Fast satellite selection algorithm for GNSS multi-system based on Sherman–Morrison formula

Efficient use of global navigation satellite system (GNSS) observations improves when applying rational satellite selection algorithms. By combining the Sherman–Morrison formula and singular value decomposition, a smaller-GDOP (geometric dilution of precision)-value method is proven for an increasing number of visible satellites. By combining this smaller-GDOP-value method with the maximum-volume-tetrahedron method, a new rapid satellite selection algorithm based on the Sherman–Morrison formula for GNSS multi-systems is proposed. The basic idea of the algorithm is as follows: First, the maximum-volume-tetrahedron method is used to obtain four initial visible satellites. Then, the other visible satellites are selected by using the smaller-GDOP-value method to reduce the GDOP value and improve the accuracy of the overall algorithm. When the number of included satellites reaches a certain value, the rate of GDOP decrease tends to approach zero. Considering the algorithm precision and the computation efficiency, reasonable thresholds and end of calculation condition equation are given, which can make the proposed algorithm autonomous. The reasonable thresholds and the end of calculation parameters are suggested by means of experiments. Under the thresholds and the end of calculation parameters, the algorithm has an adaptive functionality. Furthermore, the GDOP values of the algorithm are less than 2, indicating that this algorithm can meet one of the requirements of high-precision navigation. Moreover, compared with the computation complexity values of the optimal GDOP estimation method, which includes all visible satellites, the values of the new algorithm are about half, indicating that this algorithm has a rapid performance. These findings verify that the proposed satellite selection algorithm based on the Sherman–Morrison formula provides autonomous functionality, high-performance computing, and high-accuracy results.