改进了GNSS模糊性快速估计减少算法
Xinzhong Li1, Yongliang Xiong1, Weiwei Chen2
1Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China.
Sensors (Basel, Switzerland)
|October 28, 2023
概括
这项研究增强了LLL算法,通过减少格子基础减少时间,更快地实现全球导航卫星系统 (GNSS) 的高精度定位. 改进的方法大大减少了计算,使得模两可的解决方案更快.
科学领域:
- 地理学工程 工程地质学
- 卫星导航系统 卫星导航系统
- 计算数学 计算数学 计算数学
背景情况:
- 全球导航卫星系统 (GNSS) 的高精度定位依赖于快速准确的整数模两可的分辨率.
- 高维模糊性解决的格子理论表明,格子基础的减少是一个重要的瓶,比搜索耗费更多的时间.
- 提高格子基减小算法的效率对于推进GNSS定位至关重要.
研究的目的:
- 为了提高最小正方形与整数运算 (LLL) 算法的效率,以减少格子基础.
- 为了减少在GNSS中解决高维整数模糊性的时间消耗和计算复杂性.
- 在降低效率和稳定性方面评估改进的LLL算法的性能.
主要方法:
- 使用了户主QR分解,最小的列旋转到预排序基向量.
- 实施了部分缩小尺寸和放松的基础向量交换条件,以提高LLL算法的效率.
- 使用模拟和测量GNSS数据验证了改进的算法.
主要成果:
- 改进的LLL算法显著减少了基向量交换的数量和总体减少的时间.
- 像HSLLL和PSLLL这样的算法在使用西格尔条件时显示出更好的减少效果,但稳定性略低.
- PLLLR算法在搜索模糊性解决效率方面取得了显著的改进.
结论:
- 增强的LLL算法有效地降低了GNSS的晶格基础减少中的计算开销.
- 修改过的算法在减少效应,稳定性和在模糊性解决中的效率之间提供了权衡.
- 开发的方法有助于在GNSS应用中快速准确实现整数模两可的解决方案.
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