A Gaussian error assumption is commonly adopted in the pseudorange measurement model for global navigation satellite system (GNSS) positioning, which leads to the conventional least squares (LS) estimator. In urban environments, however, multipath and non-line-of-sight (NLOS) receptions produce heavy-tailed pseudorange errors that are not well represented by the Gaussian model. This study models urban GNSS pseudorange errors using a logistic distribution and derives the corresponding maximum likelihood estimator, termed the Least Quasi-Log-Cosh (LQLC) estimator. The resulting estimation problem is solved efficiently using an iteratively reweighted least squares (IRLS) algorithm. Experiments in light, medium, and deep urban environments show that LQLC consistently outperforms LS, reducing the three-dimensional (3D) root mean square error (RMSE) by approximately 11%-31% and the 3D error standard deviation (STD) by approximately 27%-61%. A controlled scale-mismatch analysis further shows that LQLC is more sensitive to severe underestimation than to overestimation of the logistic scale, indicating that the practical tuning requirement is to avoid overly small scale values rather than to achieve exact scale matching. In addition, the computational cost remains compatible with real-time positioning. These results indicate that logistic modeling provides a simple and practical alternative to Gaussian-based urban GNSS positioning.