Today, it is generally accepted that current methods for biophysical antenatal surveillance do not facilitate a comprehensive and reliable assessment of foetal well-being and thus, that continuing research into alternative methods is necessary to improve antenatal monitoring procedures. Here, attention has been paid to the abdominal phonogram, a signal that is recorded by positioning an acoustic sensor on the maternal womb and contains valuable information about foetal status, but which is hidden by maternal and environmental sources. To recover such information, this work describes single-channel independent component analysis (SCICA) as an alternative signal processing approach for analyzing the abdominal phonogram. The approach, based on the method of delays, the Temporal Decorrelation Source SEParation implementation (TDSEP) of Independent Components Analysis (ICA), and an automatic grouping algorithm, has managed to successfully retrieve estimates of: (1) the foetal cardiac activity (in the form of the foetal phonocardiogram, FPCG), (2) the maternal cardiovascular activity (in the form of the maternal phonocardiogram, MPCG, and/or pulse wave), (3) the maternal respiratory activity (in the form of the maternal respirograma, MResp), and (4) noise (N). These results have been obtained from a dataset of 25 single-channel phonograms and point at the possibilities of using SCICA to address a fundamental problem faced in antenatal surveillance, i.e. the extraction of information from a non-invasive signal like the abdominal phonogram. Future work will test the possibility of using SCICA to recover information regarding the foetal breathing movements (FBM), another physiological parameter of interest in foetal surveillance.