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

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