| Abstract: | Estimating derivatives from noisy displacement data is a notoriously ill-posed problem in signal processing and biomechanics. Following the work of Wood and Jennings (1978) and Hatze (1979, 1981), the present paper describes the use of optimally regularized, natural quintic splines for estimating smoothed positions, velocities, and accelerations from equidistantly sampled, noisy position measurements. It appears that the nature of the boundary conditions of the data is of some importance, since various algorithms used hitherto result in artefacts throughout the data if the true derivatives at the record ends differ significantly from zero. Natural quintic splines do not suffer from this disadvantage below the third derivative.The ill-posed character of movement analysis has some interesting implications for movement synthesis and optimization, similar to the indeterminacy of muscular co-contraction from merely external, biomechanical measurements. |
