Apparatus and method for positioning a device based on wireless local area network signals. In one embodiment, a wireless local network positioning system includes access point selection logic. The access point selection logic includes likelihood computation logic, minimum mean squared error (MMSE) estimation logic, variance computation logic, and access point exclusion logic. The likelihood computation logic is configured to compute a likelihood value for each access point and point of a positioning grid. The MMSE estimation logic is configured to compute an MMSE estimate based on the likelihood values. The variance computation logic is configured to compute an MMSE variance for the MMSE estimate. The access point exclusion logic is configured to determine whether excluding a selected one of the access points reduces the MMSE variance, and to exclude the selected access point from the access points used for positioning, based on the exclusion reducing the MMSE variance.