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The GPS has revolutionized how people, vehicles, and objects are positioned. The GPS, however, has limitations. It will only work well where a signal can be received and will not work underground, in tunnels, or even some buildings. Obtaining an accurate position estimate in these areas must therefore use alternate methods that do not rely on GPS. Promising research from the field of robotics provides an alternative approach to positioning, using a technique known as simultaneous localization and mapping (SLAM). The challenge for the SLAM algorithm is that the initial position given to the algorithm must be accurate. This paper investigates the concept of using an array of RF identification (RFID) tags placed at known positions to provide the initial position of the stationary vehicle to the SLAM algorithm. A least-squares (LS)-based position estimator is presented and evaluated in an experiment conducted in an underground potash mine and an indoor environment at the University of Saskatchewan. The estimator's average error is calculated using models with a varied number of parameters. It was found that both environments attain the best results with five model parameters that were obtained from data taken in the same environment. The results suggest that RFID-based positioning, using this LS approach, has the potential to provide relatively accurate and low-cost initial position estimation.