The star sensor is the most accurate attitude determination sensor for space applications. This sensor determines the attitude by capturing the image of the stars in the field of view. Attitude calculation by the star sensor consists of several algorithms. Among them, star identification is the most crucial one; Because the failure of the correct star identification leads to a False attitude. One of the less discussed star identification algorithms is based on using the singular value decomposition of a matrix consisting of directional vectors of the star cluster. This paper, provides a review of some star identifications based on this concept as well as the simulation, analysis, and improvement of these methods. Moreover, the effect of various numbers of stars in the cluster as well as various fields of view size on this algorithm have been studied for different methods. The identification has been considered a two-step process based on singular values and singular vectors. Also, the rate of duplicate sets in the database of different methods has been investigated. In the last part of the paper, new methods for removing the dimmer stars in the image and bright star selection based on characteristics of singular value decomposition of the image have been proposed.