Navigation with radio-signals using GNSS or a terrestrial positioning system in urban environments is susceptible to multipath propagation, which can severely degrade positioning accuracy. In a Line-of-Sight (LOS) multipath channel, the received signal is composed of a direct path component and a sum of time-shifted and attenuated replicas of the transmitted signal. When these multipath components are not accounted for in the time-delay estimation (TDE) model, they may introduce substantial estimation bias. For positioning, only the first arriving path is of interest. Therefore, it is crucial to focus on estimating the reflections that most significantly affect the TDE of this primary path, while ignoring others with negligible impact. To reduce the impact of close-in multipath in TDE, we propose Maximum Likelihood estimators that account for the strongest reflections, with models considering either one or two multi-path components. The Maximum Likelihood Estimation (MLE) problem is optimized using the Space Alternating Generalized Expectation-Maximization (SAGE) method. To reduce computational load, the delay search space for each path is constrained based on the maximum bias observed in the multipath error envelope (MPEE). To assess the ranging accuracy for the various MLE estimators that account for multiple paths, we utilize a synthetically generated channel based on the Saleh-Valenzuela model. Additionally, we benchmark the positioning performance of these estimators using channel impulse responses recorded with a terrestrial positioning prototype system tested at The Green Village on the TU Delft campus.