The node self-localization information of wireless sensor networks（WSNs）is one of the most important factor for its applications.There are numerous researches on self-localization algorithms

but most of them focus on improvement of the algorithms or the development of new algorithms

only a few longitudinal comparisons of simulations for these algorithms have been proposed.Four typical range-free algorithms is chosen and their simulated localization drawings are presented

which would be a big help for engineers to select the optimum algorithm.The approximating functions is given out

for the localization results based on the theory of curve-fitting

the four algorithms with different parameters.The localization performance function is elicited using these approximating functions.Numerical values is given out and put into the function according to practical situations.The optimum algorithm is determined.