Adaptive P-Splines for challenging filtering problems in biomechanics

Suppression of noise from recorded signals is a critically important data processing step for biomechanical analyses. While a wide variety of filtering or smoothing spline methods are available, the majority of these are not well suited for the analysis of signals with rapidly changing derivatives such as the processing of motion data for impact-like events. This is because commonly used low-pass filtering approaches or smoothing splines typically assume a single fixed cut-off frequency or regularization penalty which fails to describe rapid changes in the underlying function. To overcome these limitations we examine a class of adaptive penalized splines (APS) that extend commonly used penalized spline smoothers by inferring temporal adaptations in regularization penalty from observed data. Three variations of APS are examined in which temporal variation of spline penalization is described via either a series of independent random variables, an autoregressive process or a smooth cubic spline. Comparing the performance of APS on simulated datasets is promising with APS reducing RMSE by 48%-183% compared to a widely used Butterworth filtering approach. When inferring acceleration from noisy measurements describing the position of a pendulum impacting a barrier we observe between a 13% (independent variables) to 28% (spline) reduction in RMSE when compared to a 4th order Butterworth filter with optimally selected cut-off frequency. In addition to considerable improvement in RMSE, APS can provide estimates of uncertainty for fitted curves and generated quantities such as peak accelerations or durations of stationary periods. As a result, we suggest that researchers should consider the use of APS if features such as impact peaks, rates of loading, or periods of negligible acceleration are of interest.