Radio Frequency Identification (RFID) is a wireless system designed to identify the presence of objects attached by tags. In recent times, RFID is also used for positioning purposes. We show a scenario of wireless propagation observed by eight antennas with different polarization located in different positions. In this way, the antenna characteristics, i.e. the polarization and diagram radiation of the antennas will play a significant role in producing electromagnetic field in the region. In this work we will use the fingerprinting procedure, with this we produce some data bases containing the electric field received by RFID readers if we located the RFID tag in certain position in region of interest. In this work, two cost functions are proposed, which are to be minimized for determining the position of the tag.