Fetal Electrocardiogram Extraction from the Mother’s Abdominal Signal Using the Ensemble Kalman Filter

Figure 1. An overview of EnKF. EnKF maintains an ensemble of sample points for the state vector xn. It propagates and updates the ensemble to track the distribution of xn. The state estimation is conducted by calculating the sample mean (red five-pointed-star) and covariance (red ellipse) of the ensemble.

Figure 2. Modified data with motion noise process: (1) Recorded ECG; (2) normalized ECG between −1 and 1; (3) EKF applied for ECG extraction; (4) motion noise extracted by subtracting filtered ECG signal from recorded ECG; (5) online aECG; (6) normalized aECG between −1 and 1; (7) the generated motion noises are added to the online aECG data.

Figure 3. A phase-wrapped ECG signal of records “a01”. (a) Abdominal ECG (raw data); (b) mECG extracted using EKF; and (c) mECG extracted using our EnKF.

Figure 4. fECG extraction using the EKF and EnKF with the PhysioNet data. The fQRS annotation is shown in orange asterisk (*). The red arrows show the places that fetal QRS was wrongly detected. The blue arrows show the missing fetal QRS. (a) Abdominal ECG (raw data) of record “a03”; (b) fECG extracted using EKF of record “a03”; (c) fECG extracted using EnKF of record “a03”; (d) Abdominal ECG (raw data) of record “a01” with reversed fetal QRS complexes; (e) fECG extracted using EKF of record “a01”; (f) fECG extracted using EnKF of record “a01”.

Figure 5. fECG extraction using the EKF and EnKF with the motion artifacts added PhysioNet data. The fQRS annotation is shown in orange asterisk (*). The red arrows show the places that fetal QRS was wrongly detected. The blue arrows show the missing fetal QRS. (a) Abdominal ECG (raw data); (b) fECG extracted using EKF; and (c) fECG extracted using EnKF.

Figure 6. fECG extraction using the EKF and EnKF with our own clinical data. The fQRS annotation is shown in orange asterisk (*). The red arrows show the places that fetal QRS was wrongly detected. The blue arrows show the missing fetal QRS. (a) Abdominal ECG (raw data), (b) fECG extracted from EKF and (c) fECG extracted from EnKF”. (d) Abdominal ECG after Wavelet preprocessing; (e) fECG extracted using EKF of preprocessed data; and (f) fECG extracted using EnKF of preprocessed data. The inset shows additional peaks, likely P and T waves; they were conserved after EnKF extraction.