## 1 Introduction  
An electrocardiogram (ECG) is a record of physiological electrical signals in the human heart. ECG variation implies pathological changes of the heart, which cannot be indicated by other devices such as ultrasound and magnetic resonance. The foetal heart, in particular, cannot be detected by ultrasound or magnetic resonance imaging devices without full development, but foetal heart electricity is a good indicator of foetal heart development. Since 1906, when [PERSON] [1] first successfully detected a foetal electrocardiogram (FECG), many research achievements in FECG monitoring have been successively proposed. The research contents include various electrode development and electrode placement schemes, as well as FECG acquisition methods. FECGs are obtained in two ways: invasive scalp measurement and noninvasive abdominal skin measurement. For invasive measurements, the electrode can be attached to the scalp of a foetus while the cervix dilates during delivery. This approach provides a clear FECG, but the drawback is that it cannot be monitored for long periods of time at all stages of a mother's pregnancy. In contrast, noninvasive measurements are made by placing electrodes on the abdomen and chest of a pregnant woman and can be monitored at all stages of pregnancy [2,3]. However, what follows is that the measurement records contain a variety of noises, such as power line interference, movement artefacts and baseline wandering caused by respiratory movement and electrode movement, myoelectric noise caused by maternal muscle tension, electrode contact noise caused by poor electrode contact with the skin, etc. Besides this, they also inevitably contain a maternal electrocardiogram (MECG), with amplitude much higher than that of the FECG [4,5]. The power line interference is usually a 50 Hz (or 60 Hz) signal, and a notch device is adopted to eliminate it. The processing of FECG signals falls into two categories. One is to obtain the R peaks of the FECG by analysing and calculating the foetal heart rate (FHR) or heart rate variability (HRV). The other is to extract the pure FECG morphological waveform from the abdominal mixed signals, because the waveform contains information that could reflect more abundant FECG information used to diagnose foetal heart physiological characteristics. FECG extraction can be divided into multichannel and single-channel methods. The multichannel approach can take advantage of information redundancy in multichannel signals, so the FECG can be more clearly extracted by \"correcting\" the inaccurate signals collected by individual leads. However, multichannel extraction methods are more suitable for in-hospital detection due to the large number of electrodes, which is inconvenient for use in portable family equipment and increases the complexity and power consumption of the equipment. Single-channel methods require only one measuring electrode, which can reduce equipment consumption and improve wearing comfort. Nevertheless, without other information for \"corroboration\" or correction, single-channel extraction is vulnerable to interference. It is often necessary to analyse characteristics of the MECG and FECG to obtain corresponding prior or posterior information, so as to establish a basic function model to extract the FECG. At present, the single-channel methods include the template subtraction (TS) method [6, 7, 8, 9, 10], adaptive filtering [11, 12, 13], wavelet transform, Wigner-Ville distribution [14, 15, 16, 17], S-transform [18], sequential total variation [19], adaptive neuro-fuzzy reasoning system, extended Kalman Filtering [20], etc. However, unreasonable ECG modeling or selection of a different base function may affect FECG extraction results, which often leads to distortion of extraction and loss of nonlinear and nonstationary characteristics. Moreover, these single-channel extraction methods mostly obtain noisy FECGs requiring further denoising or enhancement processing.