We propose a state estimation methodology using a network of distributed observers. We consider a scenario in which the local measurement at each node may not guarantee the system’s observability. In contrast, the ensemble of all the measurements does ensure that the observability property holds. As a result, we design a network of observers such that the estimated state vector computed by each observer converges to the system’s state vector by using the local measurement and the communicated estimates of a subset of observers in its neighborhood. The proposed estimation scheme exploits sensor redundancy to provide robustness against faults in the sensors. Under suitable conditions on the redundant sensors, we show that it is possible to mitigate the effects of a class of sensor faults on the state estimation. Simulation trials demonstrate the effectiveness of the proposed distributed estimation scheme.