Fetal heart rate monitoring is essential for assessing fetal health. Although the fetal electrocardiogram (fECG) is the most accurate method, it is invasive and limited to specialized settings. Therefore, extracting the fECG from the maternal abdominal ECG (aECG) has gained interest as a non-invasive alternative, despite challenges like overlap with maternal ECG and noise. This study proposes an algorithm with the following stages: 1) preprocessing for signal conditioning, 2) Principal Component Analysis (PCA) to isolate fetal components from maternal ones, 3) Recursive Least Squares (RLS) adaptive filtering to reduce interference, and 4) adaptive thresholding stage for fetal R-peak detection. Validation using the publicly available Abdominal and Direct Fetal Electrocardiogram database—which includes four 5-minute aECG channels and one 5-minute fECG signal sampled at 1 kHz from five different patients—showed promising performance: 98.19% precision, 98.13% sensitivity, 96.38% accuracy, and 98.16% F1-score. These results are comparable to the 94.72% and 97.89% accuracy reported in the literature for blind source separation and neural network-based methods, respectively. R-peak location errors were low, with the largest bias being −5.51 ± 2.89 ms. Compared to recently proposed neural network approaches, this method achieves comparable results with a computational complexity that makes it suitable for real-time embedded systems, in which we are currently working on.