In many densely populated environments, there is an abundance of base stations by which a mobile station may be passively geographically located (geolocated) using various techniques that require multiple base stations. Areas in which base station density is sparse may not possess the requisite number of base stations to perform such techniques and, therefore, require different methods by which to geolocate mobile stations. In this paper, we present a passive geolocation scheme that only requires observation of the initial ranging information exchange between a mobile station and a single base station in order to determine a position estimate for the mobile station. The scheme is specifically applied to the Worldwide Interoperability for Microwave Access (WiMAX) 4G standard. The method is validated through computer simulation and field experimentation in a WiMAX network.