基于主成分分析和Melkman算法的选星策略

A Satellite Selection Strategy Based on Principal Component Analysis and Melkman Algorithm

导航定位中的选星算法是一种关键技术,用于从卫星中选择合适数量和最佳几何分布的卫星以实现最佳定位精度。针对基于二维凸包算法的选星策略在三维卫星数据降维处理中忽略垂直方向高度位置信息的问题,提出了一种基于主成分分析(PCA)和二维凸包Melkman算法的选星策略。首先,通过PCA技术将三维卫星数据投影到新的二维坐标系,新的二维数据同时保留水平平面位置信息和垂直方向高度位置信息,旨在降低维度的同时最小化信息损失。在新坐标系下,数据经过预处理后,采用二维凸包Melkman算法进行选星。实验结果显示:相较于直接投影到站心坐标系下的二维凸包选星算法,提出的选星算法不仅更准确地描述卫星的位置信息,使问题研究更加完备,还在保持相近仿真耗时的前提下,实现了较大的几何精度因子(GDOP)性能提升。

The satellite selection algorithm in navigation and positioning is a key technology used to select the appropriate number and optimal geometric distribution of satellites from the existing ones,aiming at achieving optimal positioning accuracy.In order to address the problem that the satellite selection strategy based on two-dimensional convex hull algorithms ignores the vertical height and position information in three-dimensional satellite data dimensionality reduction processing,a satellite selection strategy based on the principal component analysis(PCA)and two-dimensional convex hull Melkman algorithm is proposed.First,the PCA is used to project three-dimensional satellite data into a new two-dimensional coordinate system,which preserves both the horizontal plane position information and the vertical height position information,aiming at reducing dimensionality while minimizing information loss.In the new coordinate system,after preprocessing the data,the two-dimensional convex hull Melkman algorithm is used for satellite selection.The experimental results show that,compared with the two-dimensional convex hull satellite selection algorithm directly projected into the station center coordinate system,the proposed satellite selection algorithm not only can describe the position information of satellites more accurately and thus make the problem research more complete,but also can achieve significant geometric dilution of precision(GDOP)performance improvement while maintaining similar simulation time.