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In this paper, we consider the problem of simultaneously classifying sensor types and estimating hidden parameters in a network of sensors subject to gossip-like communication. More precisely, we consider a network of noisy sensors which measure a common scalar unknown parameter. We assume that a fraction of the nodes is subject to the same (but possibly unknown) offset. The goal for each node is to simultaneously estimate the common unknown parameter and to identify the class each node belongs to, only through local communication and computation. We propose a distributed estimator based on the maximum-likelihood (ML) approach and we show that, in case the offset is known, this estimator converges to the centralized ML as the number of sensor nodes goes to infinity. We also compare this strategy with a distributed implementation of the expectation-maximization (EM) algorithm; we show tradeoffs via numerical simulations in terms of robustness, speed of convergence and implementation simplicity.