Fetal electrocardiogram (fECG) assessment is essential throughout pregnancy to monitor the well-being and development of the fetus, and to possibly diagnose potential congenital heart defects. Due to the high noise incorporated in the abdominal ECG (aECG) signals, the extraction of fECG has been challenging. And it is even a lot more difficult for fECG extraction if only one channel of aECG is provided, i.e., in a compact patch device. Our team has been developing a novel wearable fECG monitoring system consisting of an abdominal patch that communicates with a smart device. The system has two main components: the fetal patch and the monitoring app. The fetal patch has electronics and recording electrodes fabricated on a hybrid flexible-rigid platform while the mobile app is developed for a wide range of applications. The patch collects the aECG signals and send them to the app via secure Bluetooth Low Energy (BLE) communication. The app software connects to a cloud server where processing and extraction algorithms are executed for real-time fECG extraction and fetal heart rate (fHR) calculation from the collected raw data. This thesis work focuses on algorithms for fECG extraction from the aECG signals of a pregnant mother including a novel scheme based on the Ensemble Kalman filter (EnKF) for extraction from a single-channel aECG signal. The EnKF algorithm is developed by considering a Bayesian filtering framework and formulating the fECG extraction problem as a dynamic system whose state and measurement equations are represented in a state-space form. Our work has the potential to transform the currently used fetal monitoring system to an effective distanced and tele-perinatal care.