Theoretical and Applied Informatics

The article outlines how to use the convergence of collections to determine the position of a mobile device based on the WiFi radio signal strength with the use of fuzzy sets. The main aim is the development of the method for indoor position determination based on existing WiFi network infrastructure indoors. The approach is based on the WiFi radio infrastructure existing inside the buildings and requires operating mobile devices such as smartphones or tablets. An SQL database engine is also necessary as a widespread data interface. The SQL approach is not limited to the determination of the position but also to the creation of maps in which the system dening the position of the mobile device will operate. In addition, implementation issues are presented along with the distribution of the burden of performing calculations and the benets of such an approach for determining the location. The authors describe how to decompose the task of determining the position in a client-server architecture.

There is a consensus in signal processing that the Gaussian kernel and its partial derivatives enable the development of robust algorithms for feature detection. Fourier analysis and convolution theory have a central role in such development. In this paper, we collect theoretical elements to follow this avenue but using the q-Gaussian kernel that is a nonextensive generalization of the Gaussian one. Firstly, we review the one-dimensional q-Gaussian and its Fourier transform. Then, we consider the two-dimensional q-Gaussian and we highlight the issues behind its analytical Fourier transform computation. In the computational experiments, we analyze the q-Gaussian kernel in the space and Fourier domains using the concepts of space window, cut-o frequency, and the Heisenberg inequality.