The location of a mobile robot is highly desirable for operational enhancements in indoor environments. In an in-building environment, the multipath caused by reflection and diffraction, and the obstruction and/or the blockage of the shortest path between transmitter and receiver are the main sources of range measurement errors. Due to the harsh indoor environment, unreliable measurements of location metrics such as received signal strength (RSS), angle of arrival (AOA) and time or time difference of arrival TOA/TDOA result in the deterioration of the positioning performance. Hence, alternatives to the traditional parametric geolocation techniques have to be considered. In this paper, we present a method for mobile robot location using WLAN's received power (RSS) data applied to an artificial neural network (ANN). The proposed system learns off-line the location RSS 'signatures' for line of sight (LOS) and non-line of sight (NLOS) situations. It then matches on-line the observation received from a mobile robot against the learned set of 'signatures' to accurately locate its position. The location precision of the proposed system, applied in an in-building environment, has been found to be 0.5 meter for 90% of trained data and about 5 meters for 58% of untrained data.