改进的深插LLL算法在模糊度解算中的应用

An improved deep interpolation LLL algorithm for integer ambiguity resolving

针对全球卫星导航系统(GNSS)载波相位高精度定位中的整周模糊度快速解算问题,该文利用格基规约的思想,基于基向量的Gram-Schmidt长度平方和与格基规约之间的关系对现有的深插LLL进行改进,提出了IDLLL格基规约算法。采用仿真实验与实测数据,分别从Hadamard比率、深插次数和规约效率3个方面,将IDLLL规约算法与改进前算法的格基规约性能进行对比。实验结果表明IDLLL算法在获得了跟深插LLL算法相当的规约效果的同时,提升了规约效率,平均提升率为54.18%。

This paper addresses the problem of fast integer ambiguity resolution in high-precision positioning of GNSS carrier phase,Utilizing the idea of lattice basis reduction,based on the relationship between the sum of squared lengths of Gram-Schmidt orthogonalized basis vectors and lattice basis reduction,the existing deep insert LLL algorithm was improved and the IDLLL lattice basis reduction algorithm was proposed in this paper.By conducting simulation experiments and using real measured data,the lattice basis reduction performance of the IDLLL algorithm was compared with the performance of the algorithm before improvement from three aspects:Hadamard ratio,deep insert iterations,and reduction efficiency.Experimental results showed that the IDLLL algorithm not only achieved comparable reduction effects to the deep insert LLL algorithm but also improved the reduction efficiency,with an average improvement rate of 54.18%.