Fast satellite selection algorithm for GNSS multisystems based on the Sherman-Morrison formula
Fast satellite selection algorithm for GNSS multisystems based on the Sherman-Morrison formula
复制标题
基于Sherman-Morrison公式的GNSS多系统快速选星算法
作者：
Junpeng SHI;Kezhao LI;Lin CHAI;Lingfeng LIANG;Chendong TIAN;Keke XU
采用合理的选星算法可以大大提高GNSS多系统观测数据的利用效率。这样的算法还可以提高导航的实时可靠性和准确性。结合Sherman-Morrison公式和奇异值分解（SVD），提出了一种随可见卫星数目增加而几何精度因子（GDOP）值减小的方法。将该方法与最大四面体体积法相结合，提出了一种基于Sherman-Morrison公式的GNSS多系统快速选星算法。该算法的基本思想是：首先利用四面体体积最大法获得4颗初始参考卫星;然后利用GDOP值较小法对可见卫星进行共选，降低GDOP值，提高整体算法的精度。通过设置合理的精确阈值，卫星选择算法可以在没有干预的情况下自主运行。基于实测数据的实验结果表明：（1）基于Sherman-Morrison公式的卫星选择算法在整个周期内大多数历元的GDOP值小于2。与所有可见卫星的最优GDOP估计结果相比，该算法在对应的选定卫星数达到13颗时，其结果能够满足高精度导航定位的要求。而且，随着选择的卫星数量不断增加，计算时间也会增加，但GDOP值的下降并不明显。(2)该算法包括一个自适应函数的基础上的结束指标的卫星选择计算和合理的阈值。当合理的精确阈值设置为0.01时，在大多数历元中选择的卫星数量小于13。此外，当选择的卫星的数目达到13时，GDOP值小于2，并且对应的概率为93.54%。这些研究结果验证了所提出的基于谢尔曼-莫里森公式的卫星选择算法提供了自主功能和高精度的结果。
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.