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A novel three-stage methodology for the detection of fetal heart rate (fHR) from multivariate abdominal ECG recordings is introduced. In the first stage, the maternal R-peaks and fiducial points (maternal QRS onset and offset) are detected, using band-pass filtering and phase space analysis. The maternal fiducial points are used to eliminate the maternal QRS complexes from the abdominal ECG recordings. In the second stage, two denoising procedures are applied to enhance the fetal QRS complexes. The phase space characteristics are employed to identify fetal heart beats not overlapping with the maternal QRSs, which are eliminated in the first stage. The extraction of the fHR is accomplished in the third stage, using a histogram-based technique in order to identify the location of the fetal heart beats that overlap with the maternal QRSs. The methodology is evaluated on simulated multichannel ECG signals, generated by a recently proposed model with various SNRs, and on real signals, recorded from pregnant women in various weeks during gestation. In both cases, the obtained results indicate high performance; in the simulated ECGs, the accuracy ranges from 72.78% to 98.61%, depending on the employed SNR, while in the real recordings, the average accuracy is 95.45%. The proposed methodology is advantageous since it copes with the existence of noise from various sources while it is applicable in multichannel abdominal recordings.