This thesis presents a preliminary investigation of a localization methodology which does not depend on signals from the Global Positioning System (GPS). Instead, the Received Signal Strength Indicator (RSSI) between several stationary nodes (anchor nodes) and a mobile node to predict the position of the mobile node. The main goals of the thesis are to find the optimal localization algorithm and to identify the optimal number of anchor nodes that would provide the desired localization precision. We will show that the proposed technique is affordable and can be successfully used in electronically noisy environments (e.g., indoors). The technology used is a 434 MHz RF localization system that should provide less interference than the typical 2.4 GHz systems that commonly experience interference from other domestic technologies. The results reveal the feasibility and shortcomings of these systems for creating a more accurate real-time positioning system.