The Gaussian surface fitting (GSF) is considered to be an excellent target location algorithm with high precision. But it is too expensive in computation to be utilized in real-time applications, such as dynamic tracking, dynamic measurement and autonomous navigation. By dividing the coordinate of the spot center into integer pixel value and subpixel value, a new fast algorithm, named Gaussian surface analyzing (GSA) is deduced, in which the center is located with analytical formulas and the intensity values of all pixels in the region of interest (ROI). In addition, an improved version of the traditional GSF algorithm, called fixed-coefficient Gaussian fitting (FCGF) is proposed as well, in which the expensive computation of the generalized inverse matrix is avoided. Compared to the GSF, the GSA and the FCGF have similar performanece in accuracy and robustness, however their running time is no more than 1/278 and 1/78 of the GSF respectively.