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In a recent contribution , 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 (with preliminary results) to be competitive with some other distributed localization algorithms in terms of estimation accuracy and numerical complexity. Moreover, we have conducted a statistical characterization of the position error distribution, by showing that it can be well approximated by the family of Pearson distributions. In this contribution, we first analyze with further detail the proposed ESD algorithm, and then show that the knowledge of the position error distribution 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 particular, we will report some numerical results showing that the two approaches i) running the whole positioning algorithm when having at its input ranging errors, and ii) running the localization algorithm at the atomic level when having at its input ranging and positioning errors, provide the same results, with the latter approach having the additional positive feature to be simpler to be implemented. The proposed strategy may be efficiently used for analysis and optimization of various network settings.