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.
Keywords: Volterra filter; accelerometer; cross bicoherence test; heartbeat rate monitoring; motion artifact; nonlinear modeling; photoplethysmography.