Analysis of the fetal ECG (fECG) allows physicians to detect changes in the well-being state of the fetus. But when assessing the fECG through the abdominal signals (ADS), its very low amplitude causes a problem, as the fECG representation in the ADS is buried in a mixture of other signals with stronger energy. Different methods have been proposed in the past to extract the transabdominal fECG for instantaneous fetal heart rate (fHR) computation; four representatives of them are selected for an accurate comparison of their performance in fECG extraction and in fHR estimation. A model for the ADS including all the possible disturbances is developed within this study to generate simulated data as they are required for the quantitative comparison of the algorithms. Their performances and limits considering both the enhancement of the fECG and the ability to preserve fECG morphology are analyzed using the simulated data. The results clearly show that linear methods for maternal ECG removal provide better results with respect to the extraction of the fECG morphology. The algorithms are then tested on real ADS data recorded during labor. Finally, the advantage of considering linear methods for ADS processing is discussed.