Improved Least Lncosh Based Fetal Electrocardiography Extraction in Alpha-Stable Noise

Fetal electrocardiography (FECG) presents an important avenue for continuous fetal monitoring. Nonetheless, effectively extracting FECG from maternal electrocardiogram (MECG) is one considerable challenge due to its weaker amplitude compared to MECG and the non-Gaussian nature of background noise. In this letter, we introduce alpha-stable noise to model the realistic interference due to its high scalability. To improve the accuracy of FECG extraction under impulsive noise (alpha-stable noise with strong impulses), we introduce the least Lncosh algorithm (Llncosh) and the improved Llncosh algorithm (ILL) is proposed based on the Amplitude Hyperbolic Tangent Transformation (AHTT) to optimize the preset parameter. Moreover, Monte Carlo experiments are carried out to investigate the capabilities of LMS-like algorithms and the ILL algorithm for FECG extraction. The results demonstrate that the ILL algorithm outperforms the LMS-like ones with carefully selected parameters, particularly showcasing superior robustness against impulsive noise. This work holds significance both in the theoretical research of adaptive filtering and in its practical application for FECG extraction.