Due to the inherent difficulties in accessing the state of a dynamical system, observers play a relevant role in modern state-feedback control schemes. Traditionally, observer synthesis has been tackled using models derived from first principles. Recently, data-driven methods capable of estimating the state directly from real data have gained relevance, although an important limitation lies in the physical interpretation of the variables. In this work, a data-driven observer based on an autoencoder neural network is proposed. By training the network using a (possibly noisy) database containing states and output measurements, the resulting observer is able to estimate the real states. Experimental results on a circuital model are presented to illustrate the potential of the proposed method.