Gaussian mixture models for signal mapping and positioning

Maps of RSS from a wireless transmitter can be used for positioning or for planning wireless infrastructure. The RSS values measured at a single point are not always the same, but follow some distribution, which vary from point to point. In existing approaches in the literature this variation is neglected or its mapping requires making many measurements at every point, which makes the measurement collection very laborious. We propose to use GMs for modeling joint distributions of the position and the RSS value. The proposed model is more versatile than methods found in the literature as it models the joint distribution of RSS measurements and the location space. This allows us to model the distributions of RSS values in every point of space without making many measurement in every point. In addition, GMs allow us to compute conditional probabilities and posteriors of position in closed form. The proposed models can model any RSS attenuation pattern, which is useful for positioning in multifloor buildings. Our tests with WLAN signals show that positioning with the proposed algorithm provides accurate position estimates. We conclude that the proposed algorithm can provide useful information about distributions of RSS values for different applications.