卫星轨道误差对定位精度影响的摄动分析方法
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摘要
卫星导航系统定位精度受伪距测量误差、大气时延误差、卫星原子钟钟差及卫星轨道误差等多方面因素综合影响。传统通常采用基于精度因子与用户等效伪距误差的方法对定位误差进行评估,但在其精度表征公式推导过程中需对测量方程组系数矩阵H及用户等效伪距误差分布做若干假设,因此它实际上是一个近似评估公式。此外,各类误差源中的卫星轨道误差属于三维误差,需经过坐标转换,并利用经验参数模型才能换算至用户等效伪距误差。为此,提出采用矩阵摄动数学理论研究卫星轨道误差对定位方程组解的影响,利用谱范数条件数对方程组形态进行刻画。仿真结果表明,方法能够直接反映卫星轨道误差对定位精度的影响,无需进行轨道坐标及用户等效伪距误差换算,能够更加直接和准确地评估卫星轨道误差对定位解精度的影响。
GNSS positioning accuracy is affected by pseudo-range measuring error,atmospheric time-delay error,satellite atomic clock error and satellite orbit error,et al. Traditionally,the DOP and UERE parameters are used to estimate positioning error. However,several assumptions are needed in the derivation process of precision representation formula,thus it is actually an approximate estimating formula. In addition,the satellite orbit error of various error sources belongs to three-dimensional error,which requires coordinate transformation and experience parameter model to switch to UERE. Therefore,the paper proposes using matrix perturbation mathematical theory to study the influence of satellite orbit error on positioning accuracy; and describes equation form by conditional number using spectral norm. The simulation result demonstrates that this method can reflect the influence directly without transformation of orbit coordinate and UERE error so that it is more direct and precise to assess the influence of satellite orbit error on positioning accuracy.
GNSS positioning accuracy is affected by pseudo-range measuring error,atmospheric time-delay error,satellite atomic clock error and satellite orbit error,et al. Traditionally,the DOP and UERE parameters are used to estimate positioning error. However,several assumptions are needed in the derivation process of precision representation formula,thus it is actually an approximate estimating formula. In addition,the satellite orbit error of various error sources belongs to three-dimensional error,which requires coordinate transformation and experience parameter model to switch to UERE. Therefore,the paper proposes using matrix perturbation mathematical theory to study the influence of satellite orbit error on positioning accuracy; and describes equation form by conditional number using spectral norm. The simulation result demonstrates that this method can reflect the influence directly without transformation of orbit coordinate and UERE error so that it is more direct and precise to assess the influence of satellite orbit error on positioning accuracy.
引文
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[3]谢钢.GPS原理与接收机设计[M].北京:电子工业出版社,2009.
[4]施闯,赵齐乐,李敏,等.北斗卫星导航系统的精密定轨与定位研究[J].中国科学:地球科学,2012,42(6):854-861.Shi Chuang,Zhao Qile,Li Min,et al.Precise orbit determination of Beidou Satellites with precise positioning[J].Scientia Sinica:Terrae,2012,42(6):854-861.
[5]刘伟平,郝金明,李建文,等.一种北斗卫星精密定轨方法[J].测绘科学技术学报,2013,30(3):247-250.Liu Weiping,Hao Jinming,Li Jianwen,et al.A method of precise orbit determination of Bei Dou navigation satellite[J].Journal of Geomatics Science and Technology,2013,30(3):247-250.
[6]李征航,丁文武,李昭.GPS广播星历的轨道误差分析[J].大地测量与地球动力学,2008,28(1):50-54.Li Zhenghang,Ding Wenwu,Li Zhao.Error analysis of orbit determined by GPS broadcast ephemeris[J].Journal of Geodesy and Geodynamics,2008,28(1):50-54.
[7]李济生.人造卫星精密轨道确定[M].北京:解放军出版社,1995.
[8]徐小钧,艾国祥,马利华,等.基于不同轨道高度i HCO通信卫星的CAPS星座优化研究[J].天文研究与技术——国家天文台台刊,2014,11(4):350-355.Xu Xiaojun,Ai Guoxiang,Ma Lihua,et al.A study of optimization of a CAPS constellation of i HCO communication satellites of different orbit heights[J].Astronomical Research&Technology——Publications of National Astronomical Observatories of China,2014,11(4):350-355.
[9]高为广,苏牡丹,郭树人,等.北斗系统空间信号精度测试与评估[C]//第四届中国卫星导航学术年会电子文集.2014.
[10]罗璠,李建文,黄海,等.BDS广播星历的轨道误差分析[C]//第五届中国卫星导航学术年会电子文集.2015.
[11]何旭初,苏煜城,包雪松.计算数学简明教程[M].北京:人民教育出版社,1980.
[12]数学手册编写组.数学手册[M].北京:高等教育出版,1979.
[13]施浒立,孙希延,李志刚.转发式卫星导航原理[M].北京:科学出版社,2009.
[14]王世儒,王金金,冯有前,等.计算方法[M].西安:西安电子科技大学出版社,2004.