Non-invasive fetal electrocardiography (ECG) can be used for prolonged monitoring of the fetal heart rate (FHR). However, the signal-to-noise-ratio (SNR) of non-invasive ECG recordings is often insufficient for reliable detection of the FHR. To overcome this problem, source separation techniques can be used to enhance the fetal ECG. This study uses a physiology-based source separation (PBSS) technique that has already been demonstrated to outperform widely used blind source separation techniques. Despite the relatively good performance of PBSS in enhancing the fetal ECG, PBSS is still susceptible to artifacts. In this study an augmented PBSS technique is developed to reduce the influence of artifacts. The performance of the developed method is compared to PBSS on multi-channel non-invasive fetal ECG recordings. Based on this comparison, the developed method is shown to outperform PBSS for the enhancement of the fetal ECG.