This paper introduces a practical two-stage approach to achieve the mitigation of the Non Line Of Sight condition by using space-time diversity in timing-based mobile subscribers positioning systems. The first stage performs a coarse detection of the first (Line Of Sight) arrival, certainly attenuated due to the propagation channel, by performing a serial search over an observation window. Several GLRT and LMPT detectors have been evaluated in order not to miss the first arrival. Once the window where the LOS component lies has been properly detected, high resolution timing estimation is provided as a second stage. Two methods are considered for this work: Minimum Variance (MV) and Normalized Minimum Variance (NMV) estimation. A suitable channel model has been used to evaluate both approaches in terms of SNR and delay spread. These two methods have been compared for different configurations, and their operational characteristics have been obtained. Finally, these timing-error characteristics have been plugged to a link-level simulation platform to obtain their accuracy figures within a Weighted Linear Least Squares (WLLS) positioning system.