We provide a basis to select the optimal algorithm according to the specific observational conditions in ground-based astrometry, and clarify the loss of precision in the case of not achieving optimum. The principle of the centering algorithms based on model fitting is analyzed by the method of maximum likelihood. The effective point spread function (ePSF) algorithm, which can construct an accurate model to fit the star image, and the most widely used Gaussian centering algorithm are chosen to investigate the effect of different factors on centering precision. A series of synthetic star images with different backgrounds, full width at half maximums (FWHMs) and profiles are processed by these algorithms. The profiles include the actual profiles extracted from observations and the theoretical profiles, the spatial variation of the PSF across the detector is also taken into account. Each algorithm is applied to the observations obtained from Yunnan observatory to verify the simulation results. The simulations show that ePSF fitting is obviously more precise than Gaussian fitting for a Gaussian profile star with high signal-to-noise ratio (SNR). When the center of star profile becomes sharp, or the SNR of the star decreases, the advantage of ePSF fitting will gradually decrease. The high precision of ePSF fitting is due to its appropriate weight in the weighted least squares fitting. However, a similar method using the same weight, the weighted Gaussian fitting, turned out to be poor under some conditions. The reduction results of practical observations show good agree with the simulations. For a frame of CCD image with enough stars to construct accurate ePSFs, ePSF fitting can approach the Cramer-Rao (CR) bound. Other centering algorithms may achieve the same precision under suitable conditions, but will show poor precision when not used properly.
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