The fetal heart rate (fHR) plays an important role in the determination of the good health of the fetus. Beside the traditional Doppler ultrasound technique, non-invasive fetal electrocardiography (fECG) has become an interesting alternative. However, extracting clean fECG from abdominal ECG (aECG) recordings is a challenging task due to the presence of the maternal ECG component and various noise sources. In this context, we propose a deep residual convolutional autoencoder network trained on synthetic aECG simulations followed by a transfer learning phase on real aECG recordings to extract the cleanest fECG. Afterwards, we propose to use a non-negative matrix factorization based approach on the obtained fECG to estimate the fHR. Our method is evaluated on three publicly available databases demonstrating that it can provide significant performance improvement against comparative methodologies. Clinical relevance- The presented method has the advantage of estimating the fetal heart rate from a single-channel abdominal electrocardiogram without prior knowledge on the noise sources nor the maternal R-peak locations.