Multi-channel measurements from the maternal abdomen acquired by means of dry electrodes can be employed to promote long-term monitoring of fetal heart rate (fHR). The signals acquired with this type of electrode have a lower signal-to-noise ratio and different artifacts compared to signals acquired with conventional wet electrodes. Therefore, starting from the benchmark algorithm with the best performance for fHR estimation proposed by Varanini et al., we propose a new method specifically designed to remove artifacts typical of dry-electrode recordings. To test the algorithm, experimental textile electrodes were employed that produce artifacts typical of dry and capacitive electrodes. The proposed solution is based on a hybrid (hardware and software) pre-processing step designed specifically to remove the disturbing component typical of signals acquired with these electrodes (triboelectricity artifacts and amplitude modulations). The following main processing steps consist of the removal of the maternal ECG by blind source separation, the enhancement of the fetal ECG and identification of the fetal QRS complexes. Main processing is designed to be robust to the high-amplitude motion artifacts that corrupt the acquisition. The obtained denoising system was compared with the benchmark algorithm both on semi-simulated and on real data. The performance, quantified by means of sensitivity, F1-score and root-mean-square error metrics, outperforms the performance obtained with the original method available in the literature. This result proves that the design of a dedicated processing system based on the signal characteristics is necessary for reliable and accurate estimation of the fHR using dry, textile electrodes.