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Drastic propagation conditions in wireless environments, specifically the presence of non-line-of-sight (non-LOS) propagation in urban areas, pose a major challenge to the acquisition of location information. Count-of-Beacon (COB) is a new radiolocation technique where the absence of a LOS path does not degrade the precision of the estimated position. In this technique, the distance between a mobile terminal and a base station can be derived by means of the geometry of overhearing. The geometry of overhearing models the correlation between the position and the proportion of overheard power-controlled beacon packets. However, the deviation of the attenuation that signals experience, mainly due to shadow fading, has not been considered in this model. This paper reformulates the geometry of overhearing by focusing on the effects of shadow fading. Simulation results are used to verify the validity of the new derived model at different levels of shadowing. The closed-form expression of the Cramér-Rao lower bound (CRLB) is also derived to benchmark the accuracy of the COB technique. In addition, the major source of error affecting the precision of the COB technique is identified and its statistical description is provided.