Fast satellite selection algorithm for GNSS multisystems based on the Sherman-Morrison formula

Abstract

The usage efficiency of GNSS multisystem observation data can be greatly improved by applying rational satellite selection algorithms. Such algorithms can also improve the real-time reliability and accuracy of navigation. By combining the Sherman-Morrison formula and singular value decomposition (SVD), a smaller geometric dilution of precision (GDOP) value method with increasing number of visible satellites is proposed. Moreover, by combining this smaller GDOP value method with the maximum volume of tetrahedron method, a new rapid satellite selection algorithm based on the Sherman-Morrison formula for GNSS multisystems is proposed. The basic idea of the algorithm is as follows: first, the maximum volume of tetrahedron method is used to obtain four initial reference satellites; then, the visible satellites are co-selected by using the smaller GDOP value method to reduce the GDOP value and improve the accuracy of the overall algorithm. By setting a reasonable precise threshold, the satellite selection algorithm can be autonomously run without intervention. The experimental results based on measured data indicate that (1) the GDOP values in most epochs over the whole period obtained with the satellite selection algorithm based on the Sherman-Morrison formula are less than 2. Furthermore, compared with the optimal estimation results of the GDOP for all visible satellites, the results of this algorithm can meet the requirements of high-precision navigation and positioning when the corresponding number of selected satellites reaches 13. Moreover, as the number of selected satellites continues to increase, the calculation time increases, but the decrease in the GDOP value is not obvious. (2) The algorithm includes an adaptive function based on the end indicator of the satellite selection calculation and the reasonable threshold. When the reasonable precise threshold is set to 0.01, the selected number of satellites in most epochs is less than 13. Furthermore, when the number of selected satellites reaches 13, the GDOP value is less than 2, and the corresponding probability is 93.54%. These findings verify that the proposed satellite selection algorithm based on the Sherman-Morrison formula provides autonomous functionality and high-accuracy results.