Regularized Numerical Differentiation of Depth-Sensor Data in a Fall Detection System

The research reported in this paper is related to the depth-sensor technology when applied in care services for the elderly and disabled persons. It is focused on a system for non-intrusive fall detection, in which the trajectory of the mass center of a monitored person is estimated on the basis of depth-sensor data and differentiated numerically in order to estimate the velocity of that person. The applicability of regularized methods for differentiation of measurement data in that system is assessed using both synthetic and real-world data. The central-difference method is used as a comparative reference. The results indicate that the regularized methods for numerical differentiation allow for reducing both the number of falls undetected by the addressed system for fall detection and the number of false alarms generated by that system. The best results are obtained by means of a regularized version of the central-difference method. Furthermore, those results indicate that estimates of the standard deviation of errors corrupting the depth-data-based position estimates should be used for the adjustment of the regularization parameters.