We consider the problem of estimating the position of an indoor wireless transmitter. Based on Angle of Arrival (AOA) readings from several base stations, a wireless transmitter's position has traditionally been determined using a least-squares approach. In particular, care is taken to ensure that the least-squares estimator is unbiased. Unbiased estimators are known minimize the difference between the estimate and the average value of the readings, not the actual value. Biased estimators, in contrast, have been shown to result in a lower mean-squared error, which in turn produces more accurate position estimates. We propose the use of a biased estimator to augment the traditional least-squares approach, and develop a methodology to obtain this estimator. Using real data from a commercial indoor Ultra-Wideband (UWB) Real Time Location System (RTLS), we show that our estimator produces more accurate position estimates than the traditional unbiased estimator. We also show that our simple estimator performs comparably to more complex positioning algorithms.