  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.
