The evolution of pseudolite technology has presented an opportunity to enhance user positioning accuracy. However, practical constraints, such as limited receiver channels and power consumption, necessitate judicious pseudolite selection. To tackle specific high-precision positioning challenges, a synergy of pseudolite technology with Global Navigation Satellite System (GNSS) is applicable. Precision in positioning stands as a pivotal metric in this context. Geometric dilution of precision (GDOP) serves as a critical indicator for optimizing positioning performance, but determining the subset with the optimal GDOP value involves solving an impractical combinatorial optimization problem. A compromise solution seeks to balance computational complexity while sacrificing some optimality. Consequently, finding an optimal combination of pseudo satellites with a low computational burden yet quasi-optimal GDOP value remains a challenge. In response to this challenge, a pioneering approach will be presented in this chapter: a superfast satellite selection algorithm based on power series expansion (SF-PSE). This chapter derives a Xiao-Liang formula based on power series expansion and the Sherman-Morrison formula. Using this formula, two low-computational-cost rapid iterative algorithms (F-PSE and SF-PSE) are proposed. Among these algorithms, SF-PSE notably reduces the computational burden through an approximate iterative inverse matrix-guided search method. Experimental results demonstrate that satellite combinations identified by F-PSE and SF-PSE yield nearly the same accuracy while reducing computation time by 70% and 87%, respectively, compared to the state-of-the-art methods.