Wearable photoplethysmography (WPPG) has recently become a common technology in heart rate (HR) monitoring. General observation is that the motion artifacts change the statistics of the acquired PPG signal. Consequently, estimation of HR from such a corrupted PPG signal is challenging. However, if an accelerometer is also used to acquire the acceleration signal simultaneously, it can provide helpful information that can be used to reduce the motion artifacts in the PPG signal. By dint of repetitive movements of the subjects hands while running, the accelerometer signal is found to be quasi-periodic. Over short-time intervals, it can be modeled by a finite harmonic sum (HSUM). Using the harmonic sum (HSUM) model, we obtain an estimate of the instantaneous fundamental frequency of the accelerometer signal. Since the PPG signal is a composite of the heart rate information (that is also quasi-periodic) and the motion artifact, we fit a joint harmonic sum (HSUM) model to the PPG signal. One of the harmonic sums corresponds to the heart-beat component in PPG and the other models the motion artifact. However, the fundamental frequency of the motion artifact has already been determined from the accelerometer signal. Subsequently, the HR is estimated from the joint HSUM model. The mean absolute error in HR estimates was 0.7359 beats per minute (BPM) with a standard deviation of 0.8328 BPM for 2015 IEEE Signal Processing (SP) cup data. The ground-truth HR was obtained from the simultaneously acquired ECG for validating the accuracy of the proposed method. The proposed method is compared with four methods that were recently developed and evaluated on the same dataset.
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