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The image of a beacon on the photosensitive plane of pointing sensor in a receiving terminal is usually considered as the acquisition and tracking target of optical antenna for the Free Space Optical Communications (FSOC). The receiver processes the acquired image to ascertain the position of the transmitting terminal by the relevant algorithm. The tracking veracity of the algorithm to a target position is not the same under different conditions. Improving the algorithm veracity could improve the tracking accuracy of optical antenna and guarantee the optical link stabilization. In the paper we proposed that the acquisition position should be ascertained based on the geometric centroid for terrestrial FSOC in the city. Based on the experiment of terrestrial long haul optical link, we analyzed the tracking veracity of the centroid and geometric centroid algorithms for the stationary and locomotory targets under different intensity scintillations. A comparison of the two algorithms is also studied. The results show that the geometric centroid algorithm on ascertaining the acquisition position is superior to the centroid algorithm. This work contributes to the design of FSOC systems.