This paper focuses on the problem of the distributed estimation of a parameter vector based on noisy observations regularly acquired by the nodes of a wireless sensor network and assuming that some of the nodes have faulty sensors. We propose two online schemes, both centralized and distributed, based on the Expectation-Maximization (EM) algorithm. These algorithms are able to identify and disregard the faulty nodes, and provide a refined estimate of the parameters each time instant after a new set of observations is acquired. Simulation results demonstrate that the centralized versions of the proposed online algorithms attain the same estimation error as the centralized batch EM, whereas the distributed versions come very close to matching the batch EM. Peer Reviewed