滑动式Thiele型连分式插值方法在GPS精密星历中的应用
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摘要
在动态GPS精密定位中,必须使用高精度的GPS卫星轨道数据,但是IGS组织只提供15min间隔的精密星历,无法满足间隔时间较短的动态定位要求,用多项式逼近效果很差,另外对于不同的星历插值没有高效的方法能确定最佳多项式阶数。因此,利用Thiele型连分式建立有理函数,并在此基础上提出滑动式Thiele型连分式插值的方法,简化了方法又提高了内插精度,并通过算例与Lagrange多项式和Chebyshev多项式进行了分析和比较,结果表明该插值方法可以更加有效地改进插值精度。
In dynamic GPS precise positioning, high precision GPS satellite orbit data are required, whereas IGS organization only provides a precise ephemeris with 15 min intervals which fails to fulfill the dynamic positioning requir-ements of short time intervals. In addition, data deficiency occurs around the marginal time 24: 00, so polynomial approximation cannot applied with a satisfactory effect acquired. Therefore, this paper uses Thiele-type continued fraction to establish a rational function, and on that basis raises the method of sliding Thiele-type continued fraction interpolation, with which increases both interpolation and extrapolation precisions. This paper also analyzes and compares it with Lagrange and Chebyshev polynomials, which shows this interpolation method can exert a more effective refinement on the interpolation precision.
In dynamic GPS precise positioning, high precision GPS satellite orbit data are required, whereas IGS organization only provides a precise ephemeris with 15 min intervals which fails to fulfill the dynamic positioning requir-ements of short time intervals. In addition, data deficiency occurs around the marginal time 24: 00, so polynomial approximation cannot applied with a satisfactory effect acquired. Therefore, this paper uses Thiele-type continued fraction to establish a rational function, and on that basis raises the method of sliding Thiele-type continued fraction interpolation, with which increases both interpolation and extrapolation precisions. This paper also analyzes and compares it with Lagrange and Chebyshev polynomials, which shows this interpolation method can exert a more effective refinement on the interpolation precision.
引文
[1]李征航,黄劲松.GPS测量与数据处理[M].武汉:武汉大学出版社,2005.LI Zheng-hang,HUANG Jin-song.GPS surveying and data processing[M].Wuhan:Wuhan University Press,2005.
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[4]孔巧丽.用切贝雪夫多项式拟合GPS卫星精密坐标[J].测绘通报,2006(8):1-3.KONG Qiao-li.Using Chebyshev polynomial to fit the precise satellite ephemeris[J].Bulletin of Surveying and Mapping,2006(8):1-3.
[5]Schenewerk M.A brief review of basic GPS orbit interpolation strategies[J].GPS Solutions,2003,6(4):265-267.
[6]李庆扬,王能超,易大义.数值分析[M].北京:清华大学出版社,2010.LI Qing-yang,WANG Neng-chao,YI Da-yi.Numerical analysis[M].Beijing:Tsinghua University Press,2010.
[7]洪樱,欧吉坤,彭碧波.GPS卫星精密星历和钟差三种内插方法的比较[J].武汉大学学报(信息科学版),2006,31(6):516-518+556.HONG Ying,OU Ji-kun,PENG Bi-bo.Three interpolation methods for precise ephemeris and clock offset of GPS satellite[J].Geomatics and Information Science of Wuhan University,2006,31(6):516-518+556.
[8]王兴,高井祥,王坚,等.利用滑动式切比雪夫多项式拟合卫星精密坐标和钟差[J].测绘通报,2015(5):6-8+16.WANG Xing,GAO Jing-xiang,WANG Jian,et al.Using sleek Chebyshev polynomial to fit the precise satellite coordinate and clock error[J].Bulletin of Surveying and Mapping,2015(5):6-8+16.
[9]檀结庆.连分式理论及其应用[M].北京:科学出版社,2007.TAN Jie-qing.Continued fraction theory and applications[M].Beijing:Science Press,2007.
[10]李岳生,黄友谦.数值逼近[M].北京:人民教育出版社,1978.LI Yue-sheng,HUANG You-qian.Numerical approximation[M].Beijing:People's Education Press,1978.
[11]王仁宏.数值逼近[M].北京:高等教育出版社,1999.WANG Ren-hong.Numerical approximation[M].Beijing:Higher Education Press,1999.
[2]Feng Y,Zheng Y.Efficient interpolations to GPS orbits for precise wide area applications[J].GPS Solutions,2005,9(4):273-282.
[3]Bidikar B,Rao G S,Ganesh L,et al.Satellite clock error and orbital solution error estimation for precise navigation applications[J].Positioning,2014,5(1):22-26.
[4]孔巧丽.用切贝雪夫多项式拟合GPS卫星精密坐标[J].测绘通报,2006(8):1-3.KONG Qiao-li.Using Chebyshev polynomial to fit the precise satellite ephemeris[J].Bulletin of Surveying and Mapping,2006(8):1-3.
[5]Schenewerk M.A brief review of basic GPS orbit interpolation strategies[J].GPS Solutions,2003,6(4):265-267.
[6]李庆扬,王能超,易大义.数值分析[M].北京:清华大学出版社,2010.LI Qing-yang,WANG Neng-chao,YI Da-yi.Numerical analysis[M].Beijing:Tsinghua University Press,2010.
[7]洪樱,欧吉坤,彭碧波.GPS卫星精密星历和钟差三种内插方法的比较[J].武汉大学学报(信息科学版),2006,31(6):516-518+556.HONG Ying,OU Ji-kun,PENG Bi-bo.Three interpolation methods for precise ephemeris and clock offset of GPS satellite[J].Geomatics and Information Science of Wuhan University,2006,31(6):516-518+556.
[8]王兴,高井祥,王坚,等.利用滑动式切比雪夫多项式拟合卫星精密坐标和钟差[J].测绘通报,2015(5):6-8+16.WANG Xing,GAO Jing-xiang,WANG Jian,et al.Using sleek Chebyshev polynomial to fit the precise satellite coordinate and clock error[J].Bulletin of Surveying and Mapping,2015(5):6-8+16.
[9]檀结庆.连分式理论及其应用[M].北京:科学出版社,2007.TAN Jie-qing.Continued fraction theory and applications[M].Beijing:Science Press,2007.
[10]李岳生,黄友谦.数值逼近[M].北京:人民教育出版社,1978.LI Yue-sheng,HUANG You-qian.Numerical approximation[M].Beijing:People's Education Press,1978.
[11]王仁宏.数值逼近[M].北京:高等教育出版社,1999.WANG Ren-hong.Numerical approximation[M].Beijing:Higher Education Press,1999.