In order to improve the target's detection accuracy of the acquisition, tracking, and pointing system used in satellite-to-ground optical communications, the analysis and evaluation with high precision are needed for the random errors influencing the position determination of the beacon spots on the flat-panel detector. Considering a variety of random factors influencing spot detection, a noise equivalent angle (NEA) model for the centroid localization which is not dependent on the point spread function of target signals is established and the influences of different factors on the NEA are simulated. The results show that the change trend of NEA value under each point spread function of target signals is similar. It increases with the increase of noise, decreases with the increase of signal intensity, and increases with the increase of spot radius. The NEA values calculated under different point spread functions of target signals are different, but the maximum difference is less than 30%. The research result provides a new measurement method and a theoretical analysis basis of random errors existing in target position detection, and is of great significance to the establishment and maintenance of long-distance satellite-to-ground optical communication links.