Comparison between the more recent techniques for smoothing and derivative assessment in biomechanics

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Abstract
When analysising and evaluating human motion, two strictly interconnected problems arise: the data smoothing and the determination of velocities and accelerations from displacement data. Differentiating procedures magnify the noise superimposed on the useful kinematic data. A smoothing procedure is thus required to reduce the measurement noise before the differentiation can be carried out. In the paper two techniques for derivative assessment are presented, tested and compared. One of these is the procedure known as one of the best automatic smoothing and differentiating techniques: generalised cross validatory spline smoothing and differentiation (GCVC). The other, which has recently been presented, features an automatic model-based bandwidth-selection procedure (LAMBDA). The procedures have been tested with signals presented by other authors and available in the literature, by test signals acquired using the ELITE motion analyser and by synthetic data. The results show better or similar performance of LAMBDA compared with GCVC. In the cases in which the natural conditions at the signal boundaries are not met GCVC gives bad results (especially on the third derivative) whereas LAMBDA is not affected at all. Moreover, analysis time is dramatically lower for LAMBDA.