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A conventional approach to mobile positioning is to utilize the time-of-arrival (TOA) measurements between the mobile station (MS) and several receiving base stations (BSs). The TOA information defines a set of circular equations from which the MS position can be calculated with the known BS geometry. However, when the TOA measurements are obtained from the non-line-of-sight (NLOS) paths, the position estimation performance can be very unreliable. Assuming that the NLOS probability and distribution are known and the NLOS-induced error dominates the corresponding TOA measurement, two maximum a posteriori probability (MAP) algorithms for NLOS detection and MS localization are derived in this paper. The first provides a standard MAP solution, while the second is a simplified version based on geometric constraints. It is shown that the former achieves more accurate estimation performance at the expense of higher computational cost.