This paper focuses on the achievable accuracy of center-of-gravity (CoG) centroiding with respect to the ultimate limits defined by the Cramer Rao lower variance bounds. In a practical scenario, systematic centroiding errors occur through coarse sampling of the points-spread-function (PSF) as well as signal truncation errors at the boundaries of the region-of-interest (ROI). While previous studies focused on sampling errors alone, this paper derives and analyzes the full systematic error, as truncation error become increasingly important for small ROIs where the effect of random pixel noise may be more efficiently suppressed than for large ROIs. Unbiased estimators are introduced and analytical expressions derived for their variance, detailing the effects of photon shot noise, pixel random noise and residual systematic error. Analytical results are verified by Monte Carlo simulations and the performances compared to those of other algorithms, such as Iteratively Weighted CoG, Thresholded CoG, and Least Squares Fits. The unbiased estimators allow achieving centroiding errors very close to the Cramer Rao Lower Bound (CRLB), for low and high photon number, at significantly lower computational effort than other algorithms. Additionally, optimal configurations in relation to PSF radius and ROI size and other specific parameters, are determined for all other algorithms, and their normalized centroid error assessed with respect to the CRLB.

翻译：本文聚焦于质心法（CoG）相对于克拉美-罗方差下界所定义终极极限的可达到精度。在实际场景中，系统性质心误差由点扩散函数（PSF）的粗采样及感兴趣区域（ROI）边界处的信号截断误差共同导致。先前研究仅关注采样误差，而本文推导并分析了完整系统误差——当随机像素噪声在小ROI中的抑制效果优于大ROI时，截断误差的重要性日益凸显。本文引入无偏估计量，并推导了其方差的解析表达式，详细阐述了光子散粒噪声、像素随机噪声及残余系统误差的影响。解析结果经蒙特卡洛仿真验证，并与迭代加权CoG、阈值CoG、最小二乘拟合等算法的性能进行对比。所提出的无偏估计量在低光子数与高光子数条件下，均能以显著低于其他算法的计算代价，使质心误差逼近克拉美-罗下界（CRLB）。此外，本文还确定了所有其他算法关于PSF半径、ROI尺寸等特定参数的最优配置，并评估了其归一化质心误差相对于CRLB的表现。