Characterization of Quadratic Nonlinearity between Motion Artifact and Acceleration Data and its Application to Heartbeat Rate Estimation

Abstract

Accelerometers are applied to various applications to collect information about movements of other sensors deployed at diverse fields ranging from underwater area to human body. In this study, we try to characterize the nonlinear relationship between motion artifact and acceleration data. The cross bicoherence test and the Volterra filter are used as the approaches to detection and modeling. We use the cross bicoherence test to directly detect in the frequency domain and we indirectly identify the nonlinear relationship by improving the performance of eliminating motion artifact in heartbeat rate estimation using a nonlinear filter, the second-order Volterra filter. In the experiments, significant bicoherence values are observed through the cross bicoherence test between the photoplethysmogram (PPG) signal contaminated with motion artifact and the acceleration sensor data. It is observed that for each dataset, the heartbeat rate estimation based on the Volterra filter is superior to that of the linear filter in terms of average absolute error. Furthermore, the leave one out cross-validation (LOOCV) is employed to develop an optimal structure of the Volterra filter for the total datasets. Due to lack of data, the developed Volterra filter does not demonstrate significant difference from the optimal linear filter in terms of t-test. Through this study, it can be concluded that motion artifact may have a quadaratical relationship with acceleration data in terms of bicoherence and more experimental data are required for developing a robust and efficient model for the relationship.

Heart rate tracking in photoplethysmography signals affected by motion artifacts: a review

“…The approach in [41] was different from the other researches in that first it used cross bicoherence to detect MAs in PPG. A comparatively less used approach is to use Kalman filtering (KF) to suppress or remove MAs.…”

“…Another approach of MA removal is to model them using polynomials. In studies like [41][42][43], the authors modeled MAs present in ACC signals using non-linear second-order Volterra filters. In Eq.…”

“…Cross bicoherence test [41] and Harmonic sum (HSUM) [69] are two measures which consider PPG and ACC signals occur in spaces which are normal to each other. In their work [41], the authors observed that significant bicoherence was present for highly correlated PPG and ACC data segments. These contaminated signal segments were cleaned using second-order Voltera filter.…”

Robust Assessment of Photoplethysmogram Signal Quality in the Presence of Atrial Fibrillation

“…As a continuous physiological signal, certain signal characteristics are expected to be stable over time. Accelerometry was introduced in some devices in order to identify periods with motion effect in the PPG [4], [5]. Also, the simultaneous electrocardiogram (ECG) signal synchronized with the PPG was used to identify the physiological beats from the contaminated PPG [6].…”