Choosing number of basis functions in weighted least-squares method for fusion of measurement data used for persons’ monitoring

Abstract

The research reported in this paper is related to the fusion of measurement data from the impulse-radar sensors and infrared depth sensors applied in a system for unobtrusive monitoring of elderly persons. The investigated method of data fusion consists in the approximation of a sequence of measured data by means of a linear combination of linearly independent basis functions, while the parameters of the approximation are determined using a weighted least-squares estimator. The proposed method is provided with the automatic determination of the number of basis functions by means of the so-called Stein’s unbiased risk estimator. Results of the numerical experimentation–performed on both synthetic data and real-world data-show that the proposed approach allows for robust estimation of the monitored person’s position regardless of the trajectory shape and person’s walking velocity.