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This work addresses the problem of robust distributed estimation in the presence of sensor faults when the fusion center sequentially receives quantized messages from local sensors. The mean square error (MSE) of distributed estimation schemes increases dramatically if the information received from the faulty sensors within the network is not excluded from the estimation process. Accordingly, an efficient collaborative sensor-fault detection (CSFD) scheme is proposed in which the results of a homogeneity test are used to identify the faulty nodes within the network such that their quantized messages can be filtered out when estimating the parameter of interest. Utilizing an asymptotic analytical technique, a lower bound is derived for the MSE of the proposed distributed estimation scheme. A good agreement is observed between the simulated MSE results and the lower bound values, and thus it is inferred that the lower bound provides a convenient and reliable means of predicting the performance of the proposed estimation scheme in real-world sensor networks. In addition, a low-complexity CSFD (LC-CSFD) scheme is proposed to identify faulty sensors in WSNs with a very large number of nodes. The simulation results confirm that the accuracy of the estimates obtained from the CSFD and LCCSFD schemes is significantly better than that obtained from a conventional estimation scheme when applied in sensor networks characterized by an unknown number of sensor faults of various types.