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In this paper, we study a cooperative state estimation problem that is crucial to vision-based formation control of mobile robots. Cameras mounted on the robots are employed to make relative measurements within a formation of robots. Each robot can only measure part of the relative state information, while the rest of the information is measured by other robots. We design a robust consensus method to address this cooperative state estimation problem so that the measurements made by each individual robot are integrated via an information exchange method to obtain a complete description of the formation. This method is then applied to vision-based triangular formation control of mobile robots and verified using experiments.