一种改进的LLL模糊度规约算法

整周模糊度的高效解算是GNSS高精度数据处理中的关键,基于格论进行GNSS模糊度估计时需要通过格基规约来实现最优整周模糊度向量的快速搜索。针对高维情况下常规LLL规约算法辅助整周模糊度解算存在规约耗时较长和规约性能有限的问题,引入最小列旋转QR分解技术对基向量进行预排序,采用延后尺度规约和部分尺度规约来减少规约过程中的冗余尺度规约,以改善LLL算法的执行效果。分别通过模拟和实测数据进行实验,结果表明:改进后的LLL算法可以明显降低格基规约耗时,实测环境下其规约效率相比于传统方法提高了约10倍,且能够保证较好的规约性能,从而有效提升高维模糊度的解算效率。

Improved LLL ambiguity reduction algorithm

Efficient ambiguity resolution is the key of GNSS data processing with high precision.Based on the lattice theory,the computational efficiency of searching the optimal integer ambiguity vector can be improved by using lattice reduction.According to the fact that the routine LLL reduction algorithm for ambiguity resolution under high-dimensional case has long reduction time and limited reduction performance,the QR factorization with minimum column pivoting was introduced to preorder the reduction base vectors,and the algorithms of delayed size reduction and partial size reduction were used to reduce the number of redundant size reduction.These methods were optimally combined to improve the implementation effects of LLL reduction algorithm.Experiments with simulated and real GNSS data were executed,respectively.The consequence shows that the modified LLL algorithm can effectively reduce the reduction time and provide better performance than those of current reduction methods.The computing efficiency of lattice reduction using the proposed method with real data is improved by nearly 10 times than those of traditional algorithms.Therefore the computational efficiency of ambiguity resolution under high-dimensional case can be improved significantly by using the proposed algorithm.