses the estimates and variances of all local subsystems, and the cross covariance among the local subsystems from the first fusion layer to determine the optimal matrix weights and yield the optimal fusion filter. Simulation examples are given to illustrate that the information fusion decentralized filter with a two-layer fusion structure has a better fault tolerance and robustness properties when a sensor is faulty.