Real-time Kalman filter applied to biomechanical data for state estimation and numerical differentiation

This study focused on the application of real-time Kalman filters to biomechanical data and, in particular, the simulation environment used to compare the performance of modified and standard two-state Kalman filters when estimating displacement and velocity from noisy displacement data. The modification proposed in this paper was the numerical tachometer, augmented by a median smoother. The numerical tachometer integrated the derivative estimates from finite differences of noisy sampled data into the Kalman filter structure; the median smoother acted before differentiation, to protect from grossly erroneous measurements. The numerical tachometer allowed better fits to the simulated data than can be achieved without it: the root mean square errors decreased by 10% in the displacement domain and by 54% in the velocity domain, for sampling frequencies and signal contamination levels that were typical in human movement sciences. The sensitivity to errors in the modelling of the signal and noise characteristics was less than in the standard filter implementation. The use of the median smoother improved the robustness of the filtering algorithm against additive white Gaussian measurement noise and allowed the cancellation of isolated noise spikes.