Non-invasive fetal electrocardiography appears to be one of the most promising fetal monitoring techniques during pregnancy and delivery nowadays. This method is based on recording electrical potentials produced by the fetal heart from the surface of the maternal abdomen. Unfortunately, in addition to the useful fetal electrocardiographic signal, there are other interference signals in the abdominal recording that need to be filtered. The biggest challenge in designing filtration methods is the suppression of the maternal electrocardiographic signal. This study focuses on the extraction of fetal electrocardiographic signal from abdominal recordings using a combination of independent component analysis, recursive least squares, and ensemble empirical mode decomposition. The method was tested on two databases, the Fetal Electrocardiograms, Direct and Abdominal with Reference Heartbeats Annotations and the PhysioNet Challenge 2013 database. The evaluation was performed by the assessment of the accuracy of fetal QRS complexes detection and the quality of fetal heart rate determination. The effectiveness of the method was measured by means of the statistical parameters as accuracy, sensitivity, positive predictive value, and F1-score. Using the proposed method, when testing on the Fetal Electrocardiograms, Direct and Abdominal with Reference Heartbeats Annotations database, accuracy higher than 80% was achieved for 11 out of 12 recordings with an average value of accuracy 92.75% [95% confidence interval: 91.19-93.88%], sensitivity 95.09% [95% confidence interval: 93.68-96.03%], positive predictive value 96.36% [95% confidence interval: 95.05-97.17%] and F1-score 95.69% [95% confidence interval: 94.83-96.35%]. When testing on the Physionet Challenge 2013 database, accuracy higher than 80% was achieved for 17 out of 25 recordings with an average value of accuracy 78.24% [95% confidence interval: 73.44-81.85%], sensitivity 81.79% [95% confidence interval: 76.59-85.43%], positive predictive value 87.16% [95% confidence interval: 81.95-90.35%] and F1-score 84.08% [95% confidence interval: 80.75-86.64%]. Moreover, the non-invasive ST segment analysis was carried out on the records from the Fetal Electrocardiograms, Direct and Abdominal with Reference Heartbeats Annotations database and achieved high accuracy in 7 from in total of 12 records (mean values μ < 0.1 and values of ±1.96σ < 0.1).