Reliable positioning of cellular users in a mobile environment requires accurate resolving of overlapping multipath components. However, this task is difficult due to fast channel fading conditions and data ill-conditioning, which limit the performance of least-squares-based techniques. This paper develops two overlapping multipath resolving methods (adaptive and nonadaptive), and shows how the adaptive solution can be made robust to the above limitations by extracting and exploiting a priori information about the fading channel. Also the proposed techniques are extended when there are antenna arrays at the base station. Simulation results illustrate the performance of the proposed techniques.