Regularised differentiation of measurement data in systems for monitoring of human movements

The research reported in this paper is related to assistive technologies that may be used by healthcare institutions for monitoring movements of elderly persons. The corresponding systems, based on impulse-radar sensors and depth sensors are addressed. The reported study is focused on the estimation of the walking velocity of a monitored person, which requires numerical differentiation of data representative of that person's position trajectory. Five methods of numerical differentiation are compared in terms of their applicability in such systems. The comparison is based on both synthetic data and real-world data. The results of experiments indicate the superiority of a differentiation method based on the Tikhonov regularisation. The bias and standard deviation of errors corrupting the velocity estimates, obtained by means of that method, do not exceed 0.10 m/s in the case of the impulse-radar sensors and 0.08 m/s in the case of the depth sensors.