宇航学报

宇航学报 ›› 2014, Vol. 35 ›› Issue (5): 574-580.doi: 10.3873/j.issn.1000-1328.2014.05.011

• 制导、导航与控制 • 上一篇    下一篇

基于3星子集的GPS快速选星算法

霍国平，缪玲娟，高志峰   

  1. 1.北京理工大学自动化学院, 北京 100081;  2.清华大学信息技术研究院， 北京 100081
  • 收稿日期:2013-04-07 修回日期:2013-06-05 出版日期:2014-05-15 发布日期:2014-05-25
  • 基金资助:

    国家自然科学基金（61153002）

GPS Fast Constellation Selection Based on 3 SAT Subset

HUO Guo ping,  MIAO Ling juan,  GAO Zhi feng   

  1. 1.School of Automation, Beijing Institute of Technology, Beijing 100081, China；
    2.Research Institute of Information Technology, Tsinghua University, Beijing 100084, China
  • Received:2013-04-07 Revised:2013-06-05 Online:2014-05-15 Published:2014-05-25

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摘要：

针对高精度GPS导航系统中，空间星座数量变化时由星座选择带来的运算量较大的问题，利用 Sherman Morrison 矩阵求逆引理，推导得到GDOP（Geometric Dilution of Precision）值的增量递推计算公式。 在此基础上提出一种基于由3颗GPS卫星组成“3星子集”的快速选星算法，并利用LLRB树（Left Leaning Red Black Tree）的存储搜索策略辅助快速产生最佳4星组合。相对于传统GDOP选星法，在可视星卫星数增加时，浮点数运算量（FLOPs）可减少将近一半；当可视卫星数减少时，FLOPs可降低到接近为0。实际试验结果表明，3星子集选星方法可以有效降低星座突变时由星座选择带来的时间消耗，提高星座更新的实时性。

关键词: 星座选择, 几何精度因子, LLRB树, 浮点数运算量

Abstract:

A fast constellation selection method named ‘3 SAT subset’ is presented for reducing the large amount of computation when a sudden change occurs in the sky view in high accuracy GPS navigation system. The GDOP (Geometric Dilution of Precision) recursive formula is deduced by use of the Sherman Morrison formula to reduce matrix inversion operation. Moreover, efficient storage and search strategy of LLRB Tree (Left Leaning Red Black Tree) algorithm is used to assist rapid creation of optimal 4 SAT combinations and get the minimal GDOP. With respect to the traditional GDOP constellation selection, the amount of floating point operations per second (FLOPs) can be reduced by more than half when the number of visualization satellites increases, and almost equals 0 when the number decreases. The experimental results show that, 3 SAT subset method can effectively reduce the time consumption at the mutation of constellations and improve the real time performance accordingly.
 

Key words: Constellation selection, GDOP, LLRB Tree, FLOPs

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