A novel multi-step adaptive Kalman filtering method based on dynamic noise estimation for FECG extraction

Yingbin Liu; Longxi Li; Yanbin Guo; Zibo Feng; Guoping Wang

doi:10.1177/20552076261435069

A novel multi-step adaptive Kalman filtering method based on dynamic noise estimation for FECG extraction

Digit Health. 2026 Mar 18:12:20552076261435069. doi: 10.1177/20552076261435069. eCollection 2026 Jan-Dec.

Authors

Yingbin Liu¹, Longxi Li¹, Yanbin Guo¹, Zibo Feng^{2

3}, Guoping Wang^{1

2}

Affiliations

¹ Hubei Bioinformatics & Molecular Imaging Key Laboratory, Department of Biomedical Engineering, College of Life Science and Technology, Huazhong University of Science and Technology, Wuhan, China.
² Department 2 of Wound Repair, Liyuan Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China.
³ Department of Endocrinology, Liyuan Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China.

Abstract

Objective: With the increase in women's childbearing age, the risk of fetal developmental abnormalities and fetal abortion is rising. The existing fetus monitoring methods based on Doppler ultrasound are inconvenient to use, require precise positioning of the fetal heart, and are particularly difficult to maintain for continuous long-term monitoring. Fetal electrocardiogram (FECG), as a very important physiological signal, can intuitively reflect the health status of the fetus. Affected by the strong noise and complex external components, the commonly used algorithm for extracting FECG from the abdominal electrocardiogram (AECG) of pregnant women cannot perform well enough.

Methods: Herein, we present a novel FECG extraction method based on three adaptive Kalman filters (KF). Regarding the first KF, to whiten the colored noise of the original AECG, the Expectation Maximization algorithm is used to iteratively solve the optimal parameters, and a new pseudo measurement variable named the "measurement time difference" is constructed. In addition, based on the residual vector $e_{k}$ and innovation $d_{k}$ , combined with the forgetting factor $α_{k}$ , the measurement noise covariance matrix R and the process noise covariance matrix Q are adaptively updated, which can help the second and third KFs extract a more pure FECG.

Results: The proposed method demonstrates superior performance in the extraction accuracy and quality across various datasets, including 25 groups of AECG from the FECGSYN toolbox, 10 groups of clinical AECG from the ADFECGDB database, 10 groups of clinical AECG from the FECGDARHA database, and 3 groups of real AECG collected by the independently designed, portable, and low-cost AECG hardware system, when compared to 3 other commonly used algorithms.

Conclusion: Our method enables obstetricians to more accurately assess fetal physiological state, leading to more informed preventive measures and treatment plans, ultimately improving the health outcomes for both mothers and fetuses.

Keywords: FECG extraction; Gaussian mixture model; adaptive Kalman filtering; dynamic noise estimation; expectation maximization.