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In this study, we propose a distributed method for multi-agent systems to estimate a global reference frame by constructing a common reference frame for all agents with only local measurements. Our method is a combination of formation control and similarity evaluation of feature point matching. Here, we design a distributed controller to achieve a prescribed configuration and a distributed estimator to construct a common reference frame, which calculates the similarity between the measured relative positions and the prescribed configuration. Then, we quantify the error range between the common reference frame and the global reference frame and show that the constructed common reference frame is the best. The proposed method requires only the information on the relative positions of neighbor robots through local measurements and does not require inter-robot communication or relative posture observation. Finally, we conducted simulations with 12 agents and an experiment with 8 two-wheeled robots to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]