Abstract—In two recent contributions [1], [2], we have provided a comparative analysis of various optimization algorithms, which can be used for atomic location estimation, and suggested an enhanced version of the Steepest Descent (ESD) algorithm, which we have shown to be competitive with other distributed localization algorithms in terms of estimation accuracy and numerical complexity. Moreover, therein we have conducted a preliminary statistical characterization of the positioning error distribution, by showing that it can be well approximated by the family of Pearson distributions, as well as pointed out that its knowledge may be efficiently used to speed–up the analysis of iterative–based positioning algorithms by avoiding the need of simulating the whole location discovery algorithm, and allowing simulation at the atomic level only. In this contribution, based on the preliminary results shown in [1], we propose a comprehensive statistical analysis of the positioning error ...