卫星导航的相对精度衰减因子单调性分析

Monotonicity Analysis of Relative Dilution of Precision of Satellite Navigation

相对精度衰减因子(RDOP)是衡量全球卫星导航系统相对定位性能的几何强度指标。简要给出了两种类型RDOP的描述,并分别给出了单调性证明。相对于同一参考卫星或是不同参考卫星进行双差观测,均有其RDOP随着可见导航卫星数目增加而单调递减的性质。结合编队卫星的星间相对定位背景,仿真计算了全球卫星导航系统的RDOP,给出了某时刻每颗可见卫星对RDOP的贡献,证实了RDOP的单调性;而卫星数目增加到一定程度时,RDOP的降低已不明显,因此应综合考虑可见卫星的数目和相对定位的精度需求等方面因素进行选星。

The relative dilution of precision （RDOP） is an index for evaluating the geometric strength of relative positioning performance using the global navigation satellite systems. Two types of RDOP descriptions were presented, which were followed by the monotonicity proofs. The RDOPs monotonically decreases in respect of the number of visible navigation satellites, when the double-difference observations are carried out for either the common reference satellite case or the different reference satellites case. Simulations were performed based on the background of inter-satellite relative positioning of formation flying satellites. The RDOPs were calculated and the contribution of every visible satellite at a given time was also given. The monotonicity of the RDOPs was validated. However, the decreasing extent is not so obvious when the navigation satellites increase to a certain number. The selection of satellites subset is thus recommended to rely on the aspects of the number of visible satellites and the accuracy requirements of relative positioning.