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Wearable photoplethysmography (WPPG) has recently become a common technologyin heart rate (HR) monitoring. General observation is that the motion artifactschange the statistics of the acquired PPG signal. Consequently, estimation ofHR from such a corrupted PPG signal is challenging. However, if anaccelerometer is also used to acquire the acceleration signal simultaneously,it can provide helpful information that can be used to reduce the motionartifacts in the PPG signal. By dint of repetitive movements of the subjectshands 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 instantaneousfundamental frequency of the accelerometer signal. Since the PPG signal is acomposite of the heart rate information (that is also quasi-periodic) and themotion 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 theother models the motion artifact. However, the fundamental frequency of themotion artifact has already been determined from the accelerometer signal.Subsequently, the HR is estimated from the joint HSUM model. The mean absoluteerror in HR estimates was 0.7359 beats per minute (BPM) with a standarddeviation of 0.8328 BPM for 2015 IEEE Signal Processing (SP) cup data. Theground-truth HR was obtained from the simultaneously acquired ECG forvalidating the accuracy of the proposed method. The proposed method is comparedwith four methods that were recently developed and evaluated on the samedataset.

Harmonic Sum-based Method for Heart Rate Estimation using PPG Signals Affected with Motion Artifacts