Mathematical modeling of heart rate tracking in motion affected PPG signals

Heart rate tracking using Photoplethysmography (PPG) suffers from motion artifacts, which can change signal structure in a way that the spectral peak due to motion artifacts (MAs) can mask the actual peak related to the heart rate. To handle the problem just mentioned, a novel mathematical model for heart rate (HR) tracking is introduced. Our technique is based on a mathematical model for a multichannel PPG. The model uses a fixed-resolution spectrum of Fast Fourier Transform (FFT), Chirplet Z Transform (CZT) spectra at various resolutions, confinement of spectral space, previous heart rate, range of the signal, and a golden seed (GS) algorithm to generate the next heart rate. GS algorithm is a novel technique which is introduced to handle the masking of spectral peaks related to HRs. The GS algorithm utilizes intensity profiling, the Singular Spectrum Analysis (SSA) algorithm, spectral multiplication and subtraction, and proximity clustering to enhance the masked peak. The average time taken by our technique is 21.21ms and a mean average error of 2.12 on the IEEE signal processing Cup 2015 makes it fit for the real-time applications.