切比雪夫多项式在GLONASS广播星历中的应用  

Application of Chebyshev polynomial in GLONASS broadcast ephemeris

作　　者：寇瑞雄 杨树文 化希瑞 KOU Ruixiong;YANG Shuwen;HUA Xirui(Faculty of Geomatic,Lanzhou Jiaotong University/National-Local Joint Engineering Research Center of Technologies and Applications for National Geographic State Monitoring/Gansu Provincial Engineering Laboratory for National Geographic State Monitoring,Lanzhou 730070,China)

机构地区：[1]兰州交通大学测绘与地理信息学院/地理国情监测技术应用国家地方联合工程研究中心/甘肃省地理国情监测工程实验室,兰州730070

出　　处：《导航定位学报》2021年第1期102-108,共7页Journal of Navigation and Positioning

基　　金：国家重点研发计划项目(2017YFB0504201);国家自然科学基金项目(41761082);兰州交通大学优秀平台支持项目(201806)。

摘　　要：针对格洛纳斯卫星导航系统(GLONASS)广播星历在计算卫星坐标时需要二次积分并不断迭代,在实时导航中会降低卫星坐标计算效率的问题,提出利用切比雪夫多项式拟合卫星轨道的方法:利用广播星历原有方法计算卫星坐标并与精密星历进行对比,验证GLONASS广播星历的卫星坐标精度是米级;然后利用切比雪夫多项式对卫星坐标进行拟合,可知不同因素对拟合精度有影响,在固定拟合时间间隔时,随着节点个数增加最优拟合阶数不断增大,而在不同时间间隔下,最优拟合阶数不完全一致。实验结果表明,使用切比雪夫多项式拟合GLONASS广播星历时,根据需求选择合适的拟合时间间隔和拟合阶数,其拟合精度可以满足需要。Aiming at the problem that it is easily reduced for the efficiency of satellite coordinate calculation in realtime navigation due to two integrations and constant iteration during calculating satellite coordinates by GLObal NAvigation Satellite System(GLONASS)broadcast ephemeris,the paper proposed to fit satellite orbits with Chebyshev polynomial:the satellite coordinates were calculated by the original method of broadcast ephemeris and compared with the precise ephemeris,and it was verified that the satellite coordinate precision of the GLONASS broadcast ephemeris was on meter level;then Chebyshev polynomial was used to fit the satellite coordinates,knowing the influence of different factors on the fitting accuracy,on the one hand,during the fixed fitting time interval,the optimal fitting order increased with the number of nodes getting larger,on the other hand,during different time intervals,the optimal fitting orders were not completely consistent.Experimental result showed that the fitting accuracy could meet the needs with the appropriate fitting time interval and fitting order selected according to the requirements when using Chebyshev polynomial to fit the GLONASS broadcast ephemeris.

关 键 词：格洛纳斯卫星导航系统 广播星历 切比雪夫多项式 拟合精度 

分 类 号：P228[天文地球—大地测量学与测量工程]