Traffic state estimation is an important problem with significant applications in advanced traveler information systems, transportation management and traffic control. Nonetheless, the often faulty nature of measurement sensors, especially inductive loop detectors, hinders reliable state estimation. This work proposes a systematic, model-based, network-wide, moving-horizon approach for fault-tolerant traffic state estimation. By exploiting information redundancy and fault sparsity, it achieves reliable estimation and simultaneously detects, isolates and corrects measurements from periods of faulty sensor behavior. The approach is examined in relation to the Asymmetric Cell Transmission Model, a popular and powerful macroscopic first-order traffic flow model. In the absence of any faults, the proposed approach achieves similar results with other state-of-the-art estimation approaches while it can achieve better estimation performance when some sensors are faulty. It is further demonstrated that the developed approach can successfully handle multiple faults of different types.