In this paper, we introduce a fully distributed localization algorithm based on self-synchronization mechanism. The proposed algorithm reaches consensus for the posterior distribution of the transmitter position at each base station. To reduce the communication overhead at each iteration, we propose to represent the state variable matrices of the self-synchronization mechanism with only four parameters (radial and angular means and variances). The performance of the algorithms is numerically assessed by the mean distance error and mean Kullback-Leibler divergence. Finally, we show through Monte-Carlo simulations that our approach gets very close to the direct-centralized-localization performance after a few iterations.