The independent component analysis (ICA) based methods are among the most prevalent techniques used for non-invasive fetal electrocardiogram (NI-fECG) processing. Often, these methods are combined with other methods, such adaptive algorithms. However, there are many variants of the ICA methods and it is not clear which one is the most suitable for this task. The goal of this study is to test and objectively evaluate 11 variants of ICA methods combined with an adaptive fast transversal filter (FTF) for the purpose of extracting the NI-fECG. The methods were tested on two datasets, Labour dataset and Pregnancy dataset, which contained real records obtained during clinical practice. The efficiency of the methods was evaluated from the perspective of determining the accuracy of detection of QRS complexes through the parameters of accuracy (ACC), sensitivity (SE), positive predictive value (PPV), and harmonic mean between SE and PPV (F1). The best results were achieved with a combination of FastICA and FTF, which yielded mean values of ACC = 83.72%, SE = 92.13%, PPV = 90.16%, and F1 = 91.14%. Time of calculation was also taken into consideration in the methods. Although FastICA was ranked to be the sixth fastest with its mean computation time of 0.452 s, it had the best ratio of performance and speed. The combination of FastICA and adaptive FTF filter turned out to be very promising. In addition, such device would require signals acquired from the abdominal area only; no need to acquire reference signal from the mother’s chest.