1. A method of determining that a single designated identifier is shared by at least two wireless devices and using the determination that the single designated identifier is shared by at least two wireless devices in a wireless positioning system, the method comprising: determining a set of reference points associated with any wireless devices having the single designated identifier, each reference point being (i) a geographic position at which signals from any of the wireless devices having the designated identifier were detected or (ii) a neighbor wireless device from which signals were also detected by a receiver within a selected period of time during which the signals from any of the wireless devices having the designated identifier were detected by the receiver; clustering, by the wireless positioning system, reference points of the set of reference points into at least two clusters; determining a property for each cluster of the at least two clusters; based on the property for each cluster, determining that the single designated identifier is shared by at least two wireless devices; and in response to the determination that the single designated identifier is shared by at least two wireless devices, excluding any wireless devices using the single designated identifier from being used by the wireless positioning system as a beacon for estimating a position of a client device.