天文定位中几何精度衰减因子最小值分析

天文定位是一种重要的导航定位方法，被广泛应用于大地天文测量、天文航海等领域。该方法中观测恒星的选择会影响最终的定位精度，目前缺少针对同时测定经纬度天文定位算法中最优选星问题的研究。随着观测仪器自动化水平的提高，观测数据的获取变得更加高效，这就要求研究最优的选星方案以达到最高的定位精度。本文借鉴卫星导航中几何精度衰减因子GDOP的概念，研究了天顶距法中恒星的数量以及分布对定位精度的影响，最后通过仿真试验和实测数据验证得到结论：在天顶距观测误差的统计特性一定时，GDOP能够用来描述恒星的分布对定位结果影响的优劣，且观测的恒星方位角均匀分布时定位误差最小。考虑到不同高度的恒星天顶距大气折射改正残差不同，在实际测量中应尽量采用等天顶距且方位角均匀分布的恒星。

The minimum analysis of geometric dilution of precision in celestial positioning

Celestial positioning is an important method in positioning and navigation, which is widely used in the fields of geodetic astrometry and celestial navigation. The selection of stars in this method affects the accuracy of positioning. At present, there is a lack of research on the optimal selection of stars for the celestial positioning algorithm which determinates longitude and latitude simultaneously. With the improvement of the automation level of observation instruments, the acquisition of observation data becomes more efficient. Therefore, it is necessary to study the optimal selection of stars to achieve the highest accuracy of positioning. Based on the concept of geometric dilution of precision (GDOP) in satellite navigation, this paper studies the influence of the number and distribution of stars in zenith-method on the accuracy of positioning. Finally, the conclusion is verified by the simulation experiment and the measured data. When the statistical characteristic of observation error on zenith distance is fixed, GDOP can be used to describe the effect of star distribution on the accuracy of positioning, and the error of positioning is minimal when the azimuth of stars is uniformly distributed. Considering that the residual error of atmospheric refraction correction of zenith distance of stars with different heights is different, the stars with equal zenith distance and azimuth distributed evenly should be used as far as possible in actual measurement.