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The paper considers the problem of distributed estimation of an unknown deterministic scalar parameter (the target signal) in wireless sensor networks (WSNs), in which each sensor receives a single snapshot of the field. The observation or sensing mode is only partially known at the corresponding nodes, perhaps, due to their limited sensing capabilities or other unpredictable physical factors. Specifically, it is assumed that the observation process at a node switches stochastically between two modes, with mode one corresponding to the desired signal plus noise observation mode (a valid observation), and mode two corresponding to pure noise with no signal information (an invalid observation). With no prior information on the local sensing modes (valid or invalid), the paper introduces a learning-based distributed estimation procedure, the mixed detection-estimation (MDE) algorithm, based on closed-loop interactions between the iterative distributed mode learning and estimation. The online learning (or sensing mode detection) step re-assesses the validity of the local observations at each iteration, thus refining the ongoing estimation update process. The convergence of the MDE algorithm is established analytically. Simulation studies show that, in the high signal-to-noise ratio (SNR) regime, the MDE estimation error converges to that of an ideal (centralized) estimator with perfect information about the node sensing modes. This is in contrast with the estimation performance of a naive average consensus based distributed estimator (with no mode learning), whose estimation error blows up with an increasing SNR.