A simple technique to estimate the position of a mobile node inside a building is based on the Received Signal Strength (RSS). In a previous publication, we investigated the feasibility of using circular array antennas and beamforming in order to enable an access point to estimate the position of a mobile inside a building. The approach utilized the two dimensional information (i.e. RSS for various azimuth directions) that is captured in a priori measured radio map. Generating these radio maps is not only extremely labor-intensive and time consuming but also sensitive to changes in the environment and possible source of interference. It would be interesting to find out if a deterministic propagation model such as ray tracing can be used to construct a radio map that effectively replaces the off-line manual measurements. In this paper, we investigate this issue and provide a novel positioning methodology that exhibits acceptable performance without the need for extensive set of measurements in the off-line mode. The performance for various parameters and building model accuracy will be presented and discussed.